
Nathan GlattHoltz, Tulane University
September 19th,
KAP 414, 3:30pm4:30pm 
(CAMS Colloquium Joint with Probability and Statistics Seminar) “A unified framework for MetropolisHastings Type Monte Carlo methods” (Video)
We provide an allencompassing, measure theoretic mathematical formalism that describes essentially any MetropolisHastings algorithm using three ingredients: a random proposal, an involution on an extended phase space and an acceptreject mechanism. This unified framework illuminates underappreciated relationships between a variety of known algorithms while yielding a means for deriving new methods.
As an immediate application we identify several novel algorithms including a multiproposal version of the popular preconditioned Crank Nicolson (pCN) sampler suitable for infinitedimensional target measures which are absolutely continuous with respect to a Gaussian base measure. We also develop a new class of ‘extended phase space’ methods, based on Hamiltonian mechanics. These methods provide a versatile approach to bypass expensive gradient computations through skillful reduced order modeling and/or data driven approaches. A selection of case studies will be presented that use our multiproposal pCN algorithm (mpCN) to resolve a selection of problems in Bayesian statistical inversion for partial differential equations motivated by fluid flow measurement. This is joint work with Andrew J. Holbrook (UCLA), Justin Krometis (Virginia Tech) and Cecilia Mondaini (Drexel). 



Career Advice Panel
KAP 414, 3:30pm4:30pm

Panelists: Evgeni Dimitrov, Aaron Lauda and Trevor Leslie
Susan Friedlander




Natasa Pavlovic, University of Texas, Austin
KAP 414, 3:30pm4:30pm 
“A tale of two generalizations of Boltzmann equation” (Viedo)




John Schotland, Yale University
KAP 414, 3:30pm4:30pm 
“Nonlocal PDEs and Quantum Optics”




Weiwei Hu, University of Georgia
KAP 414, 3:30pm4:30pm 
"Optimal control for suppression of singularity in chemotaxis" (Video)




Adam Larios, University of Nebraska
KAP 414, 3:30pm4:30pm 
“A Song of Water and Fire: The NavierStokes and KuramotoSivashinsky Equations” (Video)




Thomas Hou, Caltech
KAP 414, 3:30pm4:30pm 
“Stable nearly selfsimilar blowup of the 2D Boussinesq and 3D Euler equations with smooth data”




Marco Sammartino, University of Palermo

Talk CANCELLED







Robert Ghrist, University of Pennsylvania
Monday,
January 31st,
(Zoom), 3:30pm4:30pm 
“Opinion Dynamics on Sheaves” (VIDEO)




Alexis Vasseur, University of Texas Austin
Monday, February 7th, (Zoom), 3:30pm4:30pm

"Boundary vorticity estimate for the NavierStokes equation and control of layer separation in the inviscid limit" (VIDEO)
$Ae_1 $, but with layer separation energy at time T up to: $$\U(T)Ae_1\^2_{L^2}\equiv A^3T.$$ In this work we prove that at the double limit for the inviscid asymptotic $\bar{U}$, where both the Reynolds number $Re$ converges to infinity and the initial value $U_{\nu}$ converges to $Ae_1$ in $L^2$, the energy of layer separation cannot be more than:
$$\ \bar{U}(T)Ae_1\^2_{L^2}\lesssim A^3T.$$ Especially, it shows that, even if if the limit is not unique, the shear flow pattern is observable up to time $1/A$. This provides a notion of stability despite the possible nonuniqueness of the limit predicted by the convex integration theory. The result relies on a new boundary vorticity estimate for the NavierStokes equation. This new estimate, inspired by previous work on higher regularity estimates for NavierStokes, provides a nonlinear control scalable through the inviscid limit.




Jacob Bedrossian, University of Maryland
Monday, February 14th,
(Zoom), 3:30pm4:30pm 
“Positive Lyapunov exponents for 2d GalerkinNavierStokes with stochastic forcing” (VIDEO)




Tarek Elgindi, Duke University
Monday, February 28th,
(Zoom), 3:30pm4:30pm 
“Singularity formation in incompressible fluids” (VIDEO)




Hyung Ju Hwang, POSTECH, Korea
Monday, March 7th,
(Zoom), 3:30pm4:30pm 
"Deep Neural Network Solutions of PDEs and Applications to COVID19 spread model" (VIDEO)




Eitan Tadmor, University of Maryland
Monday, March 21st,
(Zoom), 3:30pm4:30pm 
“Hierarchical decomposition of images and the problem of BourgainBrezis” (VIDEO)
The analysis of such models leads to the question of expressing general L^2data, f, as the divergence of uniformly bounded vector fields, div(U). We present a multiscale approach to construct uniformly bounded solutions of div(U)=f for general f’s in the critical regularity space L^d(T^d). The study of this equation and related problems was motivated by results of Bourgain & Brezis. The intriguing critical aspect here is that although the problems are linear, construction of their solution is not. Our constructive solution for such problems is a special case of a rather general framework for solving linear equations, formulated as inverse problems in critical regularity spaces. The solutions are realized in terms of nonlinear hierarchical decomposition, U=∑_ju_j, which we introduced earlier in the context of image processing, and yield a multiscale decomposition of “objects” U. 



Mihaela Ignatova, Temple University
Monday, March 28th,
(Zoom), 3:30pm4:30pm 
“Electroconvection in Fluids” (VIDEO)




Diego Cordoba, IAS and Madrid
Monday, April 4th,
(Zoom), 3:30pm4:30pm

“Instant blowup for the Surface Quasigeostrophic equation” (VIDEO)




Jonathan Mattingly, Duke University
Monday, April 11th,
(Zoom), 3:30pm4:30pm

“A random splitting model for the 2D Euler and Navier Stokes equations” (VIDEO)




Paolo Galdi, University of Pittsburgh
Monday, April 18th,
(Zoom), 3:30pm4:30pm 
“NavierStokes Equations around a Rigid Body: Three Remarkable Open Problems” (VIDEO)




László Székelyhidi, IAS and Leipzig
Monday, April 25th,
(Zoom), 3:30pm4:30pm 
“Magnetohydrodynamic Turbulence: weak solutions and conserved quantities” (VIDEO)





Trevor Leslie, USC
Monday,
August 30th,
KAP 414, 3:30pm4:30pm 
“Sticky Particle Methods for the 1D Euler Alignment System”




Thomas Hou, Caltech
Monday, September 13th, (Zoom), 3:30pm4:30pm

"Potential singularity of 3D incompressible Euler equations and nearly singular solutions of 3D NavierStokes equations"




Sijue Wu, University of Michigan
Monday, September 20th,
(Zoom), 3:30pm4:30pm 
“The quartic integrability and long time existence of steep water waves in 2d”




Marta Lewicka, University of Pittsburgh
Monday, September 27th,
(Zoom), 3:30pm4:30pm 
“Geometry, analysis and morphogenesis: problems and prospects”




Career Advice Panel,
Monday, October 4th,
KAP 414, 3:30pm4:30pm 
Panel discussion: "Applying for Grants and Jobs: Information and Advice"
Anne Dranowski, Aaron Lauda, Cris Negron
Susan Friedlander




Lin Lin, UC Berkeley
Monday, October 11th,
(Zoom), 3:30pm4:30pm 
“Quantum numerical linear algebra” (VIDEO)




Vincent Martinez, CUNY
Monday, October 18th,
(Zoom), 3:30pm4:30pm 
“On wellposedness at critical regularity for a family of active scalar equations arising in hydrodynamics” (VIDEO)




SungJin Oh, UC Berkeley
Monday, October 25th,
(Zoom), 3:30pm4:30pm

“A tale of two tails”




Theodore Drivas, SUNY Stonybrook
Monday, November 15^{th},
(Zoom), 3:30pm4:30pm

“Simultaneous Development of Shocks and Weak Discontinuities from Smooth Data” (VIDEO)




Nathan Glatt Holtz, Tulane
Monday, November 22nd,
(Zoom), 3:30pm4:30pm 
“Some Recent Developments in the Bayesian Approach to PDE Inverse Problems: Statistical Sampling and Consistency” (VIDEO)







Virtual USC Film Screening: SECRETS OF THE SURFACE,

The Mathematical Vision of Maryam Mirzakhani The film examines the life and mathematical work of Maryam Mirzakhani, an Iranian immigrant to the United States who became a superstar in her field. In 2014, she was both the first woman and the first Iranian to be honored by mathematics’ highest prize, the Fields Medal. 

Virtual Career Advice Panel,

Susan Friedlander, Aaron Lauda and Harold Williams Will discuss some basic information concerning applying for jobs, fellowships, grants etc and urge you to ask questions. 



Katherine Bouman,
Caltech,
Monday,
3:30pm4:30pm 
Virtual Seminar: “Capturing the First Image of a Black Hole & Designing the Future of Black Hole Imaging”





Charles Collot,
Courant Institute
Monday,
KAP 414, 3:30pm4:30pm 
“Singular solutions to evolution nonlinear PDEs: key notions and recent results for certain semilinear/quasilinear equations”




Oleg Lazarev,
Columbia University, NOTE: Special Colloquium,
KAP 414, 3:30pm4:30pm

"Flexibility and rigidity in symplectic topology"




Qingtang Su,
USC
KAP 414, 3:30pm4:30pm 
“Long time behavior of rotational water waves”




Hao Jia,
University of Minnesota
Monday,

“Nonlinear asymptotic stability in two dimensional incompressible Euler equations”




POSTPONED Vincent Martinez, CUNY,

“Title: TBA”





“SECRETS OF THE SURFACE: The Mathematical Vision of Maryam Mirzakhani”
CoSponsored by 



POSTPONED Shouhong Wang, Indiana University,

“Title: TBA”




POSTPONED Eleanor Rieffel,
NASA,

“Title: TBA”




Steve Shkoller,
UC Davis,
Monday,

“Shock formation for the 3d Euler equations”
Abstract: The Euler equations are the fundamental model of gas dynamics and it has been known for some time (both numerically and analytically) that smooth solutions of these equations experience a breakdown in finite time. For solutions to the Euler equations in 1d, Lax proved in 1964 that when the initial data has a negative slope, a shock singularity will form in a finitetime. A shock occurs when the gradient of the velocity and density becomes infinite. 



POSTPONED SungJin Oh,
UC Berkeley,
Monday,

“Title: TBA”




POSTPONED Sijue Wu,
University of Michigan,
Monday,

“Title: TBA”




POSTPONED Simon Tavare,
Columbia University,
Monday,

“Title: TBA”








Tadashi Tokieda,
Stanford University
Monday, September 9th,
Irani Hall 101 (Note Location), 3:30pm4:30pm 
“Toy models”
‘Toys’ here have a special sense: objects from daily life which you can find or make in minutes, yet which, if played with imaginatively, reveal behaviors that puzzle seasoned scientists for a while. We'll see tabletop demos of a series of such toys. The theme that emerges is singularity. 



Suncica Canic,
UC Berkeley
*** Friday, September 13th,
KAP 414, 3:30pm4:30pm

"Weak solutions to fluidmeshshell interaction problem"
Abstract: We give an overview of the recent developments in the design of constructive existence proofs for nonlinear moving boundary problems involving 3D incompressible, viscous fluids and various elastic structures. A special attention will be paid to the interaction involving elastic meshsupported shells. Real life examples of such problems are many, including the interaction between blood flow and vascular walls treated with meshlike devices called stents. Examples of applications to vascular procedures will be shown.




Terence Tao,
UCLA,
Monday, September 16th,
Irani Hall 101 (Note Location), 3:30pm4:30pm 
“The global regularity problem for NavierStokes”
Abstract: We survey some recent developments towards the infamous global regularity problem for the NavierStokes equations for incompressible viscous fluids. 



Career Advice Panel,
Monday, September 23rd,
KAP 414, 3:30pm4:30pm 
“Applying for Grants and Jobs: Information and Advice”
Panelists: <> Steven Heilman <> Aaron Lauda <> Gary Rosen
Moderator: <> Susan Friedlander
All postdocs and graduate students are strongly encouraged to come and ask questions about applying for grants from organizations such as the NSF, the NSA and the Simons Foundation. We will also discuss applying for academic positions. 



Jonathan Luk,
Stanford University,
Monday, October 7th,
KAP 414, 3:30pm4:30pm 
“Stability of vacuum for the Landau equation with moderately soft potentials”
Abstract: Consider the Landau equation with moderately soft potentials in the whole space. We prove that sufficiently small and localized regular initial data give rise to unique globalintime smooth solutions. Moreover, the solutions approach that of the free transport equation as $t\to +\infty$. This is the first stability of vacuum result for a binary collisional kinetic model featuring a longrange interaction. 



Zaher Hani,
University of Michigan,
Monday, October 14 th,
KAP 414, 3:30pm4:30pm 
“On the kinetic description of the longtime behavior of dispersive PDE”
Abstract: Wave turbulence theory claims that at very long timescales, and in appropriate limiting regimes, the effective behavior of a nonlinear dispersive PDE on a large domain can be described by a kinetic equation called the "wave kinetic equation” (WKE). This is the waveanalog of Boltzmann's equation for particle collisions. A fundamental scientific question to resolve here is to provide a rigorous derivation of this kinetic equation, in a way that allows to justify its significance in describing the longtime dynamics of the Hamiltonian dispersive PDE we started with. In this talk, we shall consider the nonlinear Schrodinger equation on a large box with periodic boundary conditions, and provide a rigorous derivation of its kinetic equation on timescales that are significantly shorter than the conjectured kinetic time scale, but still long enough to exhibit the onset of the kinetic behavior. (This is joint work with Tristan Buckmaster, Pierre Germain, and Jalal Shatah). 



Wojciech Ozanski,
USC,
Monday, October 28 th,
KAP 414, 3:30pm4:30pm 
“Partial regularity results of solutions to the 3D incompressible Navier–Stokes equations and other models”
Abstract: We discuss some modern developments of the partial regularity theory for the Navier–Stokes equations, as well as other models of ï¬‚uid mechanics, since the groundbreaking work of Scheï¬€er (19761980) and Caï¬€arelli, Kohn & Nirenberg (1982). 



Huy Nguyen,
Brown University,
Monday, November 4,
KAP 414, 3:30pm4:30pm

“On regularity for the Muskat problem”
Abstract: The Muskat problem models the evolution of two immiscible fluids of varying density in a porous medium. The free interface between the two fluids obeys a quasilinear parabolic equation, which to leading order has a natural scaling. We will discuss our recent results on local and global wellposedness respectively in all subcritical Sobolev spaces and certain critical spaces, allowing for curvature singularities of the initial interface. We employ a paradifferential calculus approach which is robust enough to incorporate various features in the problem such as varying viscosity and physical boundaries. We also obtain results on the vanishing surface tension limit and the infinite depth limit. 



Anna Mazzucato,
Penn State University, Monday, November 8th,
KAP 414, 3:30pm4:30pm

“Irregular transport and mixing in fluids”
Abstract: I will discuss the effect of irregular transport on mixing properties in incompressible fluids, in particular describing measures of mixing and examples of optimal mixers. I will also discuss how mixing and transport can suppress singularity formation or lead to complete loss of regularity. 



Boris Khesin,
University of Toronto,
Monday, December 2nd,
KAP 414, 3:30pm4:30pm 
“Beyond Arnold’s geodesic framework of an ideal hydrodynamics”
Abstract: We discuss ramifications of Arnold’s grouptheoretic approach to ideal hydrodynamics as the geodesic flow for a rightinvariant metric on the group of volumepreserving diffeomorphisms. We show that problems of optimal mass transport are in a sense dual to the Euler hydrodynamics. Moreover, many equations of mathematical physics, such as the motion of vortex sheets or fluids with moving boundary, have Lie groupoid, rather than Lie group, symmetries (this is a joint work with Anton Izosimov). 



Vladimir Sverak,
University of Minnesota,
Monday, December 9^{th},
KAP 414, 3:30pm4:30pm 
“Regularity and longtime behavior for certain 1d model equations related to fluid flows”
Abstract: In the 1980s, P. Constantin, P. Lax, and A. Majda introduced a simple 1d model equation sharing certain features with the 3d incompressible Euler equation. In the 1990s, S. De Gregorio suggested a modification of the original ConstantinLaxMajda model which has some intriguing features. Since then, other interesting model equations appeared. In spite of the apparent simplicity of these models, various natural questions about them remain open. I will discuss some of the known results, as well as the relation of these models to the full 3d equations.


Vlad Vicol,
Courant Institute
*** Friday, January 11th,
KAP 414, 3:30pm4:30pm 
“Convex integration on thin sets”




Misha Vishik,
University of Texas at Austin
Monday, January 14th,
KAP 414, 4:30pm5:30pm

"Instability and nonuniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid"
Abstract: We prove nonuniqueness of the solution to Cauchy problem of the Euler equations of an ideal incompressible fluid in plane with vorticity in some L^Q(R^2) space. The lack of uniqueness is of the symmetry breaking type, with the radially symmetric external force locally integrable in time with values in the same Lebesgue space. We prove linear instability of a certain class of incompressible flows in the "linear" part of the paper.




Mimi Dai,
University of Illinois at Chicago
Monday, January 28th,
KAP 414, 3:30pm4:30pm 
“Nonuniqueness of LerayHopf weak solutions for the 3D HallMHD system”
Abstract: We will talk about the nonuniqueness of weak solutions in LerayHopf space for the three dimensional magnetohydrodynamics with Hall effect. We adapt the widely appreciated convex integration framework developed in a recent work of Buckmaster and Vicol for the NavierStokes equation, and with deep roots in a sequence of breakthrough papers for the Euler equation. 



Lenya Ryzhik,
Stanford University
Monday, February 4th,
KAP 414, 3:30pm4:30pm 
“The stochastic heat equation and KPZ in dimensions three and higher”
The stochastic heat equation and KPZ in dimensions three and higher
Abstract. I will give an introduction to the behavior of the solutions to the heat equation with a spacetime stationary random potential in d\ge 3. In these "high" dimensions, when the potential is sufficiently weak, this equation admits a spacetime stationary solution that serves as an analog of the principal eigenfunction in a periodic problem. As a consequence, one obtains an effective diffusion equation, and an EdwardsWilkinson limit for fluctuations in the long time limit. Similar results hold for the KPZ equation in d\ge 3. I will also try to explain the connection to the stochastic Burgers' equation and standard elliptic homogenization. This is a joint work with A. Dunlap, Y. Gu and O. Zeitouni. 



Susan Holmes,
Stanford University, CAMS Distinguished Lecturer
Monday, February 25th,
IRANI HALL 101 (PLEASE NOTE ROOM CHANGE), 3:30pm4:30pm 
“Hidden variables: finding latent variables in bacterial communities”
Abstract: The analyses of complex biological systems often results in output that may seem just as complex, with little useful knowledge extracted as a result of the multiple layers of information. Although distances are an important component of effective data science, we will show examples where distances taken in isolation of probability measure information give spurious results. In bioinformatics for instance standard methods for identifying taxa used fixed radii at 97% similarity regardless of sequence prevalence leading to spurious results. The standard base rate neglect fallacy (Kahneman and Tversky, 1974) still prevails even in mathematics where methods such as topological data analyses still ignore relevant changes in measure.
The use of multiscale strategies is providing useful predictions of preterm birth and a deeper understanding of resilience of the human microbiome after antibiotic perturbations. 



Kavita Ramanan,
Brown University
Monday, March 4th,
KAP 414, 3:30pm4:30pm 
“Hydrodynamic limits for randomized load balancing networks”
Abstract: Randomized load balancing algorithms allow for the efficient use of resources and are of particular importance in largescale networks. Since these networks are too complex to be amenable to an exact analysis, an established framework is instead to obtain tractable approximations that provide qualitative insight into the dynamics, and whose accuracy can be rigorously justified via limit theorems in a suitable (asymptotic) regime. However, load balancing networks with jobs having general service distributions fall outside the purview of existing methods. We introduce a novel interacting particle representation for these networks, describe their hydrodynamic scaling limits, and show how they can be used to provide insight into both transient and equilibrium performance measures of the network. 



Ian Tice,
Carnegie Mellon University
Monday, March 18th,
KAP 414, 3:30pm4:30pm 
“Trace operators for homogeneous Sobolev spaces in infinite striplike domains”
Abstract: Sobolev spaces are an indispensable tool in the modern theory of partial differential equations. Trace embeddings show that functions in Sobolev spaces, which are a priori defined as elements of $L^p$ and hence are only defined almost everywhere, can actually be restricted to sufficiently regular hypersurfaces in a bounded way. Characterizing the resulting trace spaces and constructing bounded right inverses (lifting results) then plays an essential role in using Sobolev spaces to study boundaryvalue problems in PDE. The use of Sobolev spaces to study equations in unbounded, infinitemeasure sets often requires employing homogeneous Sobolev seminorms, in which only the highestorder derivatives are controlled in $L^p$. In this setting, the classical trace results may fail for certain choices of sets that appear naturally in PDE applications, such as infinite striplike sets $\mathbb{R}^{n1}\times (0,b) \subset \mathbb{R}^n$. In this talk we will survey the classical theory and then turn to recent developments in the homogeneous trace theory and applications. In particular, we will show that in striplike sets the homogeneous trace spaces are characterized by a new type of fractional homogeneous Sobolev regularity and an interaction between the traces on the different connected components of the boundary. 



Haitian Yue, USC
Monday,March 25th,
KAP 414, 3:30pm4:30pm

“Wellposedness for the periodic cubic NLS”
Abstract: The cubic nonlinear Schrödinger equation (NLS) is energycritical with respect to the scaling symmetry in the dimensions four. The initial value problem (IVP) of cubic NLS is scaling invariant in the Sobolev norm H^1. First this talk introduce the deterministic global wellposedness result of the periodic cubic NLS in four dimensional space in the critical regime (with H^1 initial data). Second we consider the periodic cubic NLS in the supercritical regime (with H^s data, s<1). A probabilistic approach is applied to obtain an "almost sure" wellposedness result for the periodic cubic NLS in the supercritical regime. 



James Kelliher,
UC Riverside
Monday, April 1st,
KAP 414, 3:30pm4:30pm

“The strong vanishing viscosity limit with Dirichlet boundary conditions: facts, speculations, and conjectures”
Abstract: We say that the strong vanishing viscosity limit holds if solutions to the NavierStokes equations converge in the energy norm to a solution to the Euler equations uniformly over finite time as the viscosity is taken to zero. Starting with the seminal 1983 paper of Tosio Kato, we show how to establish necessary and sufficient conditions for such convergence to hold in the presence of a boundary. We extend various conditions developed by subsequent authors for noslip boundary conditions to allow nonhomogeneous Dirichlet boundary conditions, establishing a few new conditions along the way. Finally, we make a few speculations and conjectures on the strong vanishing viscosity limit. 



Yan Guo,
Brown University
Monday, April 15th,
KAP 414, 3:30pm4:30pm 
“Validity of Steady Prandtl Expansion”
Abstract: In a joint work with Sameer Iyer, the validity of steady Prandtl layer expansion is established. Our result covers the celebrated Blasius boundary layer profile, which is based on uniform quotient estimates for the derivative NavierStokes equations, as well as a positivity estimate at the flow entrance. 



Daniel Tataru,
UC Berkeley
Monday, April 22nd
KAP 414, 3:30pm4:30pm 
“Long time dynamics in two dimensional water waves”
Abstract: The water wave equations describe the motion of the free surface of a fluid (e.g. water) under the action of various physical forces. Understanding the long time properties of water wave flows is a very interesting yet also very challenging class of problems. The talk will provide an overview of recent and ongoing work in this direction. This is joint work with Mihaela Ifrim.


Angkana Rueland,
University of Leipzig
Monday, August 20th,
KAP 414, 3:30pm4:30pm 
“Microstructures in ShapeMemory Alloys: Rigidity, Flexibility and Some Numerical Experiments”




Career Panel,
USC,
Monday,August 27th,
KAP 414, 4:30pm5:30pm

Panel discussion:"Applying for Grants and Jobs: Information and Advice"
Panelists: Aravind Asok, Greta Panova, Aaron Lauda
Moderator: Susan Friedlander
All postdocs and graduate students are strongly encouraged to come and ask questions about applying for grants from organizations such as the NSF, the NSA and the Simons Foundation. We will also discuss applying for academic positions. 


Monica Visan,
UCLA,
Monday, September 10th,
KAP 414, 3:30pm4:30pm 
“KdV is well posed on H^{1}”
Abstract: While initial introduced as a model for water waves, the Korteweg  de Vries equation has grown to be one of the moststudied partial differential equations. It attracts interest as a model exhibiting solitons, as a representative dispersive PDE, and as an integrable system. In this talk, I will present a proof of wellposedness for KdV for initial data which is merely in H^{1}. The argument applies equally well for KdV posed on the line or the circle. This is based on joint work with Rowan Killip. 




Philip Isett,
Caltech,
Monday, Septemeber 17th,
KAP 414, 3:30pm4:30pm 
“Nonuniqueness and Dissipation of Energy in the Incompressible Euler Equations”
Abstract: Ideas concerning energy dissipation in turbulence have inspired the notion that solutions to the incompressible Euler equations that dissipate kinetic energy may be appropriate for describing fluid behavior in the vanishing viscosity limit. Such solutions that do not satisfy the conservation of energy must have limited regularity, and may therefore in principle be nonunique. The maximal regularity for the existence of an energy nonconserving solution was conjectured in 1949 by Lars Onsager to be the Hölder exponent 1/3.
I will discuss the proof of this conjecture up to the endpoint regularity, as well as a new result on the existence and nonuniqueness of continuous solutions that exhibit local dissipation of energy. The local dissipation of energy is a key criterion for isolating the most physically relevant weak solutions to the equations. A new approach has been required to overcome the limitations faced by previous results on the dissipation of total kinetic energy or on local energy dissipation for bounded, measurable solutions. We prove that continuous weak solutions are nonunique even if local conservation of energy is imposed. Our proof of nonuniqueness represents the first application of the probabilistic method within the method of convex integration, which we employ to obtain a family of such solutions that has positive Hausdorff dimension in the energy space emanating from a single initial datum.


Jack Xin,
UC Irvine
Monday, September 23rd,
KAP 414, 3:30pm4:30pm 
“Enhanced Diffusivity in Chaotic Flows”
Abstract: Transport phenomena in fluid flows are observed ubiquitously in nature such as smoke rings in the air, pollutants in the aquifers, plankton blooms in the ocean, and stirring drops of cream in a cup of coffee. We begin with examples of two dimensional Hamiltonian systems modeling incompressible planar flows, and illustrate the transition from ordered to chaotic flows as the Hamiltonian function becomes more time dependent. We introduce effective diffusivity and show how its enhancement in the flows relate to the existence of periodic orbits (order) and chaotic behavior of flow trajectories (disorder). Then we discuss enhanced diffusivity in three dimensional chaotic flows, viz., the ArnoldBeltramiChildress flow and the Kolmogorov flow, through recent analytical and computational findings. 



Marcelo Disconzi,
Vanderbilt,
Monday, October 8th,
KAP 414, 3:30pm4:30pm 
“A new formulation of the relativistic Euler equations”
Abstract: In this talk, we will discuss some recent results concerning the problem of regularity and shock formation for relativistic fluids, with focus on the relativistic Euler equations. Highlighting some "hidden" geometric aspects of the problem, we will present a new formulation of the relativistic Euler equations that exhibits remarkable properties. This new formulation is wellsuited for various applications, in particular for the study of stable shock formation, as we will discuss. Furthermore, using the new formulation, we establish a local wellposedness result showing that the vorticity and the entropy of the fluid are one degree more regular than one might naively expect. This is a joint work with Jared Speck. 



Christian Zillinger, USC
Monday, October 15th,
KAP 414, 3:30pm4:30pm 
“Stabilization by mixing: On linear damping for the 2D Euler equations” Abstract: In recent years, following the seminal works of Villani and Mouhot on Landau damping, phasemixing as a damping mechanism and, in particular, inviscid damping in fluids have attracted much interest. In this talk, I will provide an introduction to the underlying mechanism and discuss new linear stability and damping results near TaylorCouette flow between concentric cylinders. This is based on joint work with Michele Coti Zelati at Imperial College, London. 



Connor Mooney, Monday, October 22nd, KAP 414, 3:30pm4:30pm 
“Singular Solutions to Parabolic Systems”
Abstract: Regularity results for linear elliptic and parabolic systems with measurable coefficients play an important role in the calculus of variations. Morrey showed that in two dimensions, solutions to linear elliptic systems are continuous. We will discuss some surprising recent examples of discontinuity formation in the plane for the parabolic problem. 



Michael Wolf, University of Zurich,
Monday, November 5th,
KAP 414, 3:30pm4:30pm

“Analytical Nonlinear Shrinkage of Large Covariance Matrices”
Abstract: This paper gives the first analytical formula for optimal nonlinear shrinkage of largedimensional covariance matrices. We achieve this by identifying and mathematically exploiting a deep connection between nonparametric estimation of the Hilbert transform of the sample spectral density and nonlinear shrinkage. Previous nonlinear shrinkage methods were numerical: QuEST requires numerical inversion of a complex equation from random matrix theory, and NERCOME is a crossvalidation scheme. Analytical is more elegant and has more potential to accommodate future variations or extensions. Immediate benefits are that it is 1,000 times faster with same accuracy, and accommodates covariance matrices of dimension up to 10,000. The difficult case where the matrix dimension exceeds the sample size is also covered. 



Maciej Zworski,
UC Berkeley Monday, November 12th
KAP 414, 3:30pm4:30pm 
“Microlocal methods in chaotic dynamics”
Abstract: Microlocal analysis exploits mathematical manifestations of the classical/quantum (particle/wave) correspondence and has been a successful tool in spectral theory and partial differential equations. Recently, microlocal methods have been applied to the study of classical dynamical problems, in particular of chaotic (Anosov, Axiom A) flows. I will survey results obtained with Dyatlov and present some more recent results of, among others, Guillarmou, DangRiviere, Shen, BonthonneauWeich. 



Richard Stanley, MIT, CAMS Distinguished Lecture, Joint with the Whiteman Lecture, MondayTeusday, Nov 2627
Nov 26th: Irani Hall 101, 4:00pm5:00pm
Nov 27th: KAP 414, 3:30pm4:30pm 
“Increasing and decreasing subsequences”
Abstract: An increasing subsequence of a permutation a_1, a_2, ... , a_n of 1,2, ... , n is a subsequence b_1,b_2, ... , b_k satisfying b_1 < b_2 < ... < b_k, and similarly for decreasing subsequence. The earliest result in this area is due to Erdös and Szekeres in 1935: any permutation of 1,2, ... , pq + 1 has an increasing subsequence of length p+1 or a decreasing subsequence of length q+1. This result turns out to be closely connected to the RSK algorithm from the representation theory of the symmetric group. A lot of work has been devoted to the length k of the longest increasing subsequence of a permutation 1,2, ... , n, beginning with Ulam's question of determining the average value of this number over all such permutations. There are many interesting analogues of longest increasing subsequences, such as longest alternating subsequences, i.e., subsequences b_1,b_2, ... , b_k of a permutation a_1, a_2, ..., an satisfying b_1>b_2<b_3>b_4< ... . We will survey these highlights of the remarkable theory of increasing and decreasing subsequences.
Tuesday, November 27, KAP 414, 3:30pm4:30pm (Tea: 3:003:30pm  KAP 410)
Abstract: A parking function of length n is a sequence a_1, a_2, ... , an of positive integers whose increasing rearrangement b_1 \le b_2 \le ... \le b_n satisfies b_i \le i. Parking functions go back to Pyke in 1959; the term "parking function'' and the connection with the parking of cars is due to Konheim and Weiss (1966). Pollak gave an elegant proof that the number of parking functions of length n is (n + 1)^{n1}. There are close connections between parking functions and other combinatorial objects such as trees, noncrossing partitions, and the Shi hyperplane arrangement. Parking functions arise in several unexpected algebraic areas, such as representations of the symmetric group and Haiman's theory of diagonal harmonic. Parking functions also have a number of natural generalizations which fit together in a nice way. We will survey these aspects of the theory of parking functions. 

Marcelo Viana, IMPA, CAMS Distinguished Lecturer, Joint with the Mathematics Department Colloquium, Monday, January 17th, KAP 414, 3:30pm4:30pm 
“Random products of matrices” Abstract: By an old theorem of H. Furstenberg and H. Kesten, the norm of a random product of dbyd invertible matrices grows at a welldefined (i.e. almost certain) exponential rate, that we call the Lyapunov exponent.




Tarek Elgindi, UCSD, Monday,January 29th, KAP 414, 4:30pm5:30pm

"Singularity formation in incompressible fluids" Abstract: The rapid formation of small scale structures is a ubiquitous feature of incompressible fluids. Despite this, actually proving small scale formation analytically is highly nontrivial. In this regard, there are two major problems in the field: whether smooth solutions of the 3D Euler equations become singular in finite time and whether generic smooth solutions of the 2D Euler equations become singular in infinite time. I will discuss recent advances on both of these problems as well as our recent proof of finitetime blowup for strong solutions to the 3D Euler equations. This is a joint work with I. Jeong. 


Weiwei Hu, Oklahoma State University, Monday, February 5th KAP 414, 3:30pm4:30pm 
"Boundary Control of Optimal Mixing via Stokes and NavierStokes Flows" Abstract: We discuss the problem of optimal mixing of an inhomogeneous distribution of a scalar field via an active control of the flow velocity, governed by Stokes or NavierStokes equations, in a two dimensional open bounded and connected domain. We consider the velocity field steered by a control input that acts tangentially on the boundary of the domain through the Navier slip boundary conditions. This is motivated by the problem of mixing within a cavity or vessel by moving the walls or stirring at the boundaries. Our main objective is to design an optimal Navier slip boundary control that optimizes mixing at a given final time. Nondissipative scalars, both passive and active, governed by the transport equation will be discussed. In the absence of diffusion, transport and mixing occur due to pure advection. This essentially leads to a nonlinear control problem of a semidissipative system. A rigorous proof of the existence of an optimal controller and the firstorder necessary conditions for optimality will be presented. 




Theodore Drivas, Princeton University, Monday, February 12th, KAP 414, 3:30pm4:30pm 
"Remarks on Onsager's Conjecture and a Lagrangian formula for anomalous dissipation" Abstract: We discuss the inviscid limit of the global energy dissipation of Leray solutions of incompressible NavierStokes on the torus, assuming that the solutions have norms for Besov space B_{p}^{s,∞} with s ∈ (0,1] that are bounded in the L^{3}sense in time, uniformly in viscosity. We establish an upper bound on energy dissipation of the form O(ν^{(3s1)/(s+1)}). A consequence is that Onsager type "quasisingularities" are required in the Leray solutions, even if the total energy dissipation vanishes in the limit ν → 0, as long as it does so sufficiently slowly. We then discuss a novel Lagrangian expression of the dissipative anomaly under the same assumptions. These formulae give insight into Lagrangian time irreversibility and its connection to the direction of the turbulent cascade. In 3d turbulence, the cascade is downscale and tracer particles initially disperse faster backwardintime than forward while in 2d, the cascade is upscale and the particles initially disperse faster forward in time. The first part of the talk concerns joint work with G. Eyink. 



Jonathan Aurnou, UCLA, Monday, February 26th, KAP 414, 3:30pm4:30pm 
"Planetary Magnetohydrodynamics: The View from the Lab" Abstract: Stars and planets are broadly capable of generating their own largescale magnetic fields via magnetohydrodynamic (MHD) dynamo processes. These dynamos are likely the endproduct of turbulent MHD cascades. Presently, numerical models can generate beautiful facsimiles of geophysical and astrophysical dynamo fields. However, it is unclear that they accurately model the turbulence that exists in planetary cores and stellar convection zones. To better access MHD planetary corestyle turbulence, we have built a number of laboratory experiments. After discussing the state of planetary dynamo modeling, I will present our experiments and experimental findings. I will close with a brief discussion of future aims and the need for continual collusion with theorists. 



Andrej Zlatos, UCSD, Monday, March 5th, KAP 414, 3:30pm4:30pm 
"Stochastic homogenization for reactiondiffusion equations" Abstract: We study spreading of reactions in random media and prove that homogenization takes place under suitable hypotheses. That is, the medium becomes effectively homogeneous in the largescale limit of the dynamics of solutions to the PDE. In contrast to the original (secondorder) reactiondiffusion equations, the limiting "homogenized" PDE for this model are (firstorder) HamiltonJacobi equations, and the limiting solutions are discontinuous functions that solve these in a weak sense. A key ingredient is a new relationship between spreading speeds and front speeds for these models (as well as a new method to prove existence of these speeds). This can be thought of as the inverse of the classical FreidlinGartner formula in the case of periodic media, but we are able to establish it even for more general stationary ergodic reactions. 



Franca Hoffmann, Caltech, Monday, March 19th, KAP 414, 3:30pm4:30pm 
"Equilibria in energy landscapes with nonlinear diffusion and nonlocal interaction" Abstract: We study interacting particles behaving according to a reactiondiffusion equation with nonlinear diffusion and nonlocal attractive interaction. This class of partial differential equations has a very nice gradient flow structure that allows us to make links to variations of wellknown functional inequalities. Depending on the nonlinearity of the diffusion, the choice of interaction potential and the space dimensionality, we obtain different regimes. Our goal is to understand better the asymptotic behavior of solutions in each of these regimes, starting with the faircompetition regime where attractive and repulsive forces are in balance. This is joint work with José A. Carrillo and Vincent Calvez. 



Yuri Bakhtin, Courant Institute, Monday, March 26th, KAP 414, 3:30pm4:30pm 
"Burgers equation with random forcing" Abstract: The Burgers equation is a basic nonlinear evolution PDE of HamiltonJacobi type related to fluid dynamics and growth models. I will talk about the ergodic theory of randomly forced Burgers equation in noncompact setting. The basic objects are onesided infinite minimizers of random action (in the inviscid case) and polymer measures on onesided infinite trajectories (in the positive viscosity case). This is joint work with Eric Cator, Kostya Khanin, and Liying Li. 



Tam Do, USC, Monday, April 2nd, KAP 414, 3:30pm4:30pm

"Vorticity Growth in Axial Symmetric Euler Flows" Abstract: For twodimensional Euler flows, it is known that the L^\infty norm of the gradient of vorticity can grow at most double exponentially in time. In recent years, this bound has been proven to be sharp by Kiselev and Sverak on the unit disc. Drawing inspiration from their results, we examine the possibility of similar growth in the 3D axisymmetric setting. For flows with no swirl, the 3D axisymmetric Euler equations are globally well posed and bear similarities with the 2D Euler Equations. However, we will show that for these flows, one cannot sustain double exponential growth up to the axis of symmetry. 



Benoit Pausader, Brown University, Monday, April 16th, KAP 414, 3:30pm4:30pm 
"Global regularity for the Einstein equation with a massive scalar field" Abstract: We consider the global in time dynamics of perturbations of Minkowski space for the Einstein equation with a massive scalar field. We show that, if the perturbation is small enough, the solution will be global in time and we derive their asymptotic behavior. The difficulty when a massive scalar field is present is that some of the modes of propagation travel at a speed smaller than the speed of light, so that one cannot simply treat this model as a system of wave equations. Thus it is a good setup to develop robust methods to handle the presence of matter in Einstein's equations. 



PDE Seminar  Yu Deng, The Courant Institute, Friday, April 20th, KAP 414, 2pm 3pm 
"On 3D gravitycapillary water waves" Abstract: The global stability of water wave equation under small perturbations has been an active direction of research in recent years. When either gravity or surface tension is neglected, stability results have been obtained by several groups of authors. In this talk we present the recent work where we establish global stability when both gravity and surface tension are present. The main new ingredients are a specially designed energy estimate, and a refinement of the spacetime resonance method of GermainMasmoudiShatah. This is joint work with A. Ionescu, B.Pausader and F. Pusateri. 



John Grace, Earth Sciences Associates, Monday, April 23rd, KAP 414, 3.30pm 4.30pm 
"Automated Salt Recognition in 2D Seismic and Mapping BasinWide Salt in the Gulf of Mexico" Abstract: The most powerful and widely utilized tool for mapping subsurface geologic structure is reflection seismic technology, based on inducing sound waves at the earth's surface and measuring the energy reflected back by geologic features underground and the time it takes for waves to return. A seismic crosssection is typically 2040 miles long, 4 10 miles deep and collects several gigabytes of data. A key goal in seismic interpretation is the discrimination rock types and the thickness and areal extent of strata. Of particular importance in exploring for oil and gas in the Gulf of Mexico is identifying and mapping salt accumulations, which can form subsurface domes, or mountainlike structures, 5 to 8 miles high underground. We have developed a suite of unsupervised machinelearning algorithms to automatically discriminate salt on seismic crosssections, map its depth and assess the confidence in the results. We have applied them to a set of approximately 10,000 seismic crosssections covering the Gulf of Mexico (an area about the size of California). The approach combines analysis of the "texture" of raster images derived from the raw seismic data and vector representation of individual reflectors extracted from the rasters. Mapping several dimensions of image texture (e.g., contrast, entropy) to two exhaustive rock categories is the main goal of raster analysis; vector information contributes identifying where salt is not and separately to find the boundaries. Collectively, these dimensions are reduced to a common salt "score" at each point, which is then subject to a threshold analysis to produce two output classifications: salt and nonsalt. A map of top of salt is estimated in time and then converted to depth by a separately estimated velocity field for rocks in the Gulf of Mexico. Certainty assessment of the estimated salt/nonsalt boundary derives from the strength of the texture differences across the boundary. Joint work with Scott Morris, Shuang Li and Tony Dupont.


Career Panel, Monday, August 28th, KAP 414, 3:30pm4:30pm 
Panel discussion:"Applying for Grants and Jobs: Information and Advice" Panelists: Jay Bartroff, Juhi Jang, Aaron Lauda Moderator: Susan Friedlander All postdocs and graduate students are strongly encouraged to come and ask questions about applying for grants from organizations such as the NSF, the NSA and the Simons Foundation. We will also discuss applying for academic positions. 



Thomas Sideris, UCSB, Monday, September 18th, KAP 414, 3:30pm4:30pm

"The affine motion of 3d compressible fluids surrounded by vacuum" Abstract: In continuum mechanics, the motion of a body $B\subset\mathbb R^3$ is described by a family of diffeomorphisms $y\mapsto x(t,y)$ assigning all points $y\in B$ a position $x$ in a moving domain $\Omega_t$ at time $t$. Affine motion is one which is linear in $y$. That is, $x(t,y)=\mathbf A(t)y$, where for each time $t$, $\mathbf A(t)\in GL^+(3,\mathbb R)$, the group of invertible, orientation preserving linear transformations of $\mathbb R^3$. In the affine case, we will show that the system of partial differential equations describing the motion of a compressible fluid surrounded by vacuum reduces to a globally solvable Hamiltonian system of ordinary differential equations in $GL^+(3,\mathbb R)$. For each time $t$, the fluid domain $\Omega_t$ is an ellipsoid whose diameter grows at a rate proportional to time, as $t\to\infty$. We shall investigate the asymptotic behavior of these domains, and in particular, we will show that for a certain range of the adiabatic index there a scattering theory. 



Colette Guillope, University of Paris, Monday, September 25th, KAP 414, 3:30pm4:30pm 
"Propagation of longcrested water waves" Abstract: In this talk we will present some results about the propagation of waves such as those sometimes observed in canals and in nearshore zones of large bodies of water. A special interest will also be on waves arising in bore propagation, when a surge of water invades an otherwise constantly flowing river. The results are developed in the context of Boussinesq models, so they are applicable to waves that have small amplitude and long wave length when compared with the undisturbed depth. We will discuss the theory of wellposednses results on the long, Boussinesq time scale. In the case of bore propagation, where the mass of water has an infinite energy a priori, we will show how to use suitable approximations with which to compare the full solution. This work is in collaboration with Jerry Bona and Thierry Colin. 



Ivan Corwin, Columbia University, Monday, October 2nd, KAP 414, 3:30pm4:30pm 
"Beyond the Gaussian universality class: traffic, growth, matrices and their universal fluctuations" Abstract: The Gaussian distribution is ubiquitous across science and society. Yet, there are many complex random systems which fail to be well describe by Gaussian processes. In this talk, we will consider certain models of traffic flow, interface growth and random matrices. In their large scale limits, they surprisingly all display the same limit behaviors describe by the so called KardarParisiZhang universality class. This represents a rich universality class beyond that of the Gaussian which is widely applicable to many other types of spatial systems. 



Arieh Warshel, USC, Monday, October 9th, KAP 414, 3:30pm4:30pm 
"How to Simulate the Action of Complex Biological Systems on a Molecular Level?" Abstract: Despite the enormous advances in structural studies of biological systems we are frequently left without a clear structure function correlation and cannot fully describe how different systems actually work. This introduces a major challenge for computer modeling approaches that are aimed at a realistic simulation of biological functions. The unresolved questions range from the elucidation of the basis for enzyme action to the understanding of the directional motion of complex molecular motors. Here we review the progress in simulating biological functions, starting with the early stages of the field and the development of QM/MM approaches for simulations of enzymatic reactions (1). We provide overwhelming support to the idea that enzyme catalysis is due to electrostatic preorganization and then move to the renormalization approaches aimed at modeling long time processes, demonstrating that dynamical effects cannot change the rate of the chemical steps in enzymes (2). Next we describe the use our electrostatic augmented coarse grained (CG) model (2) and the renormalization method to simulate the action of different challenging complex systems. It is shown that our CG model produces, for the first time, realistic landscapes for vectorial process such as the actions of F1 ATPase (3,4), F0 ATPase (5) and myosinV (6,7). It is also shown that such machines are working by exploiting free energy gradients and cannot just use Brownian motions as the vectorial driving force. Significantly, at present, to the best of our knowledge, theses studies are the only studies that reproduced consistently (rather than assumed) a structure based vectorial action of molecular motors. We also describe a breakthrough in CG modeling of voltage activated ion channels (8). We also outline a simulation of the tag of war between staled elongated peptide in the ribosome and the translocon as an illustration of the power of our CG approach (9). The emerging finding from all of our simulations is that electrostatic effects are the key to generating functional free energy landscapes. 



Thomas Banks, N.C. State University, Monday, October 23rd, KAP 414, 3:30pm4:30pm 
CAMS Distinguished Lecturer "Modeling Bumble Bee Population Dynamics with Delay Differential Equations or What's the Buzz about Global Bumblebee Decline?" Abstract: We report on our continuing efforts between our group at NCSU and ecologists at California State University, Monterey Bay and the Swedish University of Agricultural Sciences, Uppsala. To provide a tool for projecting and testing sensitivity of growth and death of populations under contrasting and combined pressures, we developed a nonlinear, nonautonomous delay differential equation (DDE) model of bumblebee colonies and resources model that describes multicolony bumble bee population dynamics. We explain the usefulness of delay differential equations as a natural modeling formulation, particularly for bumble bee modeling. We then introduce a specific splinebased numerical method that approximates the solution of the delay model. We demonstrate that the model satisfies sufficient conditions to assure the subsequent theoretical developments therein in order to attain convergent approximate solutions. We report on our recent efforts on studies of response to toxic substances, in particular our simulations related to growth, death and sublethal responses to neonicotinoid exposure. 



Thomas Hou, California Institute of Technology, Monday, October 30th, KAP 414, 3:30pm4:30pm 
"Blowup or no blowup? The interplay between analysis and computation in the study of 3D Euler equations" Abstract: Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D NavierStokes Equations. A potential singularity in the 3D Euler equations is significant because it may be responsible for the onset of energy cascade in turbulent flows. We first review some recent theoretical and computational studies of the 3D Euler equations. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. We then present strong numerical evidence that the 3D Euler equations develop finite time singularities. The singularity is a ring like singularity that occurs at a stagnation point in the symmetry plane located at the boundary of the cylinder. A careful local analysis also suggests that the blowingup solution is highly anisotropic and is not of Leray type. A 1D model is proposed to study the mechanism of the finite time singularity. We have recently proved rigorously that the 1D model develops finite time singularity. Finally, we present some recent progress in developing an integrated analysis and computation strategy to analyze the finite time singularity of the original 3D Euler equations. 



Claire Vishik, Intel Corporation, Monday, November 6th, KAP 414, 3:30pm4:30pm 
"Trust and cybersecurity: In search of a multidisciplinary theory and solutions for real world problems" Abstract: Cybersecurity has become a global priority, but it encompasses a set of problems that are difficult to solve. The broad definition of cybersecurity encompasses a range of subfields, from computer and network security to cryptography, psychology, human behavior, economics, policy, and international collaboration. The interplay of these subjects is important for the theory and practice in cybersecurity, but the underlying relationships are difficult to define, thus impeding the understanding of real life problems. 



Jared Whitehead, Brigham Young University, Monday, November 13th, KAP 414, 3:30pm4:30pm

"The impact of laminar boundary layers on the search for the ultimate regime of turbulent convection" Abstract: For several decades, careful experiments and detailed numerical simulations have tried to observe the ever elusive 'ultimate' regime of turbulent RayleighBénard convection as predicted by Kraichnan in 1962, but to date no decisive evidence has been brought to light. At the same time, rigorous upper bound analysis has been used to show that this ultimate state does not occur for certain types of boundary conditions and/or asymptotic limits of the underlying Boussinesq equations. Even so, in the most general setting upper bound analysis fails to eliminate the possibility of this ultimate regime from occurring, but does not confirm its existence either. 



Gigliola Staffilani, MIT, Monday, December 4th, KAP 414, 3:30pm4:30pm 
"The many faces of dispersive and wave equations" Abstract: In recent years great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a variety of techniques from Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of problems connected with dispersive and wave equations, such as the derivation of a certain nonlinear Schrodinger equations from a quantum manyparticles system, periodic Strichartz estimates, the concept of energy transfer, the invariance of a Gibbs measure associated to an infinite dimension Hamiltonian system and nonsqueezing theorems for such systems when they also enjoy a symplectic structure. 

Amjad Tuffaha, American University of Sharjah,Monday, January 9th, KAP 414, 3:30pm4:30pm 
"Free Boundary Problems in Fluid Flow and FluidStructure Interactions" Abstract: We consider some mathematical problems involving the NavierStokes and the Euler Equations on an evolving domain and other systems of fluidstructure interaction involving the Euler or the NavierStokes equations coupled with elasticity or plate equations. We examine historical and recent developments in studying the wellposedness of these systems. 



Vlad Vicol, Princeton University,Wednesday, January 11th, KAP 414, 3:30pm4:30pm

"Turbulent weak solutions to hydrodynamic equations" Abstract: Motivated by Kolmogorov’s theory of turbulence, we prove the existence of weak solutions to formally conservative hydrodynamic models, which do not conserve the associated Hamiltonian. In particular, this shows that up to a certain regularity threshold weak solutions are not unique. For the 2D surface quasigeostrophic equations this answers an open problem posed by De Lellis and Szekelyhidi Jr. 



Messoud Efendiyev, Helmholtz Center, Munich,Monday, February 6th, KAP 414, 3:30pm4:30pm 
"Mathematical modelling of biofilms" Abstract: In this talk I will discuss spatiotemporal mesoscale biofilm models. On the mesoscale level, mathematical biofilm models must incorporate population and resource dynamics as well as the transport of growth/process controlling substrates (nutrients, antibiotics) in the surrounding aqueous phase. I will show that these models can be described by highlynonlinear densitydependent reactiondiffusiontransport equations comprising a double degeneracy. I will discuss both the hydrostatic and hydrodynamic cases. Wellposedness, longtime dynamics of solutions in terms of global attractors, and asymptotics of their Kolmogorov's entropy will be treated. 



Gerrit Welper, USC,Monday, February 13th, KAP 414, 3:30pm4:30pm 
"Interpolation of solutions of hyperbolic PDEs by transformed snapshots" Abstract: In recent years significant research efforts have been devoted to numerical simulations of PDEs with deterministic and random coefficients. Nonetheless, hyperbolic problems remain a challenge. One of the major obstructions is the prevalence of shocks, which require significant computational resources to be efficiently resolved by established methods. We improve their efficiency by introducing transformations of the physical domain that align shock discontinuities. They are computed by optimizing a training error and constructed in a way that avoids unacceptable local minima. 



Adam Larios, University of Nebraska,Monday, February 27th, KAP 414, 3:30pm4:30pm 
"The Singularity's Tale" Abstract: One of the famous seven Clay Millennium Prize Problems is to determine whether the 3D NavierStokes equations of fluid flow develop a singularity in finite time (i.e., whether the solutions "blowup"). A closely related, and potentially more challenging problem, is to decide the blowup question for the 3D Euler equations of ideal fluid flow. We will discuss some of the recent history of the search for blowup of the 3D Euler equations, and build an understanding of the phenomenon by doing live simulations of the simpler 1D Burgers equation. We will also present recent results on the computational search for blowup of the 3D Euler equations. 



Alexander Kiselev, Rice University,Monday, March 6th, KAP 414, 3:30pm4:30pm 
"Regularity and blow up in ideal fluid" Abstract: The incompressible Euler equation of fluid mechanics has been derived in 1755. It is one of the central equations of applied analysis, yet due to its nonlinearity and nonlocality many fundamental properties of solutions remain poorly understood. In particular, the global regularity vs finite time blow up question for incompressible three dimensional Euler equation remains open. 



Zaher Hani, Georgia Tech,Monday, March 20th, KAP 414, 3:30pm4:30pm 
"Effective dynamics of nonlinear Schroedinger equations on large domains" Abstract: In this talk, we will be mainly concerned with the following question: Suppose we consider a nonlinear dispersive or wave equation on a large domain of characteristic size L; what is the effective dynamics when L is very large? This question is relevant for equations that are naturally posed on large domains (like water waves on an ocean), and in turbulence theories for dispersive equations. It’s not hard to see that the answer is intimately related to the particular time scales at which we study the equation, and one often obtains different effective dynamics on different timescales. After discussing some time scales (and their corresponding effective dynamics) that hold for moreorless generic dispersive equations, we will try to go further in describing the effective dynamics over much longer time scales. This becomes more equationdependent, and here we specialize to the nonlinear Schroedinger equation (any power nonlinearity) posed on a large box of size $L$. Our main result is to exhibit a new type of dynamics that appears at a particular large time scale, (that we call the resonant time scale) defined in terms of the size of the domain L and the characteristic size of the initial data. As mentioned, going to such long time scales is partly motivated by turbulence theory for dispersive PDE, aka wave turbulence theory, in which one would like to address the effective dynamics on even longer timescales. We will touch on these topics and time scales as well. This is joint work with Tristan Buckmaster, Pierre Germain, and Jalal Shatah (all at Courant Institute, NYU). 



John Hunter, UC Davis,Monday, March 27th, KAP 414, 3:30pm4:30pm 
"Contour dynamics and front propagation in the incompressible Euler and SQG equations" Abstract: Vorticity discontinuities in the twodimensional incompressible Euler equations and temperature discontinuities in the SQG equations support surface waves that decay exponentially away from the discontinuities. These waves have constant linearized frequency on vorticity discontinuities and almost constant wave speed, with a logarithmic correction, on SQG fronts. This talk will describe approximate equations for weakly nonlinear surface waves on planar Euler and SQG fronts, obtained by expansion of suitably regularized contour dynamics equations, and discuss some of their properties. 



Michael Aizenman, Princeton University,Monday, April 3rd, KAP 414, 3:30pm4:30pm

CAMS Distinguished Lecturer "Stochastic Geometry of Correlations in StatMech and Quantum Systems" Abstract: Some of the qualitative features of interacting classical and quantum systems can be illuminated through stochastic geometric representations. In these, the correlations in some of the basic model are presented as mediated through fluctuating clusters and/or random loops. Such representations facilitate insights on a number of phenomena, including: existence of phase transitions related to the onset of long range order, dimension dependence of the critical exponents in Ising type models, the emergence of conformal invariance in critical two dimensional models and relations with the conformally invariant SLE random curves. For one dimensional quantum spin chains a stochastic geometric representation allows us to shed light on the difference between the integer and half integer cases in the spectral (Haldane) gap. 



Jonathan Mattingly, Duke University,Monday, April 17th, KAP 414, 3:30pm4:30pm 
"Building Natural Lyapunov Functions and stablization by noise" Abstract: I will discuss a number of stochastic systems where question of existence of a stochastic steady state (and invariant measure) or the convergence to equilibrium can be reduced to the proving the existence of an appropriate Lyapunov function. 



Mark Green, UCLA,Wednesday, April 19th, Mudd Hall of Philosophy, 101, 4:00pm5:00pm 
Whiteman Lecturer "The Unreasonable Effectiveness of Bayes' Theorem" Abstract: Mathematics has a way of turning out to be more useful than one might have expected. A case in point is Bayes' Theorem, a result about probabilities from the 18th century which has been used for applications as diverse as breaking the German Enigma codes in World War II, quantifying the link between smoking and lung cancer, problems in genomics and understanding the human brain. In this talk, I will discuss the power of probabilistic thinking in general, explain Bayes' Theorem and give some examples of how it is used in machine learning in general, with some examples from clustering tumors to the automated discovering "topics" in a corpus of scientific papers. 



Walter Rusin, Oklahoma State University,Monday, April 24th, KAP 414, 3:30pm4:30pm 
"Remarks and observations on active scalar equations" Abstract: We will discuss properties of active scalar equations that can be traced back to the constitutive law relating the drift velocity and the active scalar. In particular, we will focus on the properties of equations where the Fourier symbol of the multiplier generating the velocity is an even or odd function. Some results on existence of solutions will be discussed. 

Career Panel, Monday, August 29, KAP 414, 3:30 PM  4:30 PM 
"Panel Discussion: Applying for Grants and Jobs: Information and Advice": Panelists: Aravind Asok, Jay Bartroff, Aaron Lauda, Moderator: Susan Friedlander 



Jill Mesirov, UCSD, Monday, September 12, KAP 414, 3:30 PM  4:30 PM 
Joint with Computational Biology "Computational Approaches for Genomic Medicine": The acceleration of data acquisition is changing the face of biomedical research. Computational approaches can take advantage of these data and bring the promise of improved understanding and treatment of disease. 



Christian Zillinger, USC, Monday, September 19, 3:30 PM  4:30 PM 
"On linear inviscid damping, boundary effects and blowup": The Euler equations of fluid dynamics are timereversible equations and possess many conserved quantities, including the kinetic energy and entropy. Furthermore, as shown by Arnold, they even have the structure of an infinitedimensional Hamiltonian system. Despite these facts, in experiments one observes a damping phenomenon for small velocity perturbations to monotone shearflows, where the perturbations decay with algebraic rates. In this talk, I discuss the underlying phasemixing mechanism of linear inviscid damping, its mathematical challenges and will sketch how to establish decay with optimal rates for a general class of monotone shear flows and circular flows. Here, a particular focus will be on the setting of a channel with impermeable walls and an annular domain, where boundary effects asymptotically result in the formation of singularities. 



Michele CotiZelati, University of Maryland, Monday, September 26, KAP 414, 3:30 PM  4:30 PM 
"Deterministic and stochastic aspects of fluid mixing": The process of mixing of a scalar quantity into a homogenous fluid is a familiar physical phenomenon that we experience daily. In applied mathematics, it is also relevant to the theory of hydrodynamic stability at high Reynolds numbers  a theory that dates back to the 1830's and yet only recently developed in a rigorous mathematical setting. In this context, mixing acts to enhance, in certain senses, the dissipative forces. Moreover, there is also a transfer of information from large lengthscales to small lengthscales vaguely analogous to, but much simpler than, that which occurs in turbulence. In this talk, we focus on the study of the implications of these fundamental processes in linear settings, with particular emphasis on the longtime dynamics of deterministic systems (in terms of sharp decay estimates) and their stochastic perturbations (in terms of invariant measures). 



Konstantin Batygin, California Institute of Technology, Monday, October 10, KAP 414, 3:30 PM  4:30 PM 
"Planet Nine from Outer Space": 



Marta Lewicka, University of Pittsburg, Monday, October 17, KAP 414, 3:30 PM  4:30 PM 
"Prestrained elasticity and curvature constraints": 



Michael Wolf, University of Zurich, Monday, October 24, KAP 414, 3:30 PM  4:30 PM 
"Resurrecting Weighted Least Squares": 



Mahir Hadzic, Kings College London, Monday, October 31, KAP 414, 3:30 PM  4:30 PM 
"Generic melting and freezing rates in the classical Stefan problem": 



Roman Shvydkoy, University of Illinois Chicago, Monday, November 7, KAP 414, 3:30 PM  4:30 PM 
"Mechanisms for energy balance restoration in Onsager critical and supercritical flows": 



Michael Holst, University of California, San Diego, Monday, November 14, KAP 414, 3:30 PM  4:30 PM 
"A Look at Some Mathematics Research Problems in General Relativity": 



Linda Petzold, UC, Santa Barbara, Monday, November 28, KAP 414, 3:30 PM  4:30 PM, CAMS Distinguished Lecturer 
"The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems": 



Stefan Steinerberger, Yale University, Monday, December 5, KAP 414, 3:30 PM  4:30 PM 
"Mysterious Interactions between Analysis and Number Theory": 






Mohammed Ziane, USC, Monday, February 1, KAP 414, 3:30 PM  4:30 PM 
"Some regularity results for the 3DNavierStokes equations": In this talk, we will present three types of regularity results on the 3D NavierStokes equations. First we discuss, some conditions on one component of the velocity that guarantee the regularity of Leray’s weak solutions. These conditions are in the spirit of ProdiSerrin conditions. The second type of results is based on anisotropy and fast oscillations, and gives global regular solutions with large BMO^1 norms. Finally we give a partial regularity result in the sense of Caffarelli, Kohn, Nirenberg, which is based on only one component of the velocity. 



CANCELLED  Michael Shelley, Courant Institute, Wednesday, February 10, KAP 414, 3:30 PM  4:30 PM 
Joint with AME 



Benedict Gross, Harvard University, Monday, February 22, 3:30 PM  4:30 PM 
Whiteman Lecture (Gerontology: Leonard Davis Auditorium located in 124) "How large is n! = n(n1)(n2)…3.2.1 ?": 



Gunnar Carlsson, Stanford University, Monday, February 29, KAP 414, 3:30 PM  4:30 PM 
"Topology and the Big Data Problem": In recent years there has been a lot of attention given to "Big Data". In fact, many of the problems that need to be addressed relate not to the "Big", but rather in the inherent complexity of much of the important data that is being produced. What this means is that there is a need for an organizing principle for data analysis. One such organizing principle uses methods from Topology, the mathematical discipline which concerns itself with the study of shape, or rather the higher dimensional generalization of shape. The methods give rise to new methods of modeling data, as well as feature creation and invariants of the shape of the data which are readily interpretable. We will discuss these ideas, with numerous examples from various areas within the sciences and industry. 



Shanghua Teng, Computer Science, USC, Monday, March 7, KAP 414, 3:30 PM  4:30 PM 
"Through the Lens of the Laplacian Paradigm: Big Data and Scalable Algorithms  a Pragmatic Match Made On Earth": In the age of Big Data, efficient algorithms are in higher demand now more than ever before. While Big Data takes us into the asymptotic world envisioned by our pioneers, the explosive growth of problem size has also significantly challenged the classical notion of efficient algorithms: Algorithms that used to be considered efficient, according to polynomialtime characterization, may no longer be adequate for solving today's problems. It is not just desirable, but essential, that efficient algorithms should be scalable. In other words, their complexity should be nearly linear or sublinear with respect to the problem size. Thus, scalability, not just polynomialtime computability, should be elevated as the central complexity notion for characterizing efficient computation. In this talk, I will discuss the emerging Laplacian Paradigm, which has led to breakthroughs in scalable algorithms for several fundamental problems in network analysis, machine learning, and scientific computing. I will focus on three recent applications: (1) PageRank Approximation (and identification of network nodes with significant PageRanks). (2) RandomWalk Sparsification. (3) Scalable Newton's Method for Gaussian Sampling. 



Nathan GlattHoltz, Virginia Tech, Monday, March 21, KAP 414, 3:30 PM  4:30 PM 
"Asymptotic Coupling and Applications for Nonlinear Stochastic Partial Differential Equations": We introduce the notion of asymptotic coupling and explain how this formalism provides a conceptually simple means of proving unique ergodicity in certain stochastic systems whose deterministic counterpart possesses a finite number of determining modes. 



Suncica Canic, University of Houston, Monday, March 28, KAP 414, 3:30 PM  4:30 PM 
"Fluidcomposite structure interaction and blood flow": Fluidstructure interaction (FSI) problems arise in many applications. The widely known examples are aeroelasticity and biofluids. In biofluidic applications, including the interaction between blood flow and cardiovascular tissue, the coupling between the fluid and structure is highly nonlinear because the density of the structure (tissue) and the density of the fluid (blood) are roughly the same. In such problems, geometric nonlinearities of the fluidstructure interface and significant exchange in the energy between the moving fluid and structure play important roles in the physical and mathematical description of the underlying biological problem. The problems are further exacerbated by the fact that the walls of major arteries are composed of several layers, each with different mechanical characteristics. No mathematical results exist so far that analyze existence of solutions to fluidstructure interaction problems in which the structure is composed of several different layers. In this talk we summarize the main difficulties in studying the underlying problem, and present a computational scheme based on which the existence of a weak solution to this class of FSI problems was obtained. Our results reveal a new physical regularizing mechanism in FSI problems: inertia of the fluidstructure interface with mass regularizes evolution of the FSI solution. This means that in our large (muscular) arteries, the innermost layer of arterial walls, which consists of an elastic lamiae covered with endothelial cells, smooths out the propagation of the pressure wave in the cardiovasuclar system. All theoretical results will be illustrated with numerical examples. This is a joint work with Boris Muha (University of Zagreb, Croatia), and with Martina Bukac (Notre Dame University). 



Ioan Bejenaru, UCSD, Monday, April 18, KAP 414, 3:30 PM  4:30 PM 
"Multilinear Restriction Theory": I will introduce the linear and multilinear restriction theory and their relations with various fields in Mathematics: Harmonic Analysis, PDE, Number Theory, Incidence Geometry and Geometric Analysis. I will talk in more detail about the effect of the underlying geometry in the context of multilinear theory. 



Mihaela Ifrim, UC Berkeley, Monday, April 25, KAP 414, 3:30 PM  4:30 PM 
"Two dimensional water waves in holomorphic coordinates": This is joint work with Daniel Tataru, and in parts with Benjamin HarropGriffits and John Hunter. My talk is concerned with the irrotational infinite/finite depth water wave equations in two space dimensions, with either gravity or surface tension. I will also make some remarks on constant vorticity (infinite depth) case when only gravity is considered. We consider this problem expressed in positionvelocity potential holomorphic coordinates. Viewing this problem(s) as a quasilinear dispersive equation, we develop new methods which will be used to prove enhanced lifespan of solutions and also global solutions for small and localized data. For the gravity water waves there are several results available; they have been recently obtained by Wu, AlazardBurqZuily and IonescuPusateri using different coordinates and methods. In the capillary water waves and constant vorticity cases, we were the first to establish a global result, respectively a cubic lifespan existence of smooth and localized solutions. Our goal is to improve the understanding of these problems by providing a single setting for all the above cases, and presenting simpler proofs. The talk will try to be self contained. 



Daniel Spielman, Yale University, Monday, May 9, KAP 414, 3:30 PM  4:30 PM, CAMS Distinguished Lecturer 
"Laplacian Matrices of Graphs: Algorithms and Applications": The Laplacian matrices of graphs arise in many fields including Machine Learning, Computer Vision, Optimization, Computational Science, and of course Network Analysis. We will explain what these matrices are and why they arise in so many applications. We then will survey recent progress on the design algorithms that allow us to solve such systems of linear equations in nearly linear time. In particular, we will show how fast algorithms for graph sparsification directly lead to fast Laplacian system solvers. As an application, we will explain how Laplacian system solvers can be used to quickly solve linear programming problems arising from natural graph problems. 





Juhi Jang USC Monday, August 31KAP 414 3:30 PM  4:30 PM 
On the kinetic FokkerPlanck equation with absorbing barrier
We discuss the wellposedness theory of classical solutions to the Kolmogorov equation, a simplest kinetic FokkerPlanck equation in bounded domains with absorbing boundary conditions. We show that the solutions are smooth up to the boundary away from the singular set and they are Holder continuous up to the singular set. This is joint work with H.J. Hwang, J. Jung and J.L. Velazquez. 

Igor Kukavica USC Monday, September 14KAP 414 3:30 PM  4:30 PM 
The Euler equations with a free interface
We address the local existence of solutions for the water wave problem. For the space dimensions three, we show that the local in time existence holds for initial velocities belonging to $H^{2.5+\delta}$, where $\delta>0$ is arbitrary, with the initial vorticity in $H^{2+\delta}$. The result is joint with A.~Tuffaha and V.~Vicol. 

Career Panel Discussion Monday, September 21KAP 414 3:30 PM  4:30 PM 
Career Panel Discussion: "Planning your career: questions and advice"
Panelists: Andrea Appel, Eric Friedlander, Susan Montgomery, Stanislav Minsker 

Mason Porter Oxford Wednesday, September 30KAP 414 3:30 PM  4:30 PM 
Multilayer Networks and Applications
Networks provided a powerful representation of complex systems of interacting entities. One of the most active areas of network science, with an explosion of publications during the last few years, is the study of "multilayer networks," in which heterogeneous types of entities can be connected via multiple social ties that change in time. Multilayer networks include multiple subsystems and "layers" of connectivity, and it is important to take such multilayer features into account to try to improve our understanding of complex systems. In this talk, I'll give an overview of multilayer networks. I will introduce some ideas for how to find dense sets of nodes known as "communities" in multilayer networks and how this can lead to insights in applications such as political party realignment in voting networks and motortask learning in functional brain networks. I will also discuss how to measure important nodes in multilayer networks, with an example describing the measurement of the quality of mathematics programs over time, and will end by presenting a few of the current challenges in the study of multilayer networks. 

Geordie Richards University of Rochester Monday, October 5KAP 414 3:30 PM  4:30 PM 
Ergodicity Results for Stochastic Boussinesq Equations
We will review some recent results on invariant measures for stochastic Boussinesq equations (model equations for RayleighBenard convection perturbed by an additive noise). First we will discuss ergodicity and mixing results in the twodimensional periodic domain with a spatially degenerate stochastic forcing. These results generalize recent progress of Hairer and Mattingly on hypoellipticity for infinitedimensional systems. Then, with a less degenerate forcing but more physical boundary conditions, we present a simplified proof of ergodicity, and discuss some singular parameter limits. 

Juraj Földes Université Libre de Bruxelles Wednesday, October 7KAP 414 3:30 PM  4:30 PM 
Long term behaviour of maximal entropy solutions for 2D Euler equation
Two dimensional turbulent flows for large Reynold's numbers can be approximated by solutions of incompressible Euler's equation. As time increases, the solutions of Euler's equation are increasing their disorder; however, at the same time, they are limited by the existence of infinitely many invariants. Hence, it is natural to assume that the limit profiles are functions which maximize an entropy given the values of conserved quantities. Such solutions are described by methods of Statistical Mechanics and are called maximal entropy solutions. Nevertheless, there is no general agreement in the literature on what is the right notion of the entropy. We will show that on symmetric domains, independently of the choice of entropy, the maximal entropy solutions with small energy respect the geometry of the domain. 

Stanley Osher UCLA Monday, October 12KAP 414 3:30 PM  4:30 PM CAMS Distinguished Lecturer

Algorithms for Overcoming the Curse of Dimensionality for Certain HamiltonJacobi Equations Arising in Control Theory and Elsewhere
It is well known that time dependent HamiltonJacobiIsaacs partial differential equations (HJ PDE) play an important role in analyzing continuous dynamic games and control theory problems. An important tool for such problems when they involve geometric motion is the level set method. The cost of these algorithms, and, in fact, all PDE numerical approximations is exponential in the space dimensions and time. 

Richard Schoen Stanford University and UCI Monday, October 19KAP 414 3:30 PM  4:30 PM 
Optimal geometries on surfaces
The problem of finding surface geometries (metrics) of a given area which maximize their lowest eigenvalue has been studied for over 50 years. Despite some spectacular successes the problem is still not well understood for most surfaces. In this Colloquium, we will describe this question and the results which have been obtained including very recent progress. 

Vlad Vicol Princeton Monday, November 2KAP 414 3:30 PM  4:30 PM 
The regularity of the 2D Muskat equations with finite slope
We consider the 2D Muskat equation for the interface between two constant density fluids in an incompressible porous medium, with velocity given by Darcy's law. We establish that as long as the slope of the interface between the two fluids remains bounded and uniformly continuous, the solution remains regular. We provide furthermore a global regularity result for small initial data: if the initial slope of the interface is sufficiently small, there exists a unique solution for all time. This is joint work with P. Constantin, R. Shvydkoy, and F. Gancedo. 

Phil Holmes Princeton University Monday, November 9RTH 217 3:00 PM  4:00 PM 
Moving Fast and Slow: Feedforward and feedback control in insect locomotion
I will describe mathematical models for running insects, from an energyconserving biped, through a muscleactuated hexapod driven by a neural central pattern generator, to reduced phaseoscillator models that capture the dynamics of noisy gaits and external perturbations, and provide estimates of coupling strengths between legs. I will argue that both simple models and large simulations are necessary to understand biological systems, and end by describing some current experiments on fruit flies that cry out for new and improved models. 

Natasa Pavlovic University of Texas Monday, November 16KAP 414 3:30 PM  4:30 PM 
From quantum many body systems to nonlinear dispersive PDE, and back
The derivation of nonlinear dispersive PDE, such as the nonlinear Schr\"{o}dinger (NLS) from many body quantum dynamics is a central topic in mathematical physics, which has been approached by many authors in a variety of ways. In particular, one way to derive NLS is via the GrossPitaevskii (GP) hierarchy, which is an infinite system of coupled linear nonhomogeneous PDE that describes the dynamics of a gas of infinitely many interacting bosons, while at the same time retains some of the features of a dispersive PDE. 
Sylvester Gates KAP 414 3:30 PM  4:30 PM CAMS Distinguished Lecturer

How Attempting To Answer A Physics Question Led Me to Graph Theory, ErrorCorrecting Codes, Coxeter Algebras, and Algebraic Geometry
We discuss how a still unsolved problem in the representation theory of Superstring/MTheory has led to the discovery of previously unsuspected connections between diverse topics in mathematics. 

Wilfrid Gangbo KAP 414 3:30 PM  4:30 PM 
Existence of a solution to an equation arising from Mean Field Games
We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation introduced by Lions, the socalled master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton–Jacobi equations studied independently by Ambrosio–Feng and G–Swiech, and the master equation. As a consequence we recover the existence of solutions to the First Order Mean Field Games equations, first proved by Lions. We make a more rigorous connection between the master equation and the Mean Field Games equations. (This talk is based on a joint work with A. Swiech). 

Jerome Goldstein KAP 414 3:30 PM  4:30 PM 
Energy asymptotics for dissipative waves
Topics include sharp results on equipartition of energy, overdamping, and asymptotic parabolicity. These are for linear waves, and these problems have a long history, the newest being asymptotic parabolicity, which was born in G I Taylor's 1922 paper. This is joint work with G. ReyesSouto. 

Mickael Chekroun KAP 414 3:30 PM  4:30 PM 
NonMarkovian Reduced Equations for Stochastic PDEs
In this talk, a novel approach to deal with the parameterization problem of the “small" spatial scales by the “large" ones for stochastic partial differential equations (SPDEs) will be discussed. This approach relies on stochastic parameterizing manifolds (PMs) which are random manifolds aiming to provide — in a mean square sense — approximate parameterizations of the small scales by the large ones. Backwardforward systems will be introduced to give access to such PMs as pullback limits depending — through the nonlinear terms — on (approximations of) the timehistory of the dynamics on the low modes. These auxiliary systems will be used for the effective derivation of nonMarkovian reduced stochastic differential equations from Markovian SPDEs. The nonMarkovian effects are here exogenous in the sense that they result from the interactions between the external driving noise and the nonlinear terms, given a projection of the dynamics onto the modes with low wavenumbers. It will be shown that these nonMarkovian terms allow in certain circumstances to restore in a striking way the missing information due to the lowmode projection, namely to parameterize what is not observed. Noiseinduced large excursions or noiseinduced transitions will serve as illustrations. 

Geoffrey Spedding KAP 414 3:30 PM  4:30 PM 
Wake Signature Detection
The various regimes of strongly stratified flows have been studied extensively in theory, laboratory and numerical experiment. In the case of stratified, initiallyturbulent wakes, the particular applications have drawn the research into high Froude and Reynolds number regimes (an internal Froude number is a ratio between timescales of turbulent motions vs. the restoring buoyancy forces, and a Reynolds number can be viewed as a ratio of timescales of advection vs. diffusion), that quite surprisingly have turned out to have rather general application. If, as seems likely, the conditions for making persistent flows with robust pattern are widespread, then we may consider the generation of, and search for, geometric pattern as being a phenomenon that is almost ubiquitous. Here we consider cases that range from island wakes that persist for more than 10,000 km to copepod tracks that have initial scales on the order of mm. Similarities and analogies will be noted in a somewhat qualitative fashion, in the hopes of inspiring future work. 

Reception: Emmanuel Candes Monday, April 13Gerontology Courtyard 3:15 PM  4:00 PM CAMS Distinguished Lecturer

Reception


Emmanuel Candes Stanford University, Joint with the Marshall School of Business Monday, April 13Gerontology Auditorium 4:00 PM  5:00 PM CAMS Distinguished Lecturer

Around the Reproducibility of Scientific Research: A Knockoff Filter for Controlling the False Discovery Rate
The big data era has created a new scientific paradigm: collect data first, ask questions later. When the universe of scientific hypotheses that are being examined simultaneously is not taken account, inferences are likely to be false. The consequence is that follow up studies are likely not to be able to reproduce earlier reported findings or discoveries. This reproducibility failure bears a substantial cost and this talk is about new statistical tools to address this issue. Imagine that we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)the expected fraction of false discoveries among all discoveriesis not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. We introduce the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, and the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. This work is joint with Rina Foygel Barber. 

Yuri Tschinkel KAP 414 4:45 PM  5:30 PM 
Simons Foundation Discussion
The Simons Foundation Division for Mathematics and the Physical Sciences (MPS) seeks to extend the frontiers of basic research. The Division’s primary focus is on mathematics, theoretical physics and theoretical computer science. The division awards grants primarily through competitive, open, applicationbased procedures. 

Yuri Tschinkel Director of the MPS Division of the Simons Foundation and Professor at the Courant Institute Wednesday, April 15KAP 414 3:30 PM  4:30 PM 
Geometry of Numbers
I will discuss Minkowski's geometric ideas and their modern incarnations. 

Anthony Suen Hong Kong Institute of Education Monday, April 27KAP 414 3:30 PM  4:30 PM 
Existence of intermediate weak solution to the equations of multidimensional chemotaxis systems
We prove the globalintime existence of intermediate weak solutions of the equations of chemotaxis system in a bounded domain of $\mathbb{R}^2$ or $\mathbb{R}^3$ with initial chemical concentration small in $H^1$. No smallness assumption is imposed on the initial cell density which is in $L^2$. We first show that when the initial chemical concentration $c_0$ is small only in $H^1$ and $(n_0n_\infty,c_0)$ is smooth, the classical solution exists for all time. Then we construct weak solutions as limits of smooth solutions corresponding to mollified initial data. Finally we determine the asymptotic behavior of the global solutions. 

Grace Wahba University of Wisconsin Monday, May 4KAP 414 3:30 PM  4:30 PM CAMS Distinguished Lecturer

Learning Genetic Risk Models Using Distance Covariance
We extend an approach suggested by Li, Zhong and Zhu (2012) to use distance covariance (DCOV) as a variable selection method by providing the DCOV Variable Selection Theorem, which gives a principled stopping rule for a greedy variable selection algorithm. We apply the resulting DCOV Variable Selection Method in two genetic based classification problems with small sample size and large vectors of gene expression data. 