Colloquia

Career Advice Panel

Monday, September 9th, 3:30 – 4:30 pm, KAP 414

Panel Discussion: “Applying for Grants and Jobs: Information and Advice”

Panelists: Xiaohui Chen, Sheel Ganatra and Paul Tokorcheck

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.

SOME USEFUL CAREER WEB LINKS

https://www.mathjobs.org

https://www.ams.org/employment

http://www.ams.org/programs/travel-grants/AMS-SimonsTG

https://mathcareers.maa.org/

https://www.tpsemath.org/careers-outside-academia

https://www.siam.org/programs-initiatives/professional-development/career-resources/

https://www.amstat.org/your-career/asa-jobweb

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Abhishek Balakrishna, USC, Mathematics

Monday, September 23rd, 3:30 – 4:30 pm, KAP 414

Title: End Behavior Of A Flutter Model

Abstract: We will be looking at the problem of flutter in a panel placed horizontally along a subsonic flow. The system is modelled as a coupled wave-plate system. Empirical observations indicate that intrinsic panel damping stabilizes the subsonic wave-plate system to equilibria. This means that eventually, there is no panel flutter when the fluid flow is subsonic. The mathematical proof of the statement has remained open for a while. Several partial results have been previously established through regularization of the model; without doing this, classical approaches which decouple the plate and wave dynamics have fallen short. This is due to the regularity defects of the hyperbolic Neumann map. I will discuss how we may operate on the model as it appears in the engineering literature with no regularization and achieve stabilization by “microlocalizing” the wave data itself (given by the plate). This is achieved by observing that there is a compensation by the plate dynamics precisely where the regularity of the 3D wave is compromised (in the “characteristic” sector).

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Vera Gluscevic, USC, Physics

Monday, October 7th, 3:30 – 4:30 pm, KAP 414

Title: The Universe We Cannot See

Abstract: Galaxies exist because invisible dark matter outweighs normal matter by a factor of six in our universe; cosmological expansion accelerates today because dark energy dominates spacetime on cosmic scales. Neither of these phenomena is explained by known particles or forces – their existence points to tremendous gaps in our understanding of nature on the most fundamental level. Over the past two decades, high-precision observations have enabled allocation of our universe into dark matter, dark energy, radiation, and baryon components, giving rise to the backbone model of cosmology. This talk will discuss the quest to understand the microphysics of the dominant (but invisible) components of our universe. I will focus on the mass and interactions of dark matter and neutrino particles as notable examples of science targets for cosmological surveys, to illustrate how observational data that spans billions of years of cosmic history and decades in physical distance scales can pave a new path toward discoveries in fundamental physics.

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Ian Tice, Carnegie Mellon University

Monday, October 14th, 3:30 – 4:30 pm, KAP 414

Title: Stationary and slowly traveling solutions to the free boundary Navier-Stokes equations

Abstract: The stationary problem for the free boundary incompressible Navier-Stokes equations lies at the confluence of two distinct lines of inquiry in fluid mechanics.  The first views the dynamic problem as an initial value problem.  In this context, the stationary problem arises naturally as a special type of global-in-time solution with stationary sources of force and stress.  One then expects solutions to the stationary problem to play an essential role in the study of long-time asymptotics or attractors for the dynamic problem.  The second line of inquiry, which dates back essentially to the beginning of mathematical fluid mechanics, concerns the search for traveling wave solutions.  In this context, a huge literature exists for the corresponding inviscid problem, but progress on the viscous problem was initiated much more recently in the work of the speaker and co-authors.  For technical reasons, these results were only able to produce traveling solutions with nontrivial wave speed.  In this talk we will discuss the well-posedness theory for the stationary problem and show that the solutions thus obtained lie along a one-parameter family of slowly traveling wave solutions.  This is joint work with Noah Stevenson.

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Joseph Miller, Stanford University

Monday, October 28th, 3:30 – 4:30 pm, KAP 414

Title: Effective dynamics of interacting classical, quantum, and wave systems

Abstract: Interacting systems of particles and waves are foundational in many natural phenomena. This talk will outline mathematical approaches for deriving effective, statistical descriptions of such many-body dynamics by connecting them to solutions of nonlinear partial differential equations. Key examples include the Boltzmann equation, which emerges as a limit of interacting hard spheres; the nonlinear Schrödinger equation, which describes quantum particle dynamics initialized near a Bose-Einstein condensate; the Vlasov equation, which is an effective model for both non-collisional particles evolving under Newtonian dynamics or as a semiclassical limit of fermionic interactions; and the kinetic wave equations, which model the behavior of interacting waves. I will discuss my joint work on each of these equations, highlighting how to frame these PDEs as limits of the underlying particle or wave dynamics.

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Steve Shkoller, UC Davis

Monday, November 4th, 3:30 – 4:30 pm, KAP 414

Title: Spacetime geometry of shock formation for the Euler equations in multiple space dimensions

Abstract: While the compressible Euler equations are locally well-posed in Sobolev spaces with sufficient regularity, it is well-known that compressive initial conditions lead to a finite-time singularity at which certain components of the solution gradient become infinite.

While the Sobolev solution ceases to exist at this first singularity, at nearby spatial points the solution remains smooth. Our objective is to evolve the Euler solution past the first singularity, to determine the geometry of the spacetime set on which such a smooth solution can be continued, and identify the geometric coordinates and independent variables which yield uniform Sobolev bounds as the Eulerian gradient passes through a continuum of gradient catastrophes.

In this talk, we will describe a new Arbitrary Lagrangian Eulerian geometry adapted to the fast acoustic characteristic surfaces along which sound waves are propagated, and we will introduce a new set of Differentiated Riemann Variables that together allow for uniform Sobolev bounds of the Euler solutions with no derivative loss.

We will explain the geometry of the spacetime that contains such a smooth Euler solution: its future temporal boundary consists of the downstream singular set (the hypersurface of gradient catastrophes) and the upstream Cauchy horizon, which intersect on a co-dimension-2 set of pre-shocks.

This is joint work with Vlad Vicol at NYU.

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Yu Deng, University of Chicago

Monday, November 18th, 3:30 – 4:30 pm, KAP 414

Title: Long time derivation of Boltzmann equation from hard sphere dynamics

Abstract:

We provide the rigorous derivation of the Boltzmann equation from hard sphere dynamics, for arbitrarily long times that cover the full lifespan of the Boltzmann equation. This extends Lanford’s landmark theorem (1975), and is a major step towards solving Hilbert’s sixth problem.

The main ingredients of the proof include (1) a time layering argument, (2) a cumulant ansatz that memorizes the full collision history on time [0,t], (3) analysis of an integral constructed from such collision history, and (4) a carefully designed combinatorial algorithm that allows to control such integrals. This is joint work with Zaher Hani and Xiao Ma.

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Inwon Kim, UCLA

Monday, November 25th, 3:30 – 4:30 pm, KAP 414

Title: Tumor growth with nutrients: regularity of interface

Abstract: We discuss a model that describes tumor growth with nutrient, where the tumor cell grows with nutrient consumption and with a density upper bound. The model generates evolution of tumor patches, where its density is uniform, with intriguing exhibition of irregular patch boundaries. We will discuss some established results and some open questions.

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