Colloquia

Career Advice Panel

Monday, September 11th, 3:30 – 4:30 pm, KAP 414

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

Panelists: Julian Chaidez, David Crombecque and 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.

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Philip Isett, Caltech

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

Lessons from Convex Integration

Abstract: In fluid dynamics, convex integration is a method best known for its applications to proving nonuniqueness results and constructing energy non-conserving solutions. In this talk, I will discuss how tools that arose in convex integration have applications to problems outside of this usual scope. I will start by discussing a theoretical link between lower dimensional turbulent energy dissipation and intermittency of structure functions that was first postulated by Landau in the ‘40’s. I will then discuss an application to solving certain underdetermined PDE and proving related Sobolev embedding theorems. Finally, I will discuss optimal bounds for SQG and related nonlinearities that characterize the mSQG family. Based on joint works with Luigi de Rosa, with Sung-Jin Oh, and with Andrew Ma.

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Yu Deng, USC

Monday, October 2nd, 3:30 – 4:30 pm, KAP 414

Recent progress on mathematical wave turbulence

Abstract: The theory of wave turbulence, which started in the 1920s as the wave analog of Boltzmann’s kinetic theory, has been an active field of physics in the last century, with substantial scientific applications. In this talk I will review some recent works, joint with Zaher Hani, that establish the first rigorous mathematical foundation of the wave turbulence theory, by justifying the derivation of the wave kinetic equation, the fundamental equation of this subject.

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John Burns, Virginia Tech

Monday, October 16th, 3:30 – 4:30 pm, KAP 414

Title: Modeling and Digital Twins for Control, Estimation and Design
(New Paradigms for Model Based Design)

Abstract: In this talk we discuss modeling and numerical issues involved with constructing finite dimensional mathematical models that can be used for control, optimization and design of infinite dimensional systems. We focus on the approximate-then-design paradigm that is key to many new modeling and digital twins technologies. These methods are rapidly becoming the standard approach to model based system engineering and is enabled by a growth of software environments for model creation, simulation and post-processing. Roughly speaking, these software tools facilitate the construction of finite dimensional system level computational models by connecting (in software) finite dimensional component models. These component models are saved in a “library” of domain models which are linked by software to generate system level models. We consider the case where one or more of the physical components are described by partial differential equations and the process of building finite dimensional component models involves some type of discretizations. Using this process to develop system level computational models that are suitable for simulation, optimization and control leads to modeling and approximations requirements that are more stringent than models to be used only for simulation. Examples are used to demonstrate how problems can arise if these issues are ignored. In particular, we focus on optimization, estimation and control problems for PDE systems. One goal of this talk is to raise the awareness of new trends in model based system engineering and to point out some numerical issues, challenges and opportunities for research. Examples are given to illustrate some of these issues and to illustrate the importance of consistent approximations, dual convergence, parametric smoothness and numerical conditioning.

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John Hunter, UC Davis

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

Title: TBA

Abstract: TBA

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Matthew Novack, Purdue University

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

Title: TBA

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Federico Pasqualotto, UC Berkeley

Monday, November 6th, 3:30 – 4:30 pm, KAP 414

Title: TBA

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Eitan Tadmor, University of Maryland

Monday, November 13th, 3:30 – 4:30 pm, KAP 414

Title: TBA

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Hao Shen, University of Wisconsin, Madison

Monday, November 20th, 3:30 – 4:30 pm, KAP 414

Title: TBA

Abstract: TBA

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Fred Weissler, University Sorbonne Paris Nord

Monday, November 27th, 3:30 – 4:30 pm, KAP 414

Title: TBA

Abstract: TBA