### TBA by Christian Keller

- Series
- PDE Seminar
- Time
- Tuesday, November 12, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Christian Keller – University of Central Florida – christian.keller@ucf.edu

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- Series
- PDE Seminar
- Time
- Tuesday, November 12, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Christian Keller – University of Central Florida – christian.keller@ucf.edu

- Series
- PDE Seminar
- Time
- Tuesday, October 29, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Levon Nurbekyan – Emory University – levon.nurbekyan@emory.edu

- Series
- PDE Seminar
- Time
- Tuesday, October 22, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Ebru Toprak – Yale University – ebru.toprak@yale.edu

TBA

- Series
- PDE Seminar
- Time
- Tuesday, October 1, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Ming Chen – University of Pittsburgh – mingchen@pitt.edu

TBA

- Series
- PDE Seminar
- Time
- Tuesday, September 24, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Keagan Callis – Georgia Tech – kcallis3@gatech.edu

- Series
- PDE Seminar
- Time
- Tuesday, September 17, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Evan Miller – University of Alabama in Huntsville – epm0006@uah.edu

- Series
- PDE Seminar
- Time
- Tuesday, September 3, 2024 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE: https://gatech.zoom.us/j/92007172636?pwd=intwy0PZMdqJX5LUAbseRjy3T9MehD.1
- Speaker
- Mattia Martini – Laboratoire J.A. Dieudonné, Université Côte d'Azur – mattia.martini@univ-cotedazur.fr

Over the past twenty years, mean field control theory has been developed to study cooperative games between weakly interacting agents (particles). The limiting formulation of a (stochastic) mean field control problem, arising as the number of agents approaches infinity, is a control problem for trajectories with values in the space of probability measures. The goal of this talk is to introduce a finite dimensional approximation of the solution to a mean field control problem set on the $d$-dimensional torus. Our approximation is obtained by means of a Fourier-Galerkin method, the main principle of which is to truncate the Fourier expansion of probability measures.

First, we prove that the Fourier-Galerkin method induces a new finite-dimensional control problem with trajectories in the space of probability measures with a finite number of Fourier coefficients. Subsequently, our main result asserts that, whenever the cost functionals are smooth and convex, the optimal control, trajectory, and value function from the approximating problem converge to their counterparts in the original mean field control problem. Noticeably, we show that our method yields a polynomial convergence rate directly proportional to the data's regularity. This convergence rate is faster than the one achieved by the usual particles methods available in the literature, offering a more efficient alternative. Furthermore, our technique also provides an explicit method for constructing an approximate optimal control along with its corresponding trajectory. This talk is based on joint work with François Delarue.

- Series
- PDE Seminar
- Time
- Friday, April 19, 2024 - 15:00 for 1 hour (actually 50 minutes)
- Location
- CSIP Library (Room 5126), 5th floor, Centergy one
- Speaker
- Dr.Lars Ruthotto – Research Associate Professor in the Department of Mathematics and the Department of Computer Science at Emory University

In this talk, we introduce and survey continuous-time deep learning approaches based on neural ordinary differential equations (neural ODEs) arising in supervised learning, generative modeling, and numerical solution of high-dimensional optimal control problems. We will highlight theoretical advantages and numerical benefits of neural ODEs in deep learning and their use to solve otherwise intractable PDE problems.

- Series
- PDE Seminar
- Time
- Tuesday, April 9, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Juhi Jang – University of Southern California – juhijang@usc.edu

In this talk, we will discuss mathematical construction of self-similar solutions exhibiting implosion arising in gas dynamics and gaseous stars, with focus on self-similar converging-diverging shock wave solutions to the non-isentropic Euler equations and imploding solutions to the Euler-Poisson equations describing gravitational collapse. The talk is based on joint works with Guo, Hadzic, Liu and Schrecker.

- Series
- PDE Seminar
- Time
- Tuesday, March 26, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Casey Rodriguez – University of North Carolina at Chapel Hill – crodrig@email.unc.edu

In this talk, we give an overview of recent work in gradient elasticity. We first give a friendly introduction to gradient elasticity—a mathematical framework for understanding three-dimensional bodies that do not dissipate a form of energy during deformation. Compared to classical elasticity theory, gradient elasticity incorporates higher spatial derivatives that encode certain microstructural information and become significant at small spatial scales. We then discuss a recently introduced theory of three-dimensional Green-elastic bodies containing gradient elastic material boundary surfaces. We then indicate how the resulting model successfully eliminates pathological singularities inherent in classical linear elastic fracture mechanics, presenting a new and geometric alternative theory of fracture.