| Date | SPEAKER | Host |
|---|---|---|
| September 4 | Yuan Gao, Purdue University TITLE: Optimal Transport in Inhomogeneous Media: Convergence of Gradient Flows and the Effective Wasserstein Metric ABSTRACT: The Fokker--Planck equation with rapidly oscillating coefficients can be formulated as a gradient flow in Wasserstein space, involving both inhomogeneous dissipation and oscillatory free energy. Using an evolutionary Gamma-convergence approach, we derive the homogenized dynamics, which retain the gradient flow structure in a limiting homogenized Wasserstein space. We will also discuss a comparison between the limiting Wasserstein distance induced by the gradient flow and the direct Gromov--Hausdorff limit of the Wasserstein distance. |
Wang |
| September 11 | (No Seminar This Week)
TITLE : ABSTRACT : |
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| September 18 | Dallas Albritton, University of Wisconsin - Madison
TITLE : Non-uniqueness and vanishing viscosity ABSTRACT: The forced 2D Euler equations exhibit non-unique solutions with vorticity in L^p, p > 1, whereas the corresponding Navier-Stokes solutions are unique. We investigate whether the inviscid limit from the forced 2D Navier-Stokes to Euler equations is a selection principle capable of "resolving" the non-uniqueness. We focus on solutions in a neighborhood of the non-uniqueness scenario discovered by Vishik; specifically, we incorporate viscosity and consider epsilon-size perturbations of his initial datum. We discover a uniqueness threshold below which the vanishing viscosity solution is unique and radial, and at which certain vanishing viscosity solutions converge to non-unique, non-radial solutions. |
Novack |
| September 19 (Special Colloquium) | Kevin Zumbrun, Indiana University, Bloomington
TITLE : ABSTRACT: |
Novack |
| September 25 | (No Seminar This Week)
TITLE: ABSTRACT: |
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| October 2 | Nicholas McCleerey, Purdue University TITLE : Lines in the space of Kähler metrics ABSTRACT : In recent years, the metric space of Kahler metrics has played an important role in variational problems in Kahler geometry. We report on some recent investigations (joint with Tamas Darvas) into the existence of geodesic lines in this space, which can be characterized as special solutions to the homogeneous complex Monge-Ampere equation. In particular, we construct a wide range of these lines on any projective Kähler manifold, disproving a folklore conjecture popularized by Berndtsson. In the case of Riemann surfaces, we additionally classify all such lines which are locally bounded. Finally, we investigate the validity of Euclid's fifth postulate for the space of Kähler metrics. | Wang |
| October 9 | Cheng Yu, University of Florida
TITLE: Universality in the Low Mach Number Limit via a Convex Integration Framework ABSTRACT : In this talk, I will present a result on the low Mach number limit of the compressible Euler equations through the lens of convex integration. For any $L^2$-bounded solution of the incompressible Euler equations, we construct a corresponding family of global weak solutions to the compressible Euler equations using convex integration. We then prove that, as the Mach number tends to zero, this family of solutions converges to the given incompressible solution in $L^p$. This approach highlights a form of universality: any incompressible weak solution can be realized as the asymptotic limit of compressible solutions. Our results provide a rigorous framework for understanding the incompressible limit from a new perspective. This talk is based on the joint work with Ming Chen, Alexis Vasseur and Dehua Wang. |
Dixi Wang |
| October 16 | Antonio Segatti, Universita Di Pavia (Virtual)
TITLE: On a variational approximation of the Heat flow of Harmonic Maps' ABSTRACT: In this talk I will discuss a variational approximation of the heat flow of harmonic maps. This approach is based on the Weighted Energy Dissipation (WED) scheme, which is featured by a functional defined on entire trajectories and depending on a small parameter $\varepsilon$. The minimizers of this functional are shown to converge, when $\varepsilon\searrow 0$, to the (weak) solutions of the heat flow. In particular for smooth target manifolds with non positive sectional curvature we recover, via a variational argument, the well known theorem of Eells and Sampson. This is a joint work with Fang-Hua Lin, Yannick Sire and Changyou Wang. | Wang |
| October 23 | Po Chun Kuo, Purdue University
TITLE: ABSTRACT: |
Wang |
| October 30 | Changyu Guo, Shangdong University, China and University of Eastern Finland (Virtual) TITLE: ABSTRACT |
Wang |
| November 6 | Xuenan Li, Columbia University TITLE : ABSTRACT : | Wang |
| November 13 | Jiuyi Zhu, LSU TITLE: ABSTRACT : |
Geng |
| November 20 | Sean McCurdy, Universidad Nacional Autonoma de Mexico (Virtual) TITLE: ABSTRACT : |
Yeh |
| November 27 | ( No Seminar, Thanksgiving Holiday )
TITLE: ABSTRACT : |
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| December 4 | Razvan-Octavian Radu, Princeton University TITLE: ABSTRACT : | Novack |
| December 11 | Nicholas Alikakos, University of Athens, Greece (Virtual)
TITLE: ABSTRACT : | Geng |