Date/Time : 19 Jun 2020 0900
Venue : via Zoom
Speaker : Linhui Shen, Michigan State University

Join Zoom Meeting Meeting ID: 954 0477 7844 Password: 7710846 Let G be a split semi-simple algebraic group over Q. We introduce a natural cluster structure on moduli spaces of G-local systems over surfaces with marked points. As a consequence, the moduli spaces of G-local systems admit natural Poisson structures, and can be further quantized. We will study the principal series representations of such quantum spaces. It will recover many classical topics, such as the q-deformed Toda systems, quantum groups, and the modular functor conjecture for such representations. This talk will mainly be based on joint work with A.B. Goncharov.

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Date/Time : 06 Nov 2019 14:00
Venue : S17 #04-06 SR1
Speaker : In-Jee Jeong, Korea Institute for Advanced Study

We introduce the incompressible Euler equations, which describe the dynamics of volume-preserving inviscid fluids, and describe a few open problems in relation to turbulence. Then we discuss a priori estimates, which give upper bounds on the solution in function spaces. In particular, these estimates guarantee that if the initial fluid velocity is smooth, then there is a unique smooth solution for some time interval. After that, we shall review some recent results towards the opposite direction: attempts in showing lower bounds on the solution instead, with the goal of establishing finite-time singularity formation.

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Date/Time : 09 Jan 2019 15:50
Venue : S17 #04-06 SR1
Speaker : Zhang Lei, National University of Singapore

Applying Arthur’s endoscopic classification of discrete automorphic representations for classical groups, we extend Ginzburg-Rallis-Soudry’s automorphic descent from quasi-split classical groups setting to their pure inner forms. Combining with the multiplicity-free results of local Gan-Gross-Prasad conjecture, we not just provide a concrete module construction of cuspidal automorphic representations from the sauce representations of general linear groups, but also prove one direction of global Gan-Gross-Prasad conjecture. Moreover, our study leads us to many fundamental questions on the Fourier coefficients of automorphic forms, which connect to the existence of nonvanishing twist central value of L-functions for instance.

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Date/Time : 16 May 2018 15:30
Venue : IMS Seminar Room, House 3
Speaker : Wei Jiang, Wuhan University

In this talk, I will talk about our work about modeling solid-state dewetting problems. Taking the 2D case for example, I will explain the main idea behind these approaches; some extensions to the 3D case will be also presented. If time permits, I will talk about our recent work about using Onsager’s variational principle to derive reduced models with applications to solid-state dewetting.

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