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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