Date/Time : 31 Jul 2020 09:00
Venue : via Zoom
Speaker : Hao Huang , Emory University

Join Zoom Meeting  Meeting ID: 995 2080 5067 Password: 103513   Extremal Combinatorics studies how large or how small a collection of finite objects could be, if it has to satisfy certain restrictions. In this talk, we will discuss how the eigenvalue interlacing methods could lead to various interesting results in Extremal Combinatorics, including the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for discrete cubes, and the resolution of a thirty-year-old problem in Theoretical Computer Science, the Sensitivity Conjecture.

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Date/Time : 17 Jul 2020 0900
Venue : via Zoom
Speaker : Yao Yao, Georgia Institute of Technology

Join Zoom Meeting Meeting ID: 940 7048 1887 Password: 5470853 For some nonlocal PDEs, its steady states can be seen as critical points of an associated energy functional. Therefore, if one can construct perturbations around a function such that the energy decreases to first order along the perturbation, this function cannot be a steady state. In this talk, I will discuss how this simple variational approach has led to some recent progresses in the following equations, where the key is to carefully construct a suitable perturbation. I will start with the aggregation-diffusion equation, which is a nonlocal PDE driven by two competing effects: nonlinear diffusion and long-range attraction. We show that all steady states are radially symmetric up to a translation (joint with Carrillo, Hittmeir and Volzone), and give some criteria on the uniqueness/non-uniqueness of steady states within the radial class (joint with Delgadino and Yan). I will also discuss the 2D Euler equation, where we aim to understand under what condition must a stationary/uniformly-rotating solution be radially symmetric. Using a variational approach, we settle some open questions on the radial symmetry of rotating patches, and also show that any smooth stationary solution with compactly supported and nonnegative vorticity must be radial (joint with Gómez-Serrano, Park and Shi).

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Date/Time : 03 Jul 2020 0900
Venue : via Zoom
Speaker : Ruixiang Zhang, University of Wisconsin-Madison

Join Zoom Meeting Meeting ID: 929 6203 4592 Password: 4680298 Informally, Kakeya type problems ask whether tubes with different positions and directions can overlap a lot. One usually expects the answer to be no in an appropriate sense. Thanks to the uncertainty principle, such a quantified non-overlapping theorem would often see powerful applications in analysis problems that have Fourier aspects. Perhaps the most well-known Kakeya type problem is the Kakeya conjecture. It remains widely open in $\Bbb{R}^n (n>2)$ as of today. Nevertheless, in the recent few decades people have been able to prove new Kakeya type theorems that led to improvements or complete solutions to analysis problems that appeared out of reach before. I will give an introduction to Kakeya type problems/theorems and analysis problems that see their applications. Potentially reporting some recent progress joint with Du, Guo, Guth, Hickman, Rogers and Wang.

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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 : 25 Feb 2020 10:00
Venue : S17 #04-04 SR3
Speaker : Hirotaka Kakuhama, Kyoto University

Date/Time:25 Feb 2020 10:00 Venue: S17 #04-04 SR3 Speaker: Hirotaka Kakuhama, Kyoto University The Doubling $\gamma$-factor over Local Function Fields. The analytic definition of the standard local $\gamma$-factor of irreducible representations of classical groups over $\mathbb{R}$, $\mathbb{C}$, and $p$-adic fields has been established by using the doubling method by Lapid-Rallis, Gan, and the speaker. In this talk, I will discuss about the case of local function fields. First, I will explain the definition of the $\gamma$-factor. Then, I will prove that the $\gamma$-factor satisfies some properties which characterize it. Add to calendar: 

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Date/Time : 12 Feb 2020 10:00
Venue : S16 #03-04
Speaker : Ma Jiajun, Shanghai Jiao Tong University

Date/Time:12 Feb 2020 10:00 Venue: S16 #03-04 Speaker: Ma Jiajun, Shanghai Jiao Tong University Cells and Primitive Ideals The theory of left/right/two side cells of Coxeter groups has become a ubiquitous tool in the representation theory of reductive groups. In this talk, I will give a survey of some basic facts of cells. Then I will focus on the classical Weyl groups and introduce the related combinatorial objects attaching to cells/Weyl group elements. In the end, I will explain the relationship between left cells and primitive ideals in the universal enveloping algebra. Add to calendar: 

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Date/Time : 12 Feb 2020 17:00
Venue : S17 #04-06 SR1
Speaker : Ashutosh Kumar, NUS

Date/Time:12 Feb 2020 17:00 Venue: S17 #04-06 SR1 Speaker: Ashutosh Kumar, NUS On some problems in set-theoretic Eucildean Ramsey theory We shall discuss some questions in Euclidean Ramsey theory where techniques from set theory have played a role. Add to calendar: 

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Date/Time : 05 Feb 2020 10:00
Venue : S17 #04-04 SR3
Speaker : Bao Huanchen, NUS

Date/Time:05 Feb 2020 10:00 Venue: S17 #04-04 SR3 Speaker: Bao Huanchen, NUS Asymptotic Hecke algebras, part 2 We explain Lusztig’s construction of the asymptotic Hecke algebras. Add to calendar: 

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Date/Time : 29 Jan 2020 17:00
Venue : S17 #04-06 SR1
Speaker : Wang Wei, Sun Yat-Sen University, Guangzhou

Date/Time:29 Jan 2020 17:00 Venue: S17 #04-06 SR1 Speaker: Wang Wei, Sun Yat-Sen University, Guangzhou Non-standard models of arithmetic and their standard systems PA is the first order fragment of Peano’s axiomatization of the natural numbers. The natural numbers, N, is called the standard model of PA. But by compactness theorem in first order logic, there are also models of PA different from N, which are called non-standard models of arithmetic. Like in N, every element of a non-standard model M has a binary expansion, which can be regarded as the characteristic function of a subset of N. The standard system of M is the collection of all such subsets of N. It is known that standard systems of non-standard models are always Scott sets and every Scott set of cardinality less than or equal to the first uncountable cardinal is the standard system of some non-standard model. However, the general Scott set problem, whether every Scott set is the standard system of some non-standard model, remains one of the major open problems in the model theory of arithmetic. This talk will present some history of Scott set problem, as well as two constructions of non-standard models with uncountable standard systems. Add to calendar: 

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