Date/Time : 23 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Allan Merino, National University of Singapore

Date/Time:23 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Allan Merino, National University of Singapore Character Varieties Giving a pair (Gamma, G), where Gamma is a finitely generated group and G a complex algebraic reductive group, we define the GIT-quotient Hom(Gamma, G) // G: it’s the character variety corresponding to (Gamma, G). One can determine a set of generators when G = SL(V), Sp(V) and O(V) using results of Weyl and Procesi, and for G = SO(V) using a paper of Zhu-Aslaksen-Tan and a recent result of Sikora. In my talk, I will explain first how can we determine these generators. At the end, I will present an ongoing project, joint with Clement Guerin, concerning the character variety of Spin(n) and G2. Add to calendar: 

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Date/Time : 23 Oct 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Bernard Shiffman, Johns Hopkins University

Independent random points on a compact Riemann surface tend to cluster, while the zeros of a random holomorphic section of a line bundle of high degree tend to repel on account of their correlations. I shall dis-cuss asymptotic formulas for the distribution and pair correlation of zeros of Gaussian random polynomials on C^n and, more generally, of random sections of powers of a positive line bundle on a compact Kahler manifold. These formulas depend on the off-diagonal asymptotic expansion of the Bergman kernel, which also yields central limit theorems for the zeros.

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Date/Time : 17 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Li Zeyong,

Date/Time:17 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Li Zeyong A Complete Problem for Statistical Zero Knowledge This work by Amit Sahai and Salil Vadhan presents the first complete problem for SZK, the class of promise problems possessing statistical zero-knowledge proofs (against an honest verifier). The problem, called STATISTICAL DIFFERENCE, is to decide whether two efficiently samplable distributions are either statistically close or far apart. This gives a new characterization of SZK that makes no reference to interaction or zero knowledge. The talk (due to time constraint) will focus on the second half (and arguably the more insightful half) of the completeness theorem, that is, STATISTICAL DIFFERENCE is SZK-hard. It essentially gives a constructive proof that any promise problem possessing a statistical zero-knowledge proof can be reduced to an instance of STATISTICAL DIFFERENCE in polynomial time. Add to calendar: 

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Date/Time : 16 Oct 2019 16:00
Venue : S17 #06-11
Speaker : Yeong Chyuan , Chung Leiden University

Date/Time:16 Oct 2019 16:00 Venue: S17 #06-11 Speaker: Yeong Chyuan Chung, Leiden University Coarse geometry and operator algebras In this talk, we will discuss an aspect of the interplay between coarse geometry of metric spaces, operator algebras, and K-theory of these algebras. Roe algebras are operator algebras designed to encode the coarse geometry of metric spaces. In particular, they are coarse geometric invariants. The question of the extent to which Roe algebras remember the coarse geometry of the metric space is called the rigidity problem. We will describe joint work with Bruno M. Braga and Kang Li relating the rigidity problem to the coarse Baum-Connes conjecture on the K-theory of these and other related algebras. Add to calendar: 

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Date/Time : 16 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Wang Chuijia,

Date/Time:16 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Wang Chuijia Geometric constructions of local Langlands correspondence for p-adic groups (II) In this talk, we review several different approaches to geometric constructions of local Langlands correspondence which are in different flavour. Add to calendar: 

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Date/Time : 10 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Ashutosh Kumar, National University of Singapore

Date/Time:10 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Ashutosh Kumar, National University of Singapore On partitions into null sets Given a partition P of the set of reals into Lebesgue null sets, let J be the ideal of those subsets of P whose union is null. We’ll show that, consistently, J can be countably saturated. This is a joint work with Saharon Shelah. Add to calendar: 

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Date/Time : 09 Oct 2019 16:00
Venue : S17 #05-11 SR5
Speaker : CAI Yongyong, Beijing Computational Science Research Center

Date/Time:09 Oct 2019 16:00 Venue: S17 #05-11 SR5 Speaker: CAI Yongyong, Beijing Computational Science Research Center Numerical methods for Bogoliubov excitations of Bose-Einstein condensates We study the analytical properties and the numerical methods for the Bogoliubov-de Gennes equations (BdGEs) describing the elementary excitation of Bose-Einstein condensates around the mean field ground state, which is governed by the Gross-Pitaevskii equation (GPE). Three numerical methods are proposed to solve the BdGEs, including sine-spectral method, central finite difference method and compact finite difference method. Extensive numerical tests are provided to validate the algorithms and confirm that the sine-spectral method has spectral accuracy in spatial discretization, while the central finite difference method and the compact finite difference method are second-order and fourth-order accurate, respectively. Finally, sine spectral method is extended to study the elementary excitations under optical lattice potential and solve the BdGEs around the first excited states of the GPE. Add to calendar: 

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Date/Time : 09 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Wang Chuijia,

Date/Time:09 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Wang Chuijia Geometric constructions of local Langlands correspondence for p-adic groups In this talk, we review several different approaches to geometric constructions of local Langlands correspondence which are in different flavor. Add to calendar: 

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Date/Time : 09 Oct 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Hirofumi Osada, Kyushu University

I talk homogenization of diffusion in the two-dimensional Euclid space in a periodic Coulomb environment. That is, I consider a periodic point process in the plane. The diffusion has the repulsive interaction with the two-dimensional Coulomb potential with inverse temperature $\beta$ to each particle in the periodic point process. We first prove that the diffusion is diffusive with non-degenerated effective diffusion constant $\gamma$. We then remove one particle from the environment and consider the diffusive scaling limit of the diffusion. Then its new effective constant depends on inverse temperature $\beta$. It has a phase transition whose critical point is given explicitly in terms of the first effective diffusion constant $\gamma$ of the periodic homogenization problem. Using this result, we present explicit bounds for the critical point of the self-diffusion matrices of the strict two-dimensional Coulomb interacting Brownian motions for inverse temperature $\beta$. Moreover, we discuss the case d-dimensional case with d \ge 3.

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