Date/Time : 09 Jan 2019 14:30
Venue : S17 #04-06 SR1
Speaker : Ngo Bao Chau, The University of Chicago and Vietnam Institute for Advanced Study in Mathematics

Back to 2000, Braverman and Kazhdan formulate a program aiming at generalizing the Godement-Jacquet construction of principal L-function. We will recall their program with more precision and some modest progress.

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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 : 02 Jan 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Xu Jinchao, Penn State University

In this talk, I will discuss some mathematical relationships between deep neural networks, finite element and multigrid methods.

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Date/Time : 12 Dec 2018 14:00
Venue : S17 #04-06 SR1
Speaker : Alan Reid, Rice University

A consequence of Mostow-Prasad rigidity is that the trace-field of an orientable finite volume hyperbolic 3-manifold M is a number field. In addition, there is a quaternion algebra over this number field that is a natural invariant associated to M. This talk will review this background, and survey recent advances in trying to understand the trace-field and this quaternion algebra, especially in the setting of Dehn surgery on a hyperbolic knot.

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Date/Time : 30 Nov 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Yuval Peres, Microsoft Research

Date/Time:30 Nov 2018 15:00 Venue: S17 #04-06 SR1 Speaker: Yuval Peres, Microsoft Research Search games and Kakeya sets I’ll describe a search game with a surprising geometric connection. A hunter and a rabbit move on an n-vertex graph without seeing each other until they meet. At each step, the hunter moves to a neighboring vertex or stays in place, while the rabbit is free to jump to any node. Thus they are engaged in a zero sum game, where the payoff is the capture time. We show that an optimal rabbit strategy for the cycle yields a Kakeya set: a plane set of zero area that contains a unit segment in every direction. Kakeya sets have been studied intensively in harmonic analysis since their discovery by Besicovitch (1919); their connection to search games is new and yields insights in both directions. (Based on joint work with Y. Babichenko, R. Peretz, P. Sousi and P. Winkler, and on earlier work by Adler et al (2003).) Add to calendar: 

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Date/Time : 29 Nov 2018 16:00
Venue : S17 #04-06 SR1
Speaker : Yuval Peres, Microsoft Research

Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them ? “Fairly” means that each region has the same area. It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition—with exactly equal areas, no matter how the points are distributed. (See the cover of the AMS Notices at http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf or the PNAS article http://www.pnas.org/content/early/2018/09/06/1720804115 ). Our main result is that this partition minimizes, up to a bounded factor, the average distance between points in the same cell. I will also present an application to almost optimal matching of n uniform blue points to n uniform red points on the sphere, connecting to a classical result of Ajtai, Komlos and Tusnady (Combinatorica 1984). I will emphasize open problems on the diameters of the basins and the behavior of greedy matching schemes. Joint work with Nina Holden and Alex Zhai.

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Date/Time : 23 Nov 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Pang Chin How, Jeffrey, National University of Singapore

I will talk about my work on designing a distributed optimization algorithm based on dual ascent (or Dykstra’s splitting) that is asynchronous, decentralized, and has deterministic convergence. We also discuss the extension to the case of directed unreliable edges, and on using majorizations so that one can use subgradients approximations or outer approximations of constraint sets to simplify subproblems to be solved. We also studying convergence rates. I will then describe how I had started working on this area after noticing a heuristic for improving the convergence of the method of alternating projections.

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Date/Time : 12 Nov 2018 16:00
Venue : S17 #04-06 SR1
Speaker : Dilip Raghavan, National University of Singapore

I will summarize some of my work on three connected topics in set theory. The work on cardinal invariants covers both countable and uncountable cardinals, and it includes both ZFC theorems and consistency results. The work on special subsets of real numbers concentrates on techniques for constructing ultrafilters and almost disjoint families. The work on partition calculus includes results in both structural Ramsey theory and partition relations at uncountable ordinals. I will provide the necessary background to understand these results.

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Date/Time : 07 Nov 2018 16:00
Venue : S17 #05-12 SR4
Speaker : An Xinliang, National University of Singapore

Date/Time:07 Nov 2018 16:00 Venue: S17 #05-12 SR4 Speaker: An Xinliang, National University of Singapore Formation of Singularity in General Relativity III Besides black holes, can other types of singularities form in gravitational collapse? What does the singularity look like? Will the singular information be censored in universe? In this talk, I will address above questions. Add to calendar: 

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