Date/Time : 18 Jun 2021 16:00
Venue : via Zoom
Speaker : Yash Lodha, Korea Institute for Advanced Study

Join Zoom Meeting https://nus-sg.zoom.us/j/84001105600?pwd=OUc1ZGtOb21KSGtaRHhjN3VWMHJsdz09 Meeting ID: 840 0110 5600 Passcode: 346800 The classification of finite simple groups is one of the most incredible achievements of 20th century mathematics. So what do we know about infinite, finitely generated (or even finitely presented), simple groups? Starting from a beautiful example of Higman from 1951: the first example of a finitely generated infinite simple group, to the striking examples of Thompson, we shall survey this territory full of beautiful phenomena. We shall also discuss some questions that remain mysterious.

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Date/Time : 21 May 2021 09:00
Venue : via Zoom
Speaker : Yudong Chen, Cornell University

Join Zoom Meeting https://nus-sg.zoom.us/j/82907817525?pwd=bU1tWlNwTXhwbC9sa3R5eDZKOVovQT09 Meeting ID: 829 0781 7525 Passcode: 752172 We consider the problems of learning discrete structures from network data under statistical settings. Popular examples include various planted and block models, Z2 synchronization and mixture models. Semidefinite programming (SDP) relaxation has emerged as a versatile and robust approach to these problems. We show that despite being a relaxation, SDP achieves the optimal Bayes error rate in terms of distance to the target solution. Moreover, SDP relaxation is provably robust under the so-called semirandom model, which frustrates many existing algorithms. Our proof involves a novel primal-dual analysis that establishes what we call the Hidden Integrality property: the SDP relaxation tightly approximates the optimal (yet unimplementable) integer program with oracle information. Joint work with Yingjie Fei (Cornell Ph.D.), who won 2nd place in INFORMS Nicholson Student Paper Competition.

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Date/Time : 23 Apr 2021 16:00
Venue : via Zoom
Speaker : Jiange Li, Hebrew University of Jerusalem

Join Zoom Meeting Meeting ID: 872 8371 4051 Password: 226133 Abstract:  The balls into bins problem is a classical problem in probability theory that has many applications in computer science. It involves m balls and n bins. Each time, a ball is placed into a bin selected uniformly at random. We are interested in the following two-thinning variant. For each ball, after a random bin has been selected, we may choose to either accept it or place the ball into a new random bin. We are not aware of the secondary allocation before deciding whether accept the primary allocation. We show explicit strategies that can achieve nearly optimal maximum loads. Comparisons are also drawn between this two-thinning variant and the well-known two-choice variant, in which case one selects two random bins and places a ball into the less loaded bin and ties are broken arbitrarily. (This talk is based on joint work with Ohad Noy Feldheim and Ori Gurel-Gurevich.)

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Date/Time : 19 Mar 2021 09:00
Venue : via Zoom
Speaker : Dongyi Wei, Peking University

Join Zoom Meeting Meeting ID: 852 5313 6061 Password: 863217 Abstract: We study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number $Re$ in a finite or an infinite channel. It was proved that if the perturbation of the initial velocity from the Couette flow is within $c_0{Re}^{-1}$ in the $H^2$ norm, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow, and rapidly converges to a streak solution for $t >> {Re}^{1/3}$ due to the mixing-enhanced dissipation effect. This result confirms the transition threshold conjecture proposed by Trefethen et al. (Science, 1993). The most key ingredient of the proof is the resolvent estimates for the full linearized 3-D Navier-Stokes system around the flow close Couette.

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Date/Time : 19 Feb 2021 16:00
Venue : via Zoom
Speaker : Shu Shen, Sorbonne University

Join Zoom Meeting Meeting ID: 893 0855 5450 Password: 509817 Abstract: The orbital integrals appear as a fundamental object on the geometric side of the Selberg trace formula. In this talk, I will give an introduction to Bismut’s geometric approach to the orbital integrals. In particular, I will explain a recent work with Bismut, which extends the explicit geometric evaluation of orbital integrals for smooth kernels for the Casimir operator obtained by Bismut to the case of kernels for arbitrary elements in the center of the enveloping algebra.

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Date/Time : 22 Jan 2021 09:00
Venue : via Zoom
Speaker : Amol Aggarwal, Columbia University

Join Zoom Meeting Meeting ID: 896 0780 2118 Password: 815869 Abstract: Lévy matrices are symmetric matrices whose entries are random variables with infinite variance; they are governed by a parameter \alpha \in (0, 2) dictating the power law decay of their entries. For \alpha < 1, they are believed to serve as one of the few examples of a matrix model exhibiting a mobility edge, also called an Anderson transition, that separates chaotic (GOE) eigenvalue spacing statistics from ordered (Poisson) ones. In this talk we describe results concerning the statistics for the eigenvalue spacings and eigenvector entries of Lévy matrices. In particular, for \alpha \in (1, 2) their eigenvalue statistics asymptotically follow those of the GOE throughout the spectrum, and for \alpha < 1 the same statement holds around small eigenvalues. These describe joint works with Patrick Lopatto, Jake Marcinek, and Horng-Tzer Yau.

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Date/Time : 20 Nov 2020 09:00
Venue : via Zoom
Speaker : Xiaochuan Tian, University of California, San Diego

Join Zoom Meeting Meeting ID: 879 3214 5555 Password: 996723 Abstract: Nonlocal continuum models are in general integro-differential equations in place of the conventional partial differential equations.  While nonlocal models show their effectiveness in modeling a number of anomalous and singular processes in physics and material sciences, for example, the peridynamics model of fracture mechanics, they also come with increased difficulty in computation with nonlocality involved.  We present in this talk numerical methods for nonlocal models characterized by a length parameter which measures the range of nonlocal interactions.  Several numerical methods will be discussed with a focus on asymptotic compatibility of the schemes that are robust under the change of the nonlocal length parameter.

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Date/Time : 06 Nov 2020 15:00
Venue : via Zoom
Speaker : Ya Deng, Institut des Hautes Études Scientifiques

Join Zoom Meeting Meeting ID: 922 6123 0313 Password: 505350 Abstract: The study of hyperbolicity is intimately related to fascinating questions of geometry (no entire curves) and number theory (finiteness of rational points). The aim of this talk is to present recent progress on the geometric side of the problem. A conjecture by Kobayashi in 1970 states that the complement of a general hypersurface in the complex projective space of high degree is Kobayashi hyperbolic. I will first report a joint work with Damian Brotbek in 2018, in which we confirmed Kobayashi’s conjecture with an effective degree bound. In the second part, I will report my recent work on the hyperbolicity for moduli spaces of polarized manifolds, and for period domains of variation of Hodge structures. This includes a solution of a conjecture by Viehweg-Zuo in 2003.

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Date/Time : 23 Oct 2020 09:00
Venue : via Zoom
Speaker : Georgios Moschidis, University of California, Berkeley

Join Zoom Meeting Meeting ID: 833 7724 5924 Password: 105581 In the presence of a negative cosmological constant, the Einstein equations admit solutions which are asymptotically anti-de Sitter. These solutions, which play a key role in the putative AdS/CFT correspondence in high energy physics, possess a timelike conformal boundary at infinity, which can act as a mirror for gravitational perturbations. The resulting confinement of the gravitational evolution is believed to lead to the emergence of weakly turbulent phenomena: According to the AdS instability conjecture, under reflecting conditions at conformal infinity, arbitrarily small perturbations of anti-de Sitter spacetime are expected to collapse into black holes after sufficiently long time.  During the last decade, a large number of numerical and heuristic works have been dedicated to understanding the dynamics of the Einstein equations in a neighborhood of anti-de Sitter spacetime. In this talk, I will discuss the complex picture revealed by these works. I will then proceed to present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein–scalar field system.

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