Date/Time : 29 Oct 2021 09:00
Venue : via Zoom
Speaker : Luca Spolaor, University of California San Diego

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https://nus-sg.zoom.us/j/86945333380?pwd=Q0VEM2drc0YrKzFUc3VHbFVqNjRCQT09

Meeting ID: 869 4533 3380
Passcode: 583463

Abstract:  In this talk I will discuss some results about isolated singularities of minimal surfaces arising from minimization and Min-Max. In particular, I will focus on the local description of minimal surfaces at such singularities and on their generic behavior with respect to a change in the ambient metric.

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Date/Time : 24 Sep 2021 09:00
Venue : via Zoom
Speaker : Qianxiao Li, National University of Singapore

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https://nus-sg.zoom.us/j/84334390977?pwd=SXVUWm50R1RNSlY1NnplTXJJQ20xdz09

Meeting ID: 843 3439 0977
Passcode: 186685

Abstract:  In this talk, we discuss some recent work on the connections between machine learning and dynamical systems. These come broadly in three categories, namely machine learning via, for and of dynamical systems. In the first direction, we introduce a dynamical approach to deep learning theory with particular emphasis on its connections with approximation and control theory. In the second direction, we discuss the approximation and optimization theory of learning input-output temporal relationships using recurrent neural networks and variants, with the goal of highlighting key new phenomena that arise in learning in dynamic settings. In the last direction, we discuss some principled methods that learns stable and interpretable dynamical model from data arising in scientific applications. We conclude with some discussion on future directions in this rapidly developing field.

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Date/Time : 27 Aug 2021 09:00
Venue : via Zoom
Speaker : Yufei Zhao, MIT

Join Zoom Meeting https://nus-sg.zoom.us/j/87977920058?pwd=R1FxeXJHeGVGeHQ5RGhYR0xwOXVsZz09 Meeting ID: 879 7792 0058 Passcode: 458785 Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity. My talk will discuss these problems and their connections, along with extensions and open problems (e.g., what is the maximum possible second eigenvalue multiplicity of a connected bounded degree graph?). Joint work with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang.

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Date/Time : 30 Jul 2021 09:00
Venue : via Zoom
Speaker : Hao Shen, University of Wisconsin – Madison

Join Zoom Meeting https://nus-sg.zoom.us/j/86176910318?pwd=NnQ5SFcxTk9BRFc1TklwSFRhYS9nZz09 Meeting ID: 861 7691 0318 Passcode: 016860 Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a “solution”. The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.

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Date/Time : 23 Jul 2021 09:00
Venue : via Zoom
Speaker : Jingrui Cheng, State University of New York at Stony Brook

Join Zoom Meeting https://nus-sg.zoom.us/j/86843946871?pwd=eXk1ZmF6OElwY2s3MjdzM1piV2VQQT09 Meeting ID: 868 4394 6871 Passcode: 398037 I will explain the a priori estimates for the cscK equation on a compact manifold, and how to use these estimates to obtain existence when the associated energy functional is “coercive”. If time permits, I will also explain how we can hope to get existence from a more “algebraic” condition, which might be easier to check in practice.

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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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