Date/Time : 09 Mar 2021 14:00
Venue : via Zoom
Speaker : Shilin Yu, Xiamen University

Join Zoom Meeting https://nus-sg.zoom.us/j/83991095732?pwd=bG9Ramlwc1NGajVDUjZGQitSNUE3UT09 Meeting ID: 839 9109 5732 Password: 858523 Abstract:  The “coadjoint orbit method” philosophy of Kirillov and Kostant suggests that there is a close connection between the unitary dual of a Lie group G, which is the set of all irreducible unitary representations of G, and the set of coadjoint orbits in the dual of its Lie algebra. Roughly, one expects that the representations arise as “quantizations” of certain vector bundles on the coadjoint orbits, which are naturally symplectic manifolds. When the Lie group is a noncompact real semisimple group, both the unitary dual and the orbit method are far from being fully understood, yet a lot of deep and interesting mathematics have been developed to study this case. Vogan suggested the candidates for the vector bundles on the coadjoint orbits to be quantized, which he called admissible vector bundles. In this talk, we show that these admissible vector bundles indeed correspond to representations, with some exceptions. The tools used here are deformation quantization of symplectic varieties and their Lagrangian subvarieties. The talk is based on a joint paper with Conan Leung and an ongoing joint work with Ivan Losev.

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Date/Time : 05 Mar 2021 16:00
Venue : via Zoom
Speaker : Eric Moulines, Ecole Polytechnique

Join Zoom Meeting Meeting ID: 822 6641 6347 Password: 603563 Abstract: Statistical learning is rich in inference problems involving probability distributions (e.g. requiring to sample complex distributions, compute normalizing constants, approximate high-dimensional integrals, etc.). Examples include (Bayesian) uncertainty quantification, inference and sampling of generative models, aggregation of predictors. The classical approach to address these challenging problems in computational statistics is to use Monte Carlo techniques. Markov Chain Monte Carlo algorithms (equipped with numerus bonuses) has long provided the gold standard in this area. The situation radically changes 10 years ago with the development of deep learning: classical MCMC algorithms (Gibbs sampler, simple Metropolis-Hastings methods) fare badly for models now routinely used in today AI. This has triggered a lot of efforts in the last decade, with some initial successes, but opening new research avenues. In this talk, I will describe two approaches to raise (partially !) these issues. I will present a novel generation of methods based on non-equilibrium distributions which might be seen as a way to combine either optimization and / or normalizing flows and can be used both to sample distributions and compute normalizing constants. I will also cover new research directions allowing to enrich variational approaches with MCMC technique, a way to bridge the gap between variational inference and “plain” Monte Carlo.

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Date/Time : 04 Mar 2021 16:00
Venue : via Zoom
Speaker : Ariel Neufeld, Nanyang Technological University

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Abstract: In this talk, we first recall the mathematical concept of neural networks and its universal approximation property. Then we will show how one can combine neural networks together with tools from Stochastic Calculus, particularly the Feynman-Kac representation, to build a neural network based algorithm that can approximately solve high-dimensional nonlinear PDEs in up to 10’000 dimensions with short run times. We apply this algorithm to price high-dimensional financial derivatives under default risk.

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Date/Time : 03 Mar 2021 17:00
Venue : via Zoom
Speaker : Desmond Lau,

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract: Martin’s Maximum^{++} and Woodin’s axiom (*) are two statements independent of, but consistent with, ZFC. I will present the common reasons they are appealing as set-theoretic axioms, before comparing the sense in which they are “maximal”. I will also run through an exposition of the recent work by Aspero and Schindler, which shows Martin’s Maximum^{++} implies (*), effectively “unifying” the statements.

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Date/Time : 03 Mar 2021 10:00
Venue : via Zoom
Speaker : Xiuyuan Cheng, Duke University

Join Zoom Meeting https://nus-sg.zoom.us/j/82863583302?pwd=eHlCQkg3UWs5NDNwNXZXUytQSkNUQT09&from=addon Meeting ID: 828 6358 3302 Password: 860921 Abstract:  The recent success of generative adversarial network (GAN) and variational learning suggests that training a classification network may work well in differentiating two distributions from data samples, known as the classical two-sample problem. An important consideration here is the geometric properties of data distributions. In this talk, we focus on the situation where data samples lie on or near to low-dimensional manifolds embedded in a possibly high-dimensional space. After reviewing some background knowledge of kernel-based two-sample methods, especially the kernel Maximum Mean Discrepancy (MMD) test, we introduce a neural network test using the logit function of a trained classifier motivated by the D-net in GAN. The classification logit function provides the “witness function” under the MMD framework, namely the test function indicating where the two distributions differ and thus is of central application interest. Theoretically, with Lipschitz regularization of the network functions, both the approximation and estimation error of the neural network method are proved to only scale with the intrinsic dimensionality of the data. We discuss applications to biomedical datasets, particularly the differential abundance analysis of single-cell RNA sequencing data. Joint work with Alexander Cloninger (UCSD) and Kluger’s lab (Yale School of Medicine).

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Date/Time : 03 Mar 2021 15:00
Venue : via Zoom
Speaker : Eyal Kaplan, Bar Ilan University

Join Zoom Meeting https://nus-sg.zoom.us/j/89277873740?pwd=M09uNUdjMVVDT21CcHkrOUVaUi9Idz09 Meeting ID: 892 7787 3740 Password: 469660 Abstract: In recent works, the doubling method of Piatetski-Shapiro and Rallis from the 80s has been generalized in several aspects with interesting applications, including a result on global functoriality, and progress in the study of L-functions and local factors for representations of covering groups.  In this talk I will describe the new ingredients, which help complete the (global and local) picture: The multiplicity one result obtained in a joint work with Aizenbud and Gourevitch, and a new family of GL(c) x GL(k) doubling integrals. Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.

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Date/Time : 24 Feb 2021 14:00
Venue : via Zoom
Speaker : Chen Rui, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/86900644508?pwd=S0FUdkI2RzhGTWJwV1R1Y1F6SmpBUT09 Meeting ID: 869 0064 4508 Password: 895425 Abstract:   This is a sequel to Jialiang’s talk, we shall consider some local counter part of that talk. We describe some behavior of local Arthur packets under the stable range theta correspondence using Moeglin’s explicit construction of local Arthur packets for quasi-split classical groups. In some sense our results could be regarded as giving a proof of Adams conjecture in the stable range case.

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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 : 17 Feb 2021 10:00
Venue : via Zoom
Speaker : Luo Yusheng, University of Michigan

Join Zoom Meeting https://nus-sg.zoom.us/j/83866564646?pwd=UnBpaEZqTjc1aXlZeGJZaEZCS2dqdz09 Meeting ID: 838 6656 4646 Password: 332346 Abstract:  The Sullivan dictionary provides a conceptual framework for understanding the connections between dynamics of rational maps and Kleinian groups. In this talk, we will explain how an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps can be established. As an application, we show how this dynamical correspondence allows us to solve mating problems. We further establish a connection on the parameter/deformation space by proving an analogue of Thurston’s compactness theorem for acylindrical hyperbolic 3-manifolds in the rational map setting. If time permits, we will also talk about some open questions and further studies.

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