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 : 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 : 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 17:00
Venue : via Zoom
Speaker : Xiao Ming, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract: Order dimension is a classical combinatorial object and has been widely studied by set theorists, combinatorists and computer scientists since its introduction by Dushnik and Miller in 1941. We focus on the partial orderings that are definable as a Borel subsets in a Polish space and analyze the order dimension that can be realized by Borel definable orders and show that there are some interesting behaviors that can be quite different from the classical order dimension using arbitrary realization. This is a joint work with Dilip Raghavan.

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Date/Time : 17 Feb 2021 10:00
Venue : via Zoom
Speaker : Zhizhen Zhao, UIUC

Join Zoom Meeting https://nus-sg.zoom.us/j/82194201907?pwd=aDJnUTlqM0lXaXl0ZW5ORUsvTDE0QT09 Meeting ID: 821 9420 1907 Password: 953495 Abstract: In this talk, I will introduce a new unsupervised learning framework for data points that lie on or close to a smooth manifold naturally equipped with a group action. In many applications, such as cryo-electron microscopy image analysis and shape analysis, the dataset of interest consists of images or shapes of potentially high spatial resolution, and admits a natural group action that needs to be quotient out before useful information is revealed. For such datasets, we can evaluate group-invariant distance and optimal alignment between data points. From noisy observations and pairwise relations, our goal is to robustly learn the nonlinear geometrical structure of the data and improve the nearest neighbor identification. In the first part, I will focus on a specific application–cryo-electron microscopy single particle class averaging. Cryo-electron microscopy single particle reconstruction is an entirely general technique for 3D structure determination of macromolecular complexes. However, because the images are taken at low electron dose, it is extremely hard to visualize the individual particle with low contrast and high noise level. I will introduce the multi-frequency class averaging (MFCA) algorithm to classify images of similar views and discuss the associated spectral properties of the MFCA matrices that ensure the stability of the algorithm. In the second part, I will extend the discussion to general manifold and compact Lie group structures. The key idea is to define robust similarity measures for the data based on the cycle consistency and algebraic relations of the group transformations under multiple irreducible representations.

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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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Date/Time : 17 Feb 2021 14:00
Venue : via Zoom
Speaker : Zou Jialiang, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/83550826419?pwd=aUtXWDA1eU1naDVUT1hIU0E0QW1iQT09 Meeting ID: 835 5082 6419 Password: 223252 Abstract:  Based on a result of J-S Li on global theta lifts in the stage range, Gan-Ichino established a multiplicity formula for the tempered part of discrete spectra for $MP_2n$ by transporting the multiplicity formula of quasi-split special orthogonal groups. In this talk, I will describe how to use this idea to obtain the same results for non quasi-split even orthogonal and unitary groups. Moreover, we can also obtain a multiplicity formula for the full discrete spectra of anisotropic unitary and even orthogonal groups.

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