Date/Time : 18 Nov 2021 09:00
Venue : via Zoom
Speaker : Yusheng Lei, Boston College

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https://nus-sg.zoom.us/j/83129514590?pwd=U2VWNnhCUGtQR1NpUGo5Zlh3TUhxdz09

Meeting ID: 831 2951 4590
Passcode: 415969

Abstract:  In 2003, Bump-Friedberg-Ginzburg constructed the generalized global theta representation on a metaplectic double cover of an odd special orthogonal group. which was used later to construct the non-minimal theta liftings between double covers of orthogonal groups. This can be viewed as a generalization of the classical theta correspondence. In particular, it enjoys the tower property similar to the Rallis tower in the classical setting. This raises the question of when the first non-zero lifting will occur for a fixed theta tower. Bump-Friedberg-Ginzburg analyzed this problem when the automorphic representations are generic. In this talk, we will show the way to construct such theta liftings and talk about some progress towards understanding the non-generic cases.

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Date/Time : 12 Nov 2021 16:00
Venue : via Zoom
Speaker : Noga Alon, Princeton and Tel Aviv

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https://nus-sg.zoom.us/j/84886693609?pwd=ODArd3JMUDBlVjB2RTBTZlBjVnViUT09

Meeting ID: 848 8669 3609
Passcode: 821993

Abstract:  I will show how basic properties of polynomials can be used in the study of problems in Combinatorics, Additive Number Theory, Combinatorial Geometry and Graph Theory, describing recent and less recent results, problems and algorithmic challenges.

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Date/Time : 12 Nov 2021 10:00
Venue : via Zoom
Speaker : Clement Canonne, University of Sydney

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: In this talk, I will introduce the primitive of “domain compression” over the probability simplex, which enables us to reduce the domain size from k to L while contracting (with high probability) the pairwise total variation distances by a factor at most √(L/k). This can equivalently be seen as some type of dimensionality reduction for probability distributions, preserving (in a one-sided way) the L1 distances.

Starting with the corresponding statement for L=2, I will show how to perform this domain compression in a randomness-efficient fashion, and discuss its optimality. As an application, I will describe how this yields sample-optimal algorithms for goodness-of-fit under various constraints, such as communication (bandwidth) constraints, local privacy, and shuffle privacy.

Based on joint works with Jayadev Acharya, Cody Freitag, Yanjun Han, Ziteng Sun, and Himanshu Tyagi (in particular, (https://arxiv.org/abs/1907.08743; COLT 2020)); and some insights from a paper by Amin, Joseph, and Mao (https://arxiv.org/abs/1911.01452; COLT 2020).

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Date/Time : 12 Nov 2021 16:00
Venue : via Zoom
Speaker : Alexandros Beskos, University College of London

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: Bayesian inference for nonlinear diffusions, observed at discrete times,is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology – borrowing ideas from statistical physics and computational chemistry – for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint configurations of the underlying process noise and of parameters, mapping onto diffusion paths consistent with observations, form an implicitly defined manifold. Then, by making use of a constrained Hamiltonian Monte Carlo algorithm on the embedded manifold, we are able to perform computationally efficient inference for a class of discretely observed diffusion models. Critically, in contrast with other approaches proposed in the literature, our methodology is highly automated, requiring minimal user intervention and applying alike in a range of settings, including: elliptic or hypo-elliptic systems; observations with or without noise; linear or non-linear observation operators. Exploiting Markovianity, we propose a variant of the method with complexity that scales linearly in the resolution of path discretisation and the number of observation times. Example Python code is given at git.io/m-mcmc.

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Date/Time : 11 Nov 2021 16:00
Venue : via Zoom
Speaker : Ruiwen Shu, University of Oxford

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https://nus-sg.zoom.us/j/82284835444?pwd=ZDFaR1RDeDFWQU1iQmFidHYwbUhCQT09

Meeting ID: 822 8483 5444
Passcode: 965013

Abstract:  Erdős and Turán proved a classical inequality on the distribution of roots for a complex polynomial in 1950, depicting the fundamental interplay between the size of the coefficients of a polynomial and the distribution of its roots on the complex plane. Various results have been dedicated to improving the constant in this inequality, while the optimal constant remains open. In this paper, we give the optimal constant, i.e., prove the sharp Erdős-Turán inequality. To achieve this goal, we reformulate the inequality into an optimization problem, whose equilibriums coincide with a class of energy minimizers with the logarithmic interaction and external potentials. This allows us to study their properties by taking advantage of the recent development of energy minimization and potential theory, and to give explicit constructions via complex analysis. Finally the sharp Erdős-Turán inequality is obtained based on a thorough understanding of these equilibrium distributions.

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Date/Time : 11 Nov 2021 09:00
Venue : via Zoom
Speaker : Yaping Yang, University of Melbourne

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https://nus-sg.zoom.us/j/85407853911?pwd=b3E4ZXNERkFaOGtQalNFKzN4MldrUT09

Meeting ID: 854 0785 3911
Passcode: 295101

Abstract:  In this talk, I will explain a connection between stable homotopy theory and representation theory. I will focus on one application of this idea to a problem arising from the modular representation theory. More explicitly, we study a family of new quantum groups labelled by a prime number and a positive integer constructed using the Morava E-theories. Those quantum groups are related to Lusztig’s 2015 reformulation of his conjecture from 1979 on character formulas for algebraic groups over a field of positive characteristic. This talk is based on my joint work with Gufang Zhao.

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Date/Time : 10 Nov 2021 16:00
Venue : via Zoom
Speaker : Maxime Wolff, Sorbonne University

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: In this talk I will present joint works with Kathryn Mann, in which we take advantage of strong rigidity properties of the actions of some Fuchsian groups on the circle. From this, we derive rigidity properties of some larger groups acting on the circle, such as mapping class groups of pointed surfaces, as well as the existence of groups of critical regularity.

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Date/Time : 10 Nov 2021 16:00
Venue : via Zoom
Speaker : Manat Mustafa, Nazarbayev University

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract: The talk employs the punctuality paradigm in the studies of numberings. We consider the punctual numberings, i.e. uniform computations for families of primitive recursive functions. The punctual reducibility between numberings is induced by primitive recursive functions. This approach gives rise to upper semilattices of degrees, which are called Rogers pr-semilattices. The main focus of the talk will be the structural properties of Rogers pr-semilattices. We will show several examples, which highlight further contrasts between the punctual framework and the classical theory of computable numberings.

All results are obtained in joint work with Nikolay Bazhenov and Sergei Ospichev.

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Date/Time : 03 Nov 2021 16:00
Venue : via Zoom
Speaker : Zhong Guolei, National University of Singapore

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract:  We consider a projective klt pair (X,D) of arbitrary dimension with the anti-log canonical divisor -(K+D) being strictly nef. In this talk, I will first show that such X is rationally connected. In particular, when X is a threefold, we show that -(K+D) is indeed ample, which gives a positive answer to the singular version of Campana-Peternell’s conjecture (for the threefold case). Finally, we extend our first result to the (relative) fibration case and study the geometric structure of this fibration. This is a joint work with Jie Liu, Wenhao Ou, Juanyong Wang and Xiaokui Yang.

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