Date/Time : 26 Oct 2022 14:00
Venue : via Zoom
Speaker : Yuval Wigderson, Tel Aviv University

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https://nus-sg.zoom.us/j/89613913454?pwd=Q3N5VWdFUUZGRmEzRFhOU1p1QmpCdz09

Meeting ID: 896 1391 3454
Passcode: 23571113

Abstract: The Ramsey number r(G) of a graph G is the minimum N so that every red/blue edge-coloring of K_N contains a monochromatic copy of G. Conlon, Fox, and Sudakov conjectured that if we delete a single vertex from G, then the Ramsey number can decrease by at most a constant factor. Though very natural (and true in a variety of special cases), this conjecture turns out to be false in general. In this talk, I’ll explain how one disproves this conjecture, as well as the connections this problem has to a number of other questions in Ramsey theory.

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Date/Time : 25 Oct 2022 15:00
Venue : via Zoom
Speaker : Ting-Kam Leonard Wong, University of Toronto

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https://nus-sg.zoom.us/j/85146635817?pwd=NDFXTW5rOWNlZDJKZTk5QThKVmE4QT09

Meeting ID: 851 4663 5817
Passcode: 543073

Abstract: Information geometry is the geometric study of statistical manifolds which are spaces of probability or nonnegative measures. It originated from statistical inference and has been applied in diverse fields including statistical physics and machine learning. This short course is an introduction to information geometry and some of its recent developments. Mathematical prerequisites such as differential geometry and convex analysis will be introduced as needed. In the first part, we will introduce statistical manifolds, divergence functionals and the induced dualistic geometry. In the second part, we will discuss some relations between information geometry and optimal transport.

Further update : Information and updates about this course (including current and future Zoom links) will also be available on the webpage https://ujangangopadhyay.github.io/information_geometry.html

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Date/Time : 19 Oct 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Abdul Basit,

Abstract: The shatter function, a combinatorial function associated to a family of sets, is an important measure of its complexity. For example, it is related to the popular notions of VC dimension and VC density. We show that the shatter function of a semilinear family (i.e., a family definable in (R, + , <)) is asymptotic to a polynomial. This implies, in particular, that any semilinear family has integer VC density, which confirms a conjecture by Artem Chernikov.

This is joint work with Tran Chieu Minh

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Date/Time : 19 Oct 2022 14:00
Venue : S17 #04-04 (SR3)
Speaker : Yang Tianchi, National University of Singapore

Abstract: The study of the 4-cycle has an important enlightening effect on the development of Turan type problems, especially the degenerate cases. In this talk, we focus on two conjectures about 4-cycles: a conjecture of Erdos on the upper bound of the Turan number ex(n,C_4), and a conjecture of Erdos-Simonovits on the supersaturation problem of 4-cycles.

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Date/Time : 18 Oct 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

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https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

Abstract: This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling

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Date/Time : 18 Oct 2022 15:30
Venue : S17 #06-11 (SR6)
Speaker : Richard Canary, University of Michigan

Abstract: The Hitchin component of representations of a closed surface group into SL(d,R) is one of the primary examples of a Higher Teichmuller space (a component of the space of representations of a surface group into a Lie group which consists entirely of discrete, faithful representations). We discuss a theory of cusped Hitchin representations of geometrically finite Fuchsian groups into SL(d,R). These cusped Hitchin representations arise naturally by “pinching” Hitchin representations. We show that cusped Hitchin representations are cusped Borel Anosov and establish counting and equidistribution results.

The long term goal of this project is to develop a metric theory of the augmented Hitchin component which generalizes the fact that augmented Teichmuller space is the metric completion of Teichmuller space with the Weil-Petersson metric. (This is joint work with Tengren Zhang and Andy Zimmer, and with Harry Bray, Nyima Kao and Giuseppe Martone).

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Date/Time : 14 Oct 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Le Nhat Hoang, National University of Singapore

Abstract: The local Gan-Gross-Prasad (GGP) conjecture studies a family of restriction problems for classical groups and proposes precised answers to these problems using the local Langlands correspondence. It also has a twisted variant in the Fourier-Jacobi case. In this talk, I will present my proof for the tempered part of the local twisted GGP conjecture for (GL(V),U(V)), which is obtained by adapting Waldspurger and Plessis’s method to construct a local trace formula and comparing its spectral and geometric sides. Moreover, I will talk about how the geometric multiplicity formula looks like in the remaining case, when we consider an another quadratic extension K/F and have the local twisted GGP conjecture for (U(V)(K),U(V)).

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Date/Time : 13 Oct 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

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https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

Abstract: This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling

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Date/Time : 13 Oct 2022 15:30
Venue : S17 #05-11 (SR5)
Speaker : Chen Junkai Alfred, National Taiwan University

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

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: In minimal model program, divisorial contractions, flip and flops are considered to be the elementary maps. Divisorial contractions to points are well-understood and can be realized as weighted under certain embeddings. In this talk, we will present the recent developments toward the classification of divisorial contractions to curves. We will provide an outline of our proposed program and demonstrate some new examples. If time permits, we will talk about their factorizations as well. The talk is based on the joint work in progress with Hsin-Ku Chen and Jheng-Jie Chen.

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