Date/Time : 28 Oct 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Gu Yejun, Institute of High Performance Computing, A*STAR

Abstract:  The mechanical properties of metallic materials are strongly dependent on their microstructural features (e.g. morphology and distribution of dislocations, grains, and other defects). Thus it necessitates a comprehensive understanding of the microstructure evolutions in materails during deformation. I will present some attempts of applying mathematical methods to address this problem. The presentation consists of two parts: one is the fast algorithms for solving partial differential equations, in order to precisely describe the microstructure evolutions; the other is the probabilistic description and statistical analysis, which are employed to quantify the relationship between the microstructures and mechanical properties.

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Date/Time : 27 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/81251294825?pwd=aVNqdEs4R0J0c3lMTnRDVmxOWGlZZz09

Meeting ID: 812 5129 4825
Passcode: 898472

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 : 27 Oct 2022 15:30
Venue : S17-05-11 (SR 5)
Speaker : Takashi Kishimoto, Saitama University

Abstract: We address the following questions: ”(1) How to construct a Mori fiber space (Mfs) X containing the affine space Ank as an open subset ?” and ”(2) In which Mfs as in (1), the translations on Ank can be extended to automorphisms on X, namely X can be an equivariant completion of the vector group Gna,k ?” As for (1), we will present a certain machinery to construct Mfs over P1k, which contains the affine space, with birationally rigid Fano varieties being general fibers. Note however that such completions X are never equivariant ones, more precisely, the unipotent radical of Aut0(X) is at most of dimension one. Actually, it turns out that there are few equivariant completions. Then we will focus on forms defined over any field of characteristic zero of quintic del Pezzo varieties. The main result lies in clarifying which ones among them can be equivariant completions and determining their automorphism groups. The talk is based on two joint works, one of which is with Adrien Dubouloz and Karol Palka, and the other of which is with Adrien Dubouloz and Pedro Montero.

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Date/Time : 26 Oct 2022 14:00
Venue : S17 #04-06 (SR1)
Speaker : Cai Zhenning, National University of Singapore

Abstract: The gas kinetic theory is usually employed to solve rarefied gas dynamics. The fundamental mathematical model for the gas kinetic theory is the Boltzmann equation, which describes the fluid states using the distribution function defined over the joint position-velocity space. Due to its high dimensionality and a complicated integral operator, straightforward discretization of the Boltzmann equation will lead to high computational cost. Therefore, we need either highly effective numerical schemes or reduced kinetic models to make simulations feasible. In this talk, I will introduce our improvement on the classical Fourier method to preserve all physical properties including the conservation laws and the entropy dissipation. Also, we will discuss methods for kinetic model reductions including the simplification of the collision operator and the moment methods. Our simplified collision operator includes a parameter that can be adjusted to balance the computational cost and the accuracy, and this parameter can be tuned adaptively during the simulation of the dynamics. As for the moment methods, we study the linear Boltzmann equation and introduce the regularized 13-moment equations with stable boundary conditions, which can be applied to solve slow-moving gases with moderate rarefaction effects.

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Date/Time : 26 Oct 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Sun Mengzhou, National University of Singapore

Abstract: Paris and Kirby showed that a countable model satisfies B Sigma_{n+2} if and only if it has an (n+2)-elementary proper end extension. Later Kaufman asked whether we can always end extend countable models of B Sigma_{n+2} to some model of B Sigma_{n+1}. We briefly discuss what we have now related to this question and what is the difficulty here.

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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

Join Zoom Meeting
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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