Date/Time : 11 Feb 2022 09:00
Venue : via Zoom
Speaker : Geordie Williamson, University of Sydney

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https://nus-sg.zoom.us/j/86817881669?pwd=T1dVRWRQVjJRTjZNbDE0QUpsa3E0QT09

Meeting ID: 868 1788 1669
Passcode: 432904

Abstract: The combinatorial invariance conjecture is a fascinating conjecture in Representation Theory. Basically it says that certain important polynomials (“Kazhdan-Lusztig polynomials”) are determined in a very non-trivial way by a directed graph. About 2 years ago, I began working on this problem with DeepMind, an AI lab based in London. (DeepMind is famous for their AlphaGo program which was the first program to defeat the best human Go players.) Our goal was to try to discover whether modern Machine Learning techniques are helpful in approaching problems in Pure Mathematics. I will outline how the Machine Learning models work, how successful they were and (by far the trickiest part) how we went about extracting new mathematics from these models. The result is a formula which sheds light on the combinatorial invariance conjecture. This is joint work with the DeepMind team: Charles Blundell, Lars Buesing, Alex Davies and Petar Veličković.

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Date/Time : 14 Jan 2022 09:00
Venue : via Zoom
Speaker : Alexander Kiselev, Duke University

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https://nus-sg.zoom.us/j/81290641127?pwd=eUowVGZYN3REWndWVHRKK2piQ1pUUT09

Meeting ID: 812 9064 1127
Passcode: 612753

Abstract: The Euler equation describing motion of ideal fluid goes back to 1755. The analysis of the equation is challenging since it is nonlinear and nonlocal. Its solutions are often unstable and spontaneously generate small scales. The fundamental question of global regularity vs finite time singularity formation remains open for the Euler equation in three spatial dimensions. In this lecture, I will review the history of this question and its potential connection with the arguably greatest unsolved problem of classical physics, turbulence. Results on small scale and singularity formation in two dimensions and for a number of related models will also be presented.

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Date/Time : 19 Nov 2021 10:00
Venue : via Zoom
Speaker : Po-Shen Loh, Carnegie Mellon University

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https://nus-sg.zoom.us/j/84707855085?pwd=dVVUa0puWjlMT3NvN3hRWUV4N016QT09

Meeting ID: 847 0785 5085
Passcode: 687520

Abstract: We introduce a categorically new approach for pandemic control, which transforms selfish human behavior from a liability to an asset. Amidst a high-lethality pandemic, it could leverage individual survival instincts across the entire population, naturally incentivizing system-wide behavior that mitigates pandemic spread.

One of the central tools in pandemic control is contact tracing, which informs people after they have already been exposed to an infected person, and asks all of those people to remove themselves from society, to protect everyone else from themselves.

Informed by Game Theory, we reverse the incentives with a new infrastructure based on mobile devices which helps individuals directly reduce their own chance of infection (protecting themselves from everyone else). The core concept is to inform every participating user of their network-theoretic distance to each newly reported case, against the network of frequent close physical contacts.

This is fundamentally different from contact tracing, because it does not seek to control individuals after they are exposed, but rather empowers not-yet-exposed individuals to take selfish action to avoid exposure in the first place. It is analogous to arming every individual with their personal pandemic network radar. This opportunity was only recently unlocked by the mass proliferation of connected mobile devices, and opens a new category of intervention at the intersection of Game Theory, Technology, and Health.

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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 : 08 Oct 2021 16:00
Venue : via Zoom
Speaker : Siddhartha Mishra, ETH Zürich

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https://nus-sg.zoom.us/j/88995092115?pwd=UmxidFJqTzZyQ2JRLyt5SGNnaHhnUT09

Meeting ID: 889 9509 2115
Passcode: 309203

Abstract:  We will describe PINNs and illustrate several examples for using PINNs for solving PDEs. Our aim would be to elucidate mechanisms that underpin the success of PINNs in approximating classical solutions to PDEs by deriving rigorous bounds on the resulting error. Examples of a variety of linear and nonlinear PDEs will be provided including PDEs in high dimensions and inverse problems for PDEs.

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Date/Time : 10 Sep 2021 09:00
Venue : via Zoom
Speaker : YanYan Li, Rutgers University

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https://nus-sg.zoom.us/j/84328425455?pwd=MXpPQWYxZ0hvQ2UzOW1sbUREUG5XZz09

Meeting ID: 843 2842 5455
Passcode: 204458

Abstract:  We will first recall the Nirenberg problem and the Yamabe problem, together with some previous results on the existence and compactness of solutions to the problems. We will then discuss the σ_k-Nirenberg problem and the σ_k-Yamabe problem, the study of which requires solving fully nonlinear elliptic equations involving Schouten tensor on Riemannian manifolds. Some recent works and open problems will be discussed.

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Date/Time : 13 Aug 2021 09:00
Venue : via Zoom
Speaker : Toshiyuki Kobayashi, University of Tokyo

Join Zoom Meeting https://nus-sg.zoom.us/j/83343417958?pwd=S2lJU29jbldIUzFRaWVBYXhHWmhEdz09 Meeting ID: 833 4341 7958 Passcode: 149725 The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as pseudo-Riemannian geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprisingly little is known about global properties of the geometry even if we impose a locally homogeneous structure. In this colloquium, I plan to discuss two topics. Global geometry: Existence problem of compact manifolds modelled locally on homogeneous spaces, and their deformation theory. Spectral analysis: Construction of periodic eigenfunctions for the (indefinite) Laplacian, and stability question of eigenvalues under deformation of geometric structure by using representation theory.

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Date/Time : 16 Jul 2021 16:00
Venue : via Zoom
Speaker : Anna Wienhard, Heidelberg University

Join Zoom Meeting https://nus-sg.zoom.us/j/81534494468?pwd=dHJqL1NOSjBVR09ZcG9iRk5EN3daZz09 Meeting ID: 815 3449 4468 Passcode: 717949 Semi-simple Lie groups play a role in many areas of mathematics. They are closely related to and naturally arise as isometry groups of symmetric spaces. A key tool in the investigation of discrete subgroups of semisimple Lie groups is the their action on this symmetric space, and on its compactifications. There is a basic dichotomy between rank one Lie groups, when the symmetric space is of strict negative curvature, and Lie groups of higher rank, when the symmetric space is only non-positively curved. For many years, starting with Margulis celebrated superrigidity theorem, rigidity has been the overarching paradigm in higher rank. In recent years we have seen a shift of this paradigm towards a combination of flexibility and rigidity which opened up new research directions. In this talk I will describe some of the key properties of symmetric spaces, describe some of the recent developments, and discuss how the intricate geometry of symmetric spaces can also be leveraged in the context of graph embeddings and in representation learning.

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Date/Time : 04 Jun 2021 16:00
Venue : via Zoom
Speaker : Yves Benoist, CNRS and Université Paris-Saclay

Join Zoom Meeting https://nus-sg.zoom.us/j/85852787585?pwd=MDZWUjV5SlNoaFJDM0trWnRJMWdIdz09 Meeting ID: 858 5278 7585 Passcode: 236000 In this expository talk, I will give three examples where p-adic Lie groups are crucial tools to understand dense subgroups in compact real Lie groups. The first one is the Tits alternative. The second one is the Prasad-Rapinchuk regularity theorem. The third one is the Sarnak spectral gap conjecture for random walk on subgroups with algebraic coefficients.

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