Date/Time : 04 Nov 2022 15:00
Venue : via Zoom
Speaker : Ting-Kam Leonard Wong, University of Toronto

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https://nus-sg.zoom.us/j/83007497441?pwd=cmJmSEpuTWRUVHhJc3JJZ2h3dFNZdz09

Meeting ID: 830 0749 7441
Passcode: 087943

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 : 03 Nov 2022 10:00
Venue : S17 #05-11 (SR5)
Speaker : Michael Choi, National University of Singapore

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

Meeting ID: 977 560 6531
Passcode: 123321

This talk centers around a technique that we call landscape modification. The core idea is that the Hamiltonian function is suitably modified in a way for rapid mixing while maintaining proximity with the original target distribution. We first present model-independent results that give rapid mixing and tunneling in the low-temperature regime. Building upon these results, we investigate the effect of landscape modification on some prototypical statistical physics models including the Ising model on various deterministic and random graphs as well as Derrida’s random energy model. This talk highlights a novel use of the geometry and structure of the landscape, in particular the global minimum value or its estimate, to the design of accelerated samplers or optimizers.

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Date/Time : 02 Nov 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Wu Guohua, Nanyang Technological University

Abstract: Many constructions in rings involve applications of various axioms, which guarantee the existence of wanted objects. In this talk, I will present examples of such constructions, and show how these axioms are applied and really needed.

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Date/Time : 02 Nov 2022 16:30
Venue : via Zoom
Speaker : Ting-Kam Leonard Wong, University of Toronto

Join Zoom Meeting
https://nus-sg.zoom.us/j/83007497441?pwd=cmJmSEpuTWRUVHhJc3JJZ2h3dFNZdz09

Meeting ID: 830 0749 7441
Passcode: 087943

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 : 02 Nov 2022 14:00
Venue : via Zoom
Speaker : Zilin Jiang, Arizona State University

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https://nus-sg.zoom.us/j/81639604748?pwd=UXZXTnhwZHRmQTFrZEs0VEtWYjRVUT09

Meeting ID: 816 3960 4748
Passcode: 23571113

A set of unit vectors in a Euclidean space is called a spherical two-distance set if the pairwise inner products of these vectors assume only two values α and β. It is known that the maximum size of a spherical two-distance grows quadratically as the dimension of the Euclidean space grows. However when the values α and β are held fixed, a very intricate behavior of the maximum size emerges. Building on our recent resolution in the equiangular case, that is β = -α, we make a plausible conjecture which connects this behavior with spectral theory of signed graphs in the regime β < 0 ≤ α, and we confirm this conjecture when α + 2β < 0 or (1 – α)/(β-α) < 2.0198. Joint work with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao.

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Date/Time : 01 Nov 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 : 31 Oct 2022 15:00
Venue : via Zoom
Speaker : Ting-Kam Leonard Wong, University of Toronto

Join Zoom Meeting
https://nus-sg.zoom.us/j/83007497441?pwd=cmJmSEpuTWRUVHhJc3JJZ2h3dFNZdz09

Meeting ID: 830 0749 7441
Passcode: 087943

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 : 28 Oct 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Koh Shiwei Isaac, National University of Singapore

Abstract:   The concept of cellularity, defined by Graham and Lehrer, has proven extremely useful in the fundamental problem of classifying the irreducible representations of a given finite-dimensional algebra. By definition, a cellular algebra comes with a finite chain of ideals whose subquotients, called cells, are isomorphic to a matrix ring over a Noetherian domain k with a twisted multiplication. Examples of cellular algebras include many finite-dimensional Hecke algebras and Temperely Lieb algebras.

Koenig and Xi have generalised this concept to algebras over a Noetherian domain k of not necessarily finite dimension, by introducing the notion of an affine cellular algebra. We keep the same idea of having a filtration by a finite chain of ideals, but the ideals are now allowed to be of infinite dimension. A cell is now allowed to be isomorphic to a matrix ring (of finite rank) over a quotient of a polynomial ring over k, with a twisted multiplication. An example of an affine cellular algebra is the extended affine Hecke algebra of type A.

In this talk, we will introduce the aforementioned concepts and discuss some possible work to be done in the future

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Date/Time : 28 Oct 2022 15:00
Venue : S17 #04-06 (SR1)
Speaker : Ting-Kam Leonard Wong, University of Toronto

Abstract: Macroscopic properties of equity markets present interesting problems in portfolio management and stochastic modeling. If we think of stocks as stars in a galaxy, a macroscopic property would be how the galaxy spirals. We begin by presenting some empirical observations about the capital distribution curve, market diversity and intrinsic volatility, and discuss why these macroscopic properties are difficult to capture probabilistically. One way to exploit these properties is to use functionally generated portfolios in stochastic portfolio theory.

Financially, they capture market volatility by systematic rebalancing. Mathematically, they are generalized gradient fields of exponentially concave functions, i.e., functions whose exponentials are concave. We show that these portfolios solve an optimal transport problem whose cost function is related to the Dirichlet distribution. Finally, motivated by online portfolio selection, we consider construction of prior (probability) distributions on spaces of concave functions and present some interesting limit theorems.

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