Date/Time : 13 Jan 2025 11:00
Venue : S17 #05-11 (SR5)
Speaker : Stephen Wright, University of Wisconsin-Madison

Complexity analysis in optimization seeks upper bounds on the amount of work required to find approximate solutions of optimization problems in a given class with a given algorithm. There is also study of lower bounds, usually in the form of a worst-case example from a given problem class for a given algorithm class. The relationship between theoretical complexity bounds and practical performance of algorithms on “typical” problems varies widely across problem and algorithm classes, and relative interest among researchers between the theoretical and practical aspects of algorithm design and analysis has waxed and waned over the years. This talk surveys complexity analysis and its relationship to practice in optimization, with an emphasis on linear programming and convex and nonconvex nonlinear optimization, providing historical (and cultural) perspectives on research in these areas.

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Date/Time : 10 Jan 2025 14:00
Venue : S17 #04-06 (SR1)
Speaker : Govind Menon, Brown University

We study the training dynamics of the Deep Linear Network (DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results by several authors are unified into a thermodynamic framework for deep learning. The analysis begins with a characterization of the invariant manifolds and Riemannian geometry in the DLN. This is followed by exact formulas for a Boltzmann entropy, as well as stochastic gradient descent of free energy using a Riemannian Langevin Equation. Several links between the DLN and other areas of mathematics are discussed, along with some open questions.

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Date/Time : 10 Jan 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Yufeng Wu, University of Connecticut

Suppose a person collected his/her own genome and wants to learn something about his/her ancestry. Further suppose this person’s genome originates from multiple ancestral populations, a phenomenon called population admixture in genetics. The genome of an individual from an admixed population consists of segments originated from different ancestral populations. Most existing ancestry inference approaches can provide an estimate of the percentage (called admixture proportion) of the genome originated from a specific ancestral population. Now what if someone wants to estimate admixture proportions of recent ancestors from his/her own genome? For example, let us say an individual has 50% European and 50% Asian ancestry. This individual’s parents can be also 50-50 European/Asian ancestry, but it is also possible one is 100% European and the other is 100% Asian. More generally, can one learn more about the ancestry of recent ancestors from his/her own genome?

In this talk, I will present research results on ancestry inference for estimating admixture proportions of recent ancestors from an extant genome. I will first briefly describe PedMix, one of the first methods for such inference. A major downside of PedMix is that it can only estimate admixture proportions for parents and grandparents, and cannot scale for more distantly related ancestors. I will then focus on PedMix2, a general approach that can estimate admixture proportions of all recent ancestors of this individual. This approach was published recently in PNAS (2024). To the best of our knowledge, there is no other method that can practically infer ancestors beyond grandparents from an extant individual’s genome. I will present results on both simulated and real data show that PedMix2 performs well in ancestry inference.

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Date/Time : 09 Jan 2025 16:00
Venue : S17 #04-06 (SR1)
Speaker : Govind Menon, Brown University

We study the training dynamics of the Deep Linear Network (DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results by several authors are unified into a thermodynamic framework for deep learning. The analysis begins with a characterization of the invariant manifolds and Riemannian geometry in the DLN. This is followed by exact formulas for a Boltzmann entropy, as well as stochastic gradient descent of free energy using a Riemannian Langevin Equation. Several links between the DLN and other areas of mathematics are discussed, along with some open questions.

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Date/Time : 09 Jan 2025 15:00
Venue : S17 #04-05 (SR2)
Speaker : Gianluca Ceruti, University of Innsbruck

The curse of dimensionality presents a formidable challenge in many fields, from molecular quantum dynamics to computer vision and kinetic equations. This phenomenon, characterized by an exponential growth in parameters with increasing system complexity, demands innovative approaches to enable efficient computation and data handling. In this talk, we delve into the promise of Dynamical Low-Rank Approximation (DLRA) as a model order reduction technique for addressing large-scale, time-dependent problems. By dynamically projecting the dynamics of high-dimensional systems onto a manifold of reduced complexity, DLRA reduces computational costs while preserving essential structural properties. Key to this approach are advanced tensor decompositions, such as the tensor train and hierarchical Tucker formats, which provide a foundation for efficient representation and computation. We will highlight recent advances, including the Basis-Update and Galerkin (BUG) integrator and its extensions, which enhance DLRA’s capabilities for preserving system dynamics and reducing memory requirements. Applications will illustrate DLRA’s versatility, from solving time-dependent partial differential equations to enhancing machine learning inference efficiency and reducing training costs in computer vision.

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Date/Time : 09 Jan 2025 09:15
Venue : S17 Level 3, IMS Executive Seminar Room
Speaker : Various,

Organizing Committee

Co-chairs

• Jun Le Goh (National University of Singapore)

• Yue Yang (National University of Singapore)

To honor Professor Chi Tat Chong on the occasion of his retirement after an extraordinary 50 years of service at the National University of Singapore (NUS), a conference will be held on 9–10 January 2025 at the Institute for Mathematical Sciences (IMS), NUS.

Professor Chong has made profound contributions to the fields of recursion theory, reverse mathematics, and mathematical logic. This conference will highlight his impactful work in computability, definability, and provability, areas where his scholarly influence has been deeply felt.

Beyond his academic achievements, Professor Chong has played a pivotal role in nurturing the mathematical community in Singapore, China, and across Asia. Notably, in 2000, he collaborated with colleagues at NUS to establish the Institute for Mathematical Sciences. In addition, since the Reform and Opening-up in China, he has mentored and supported a new generation of logicians, leaving a lasting legacy in the region.

The two-day conference is jointly organized by the Department of Mathematics, the Faculty of Science, and the Institute for Mathematical Sciences. It will feature a diverse program of talks by distinguished scientists from around the world. The event will bring together Professor Chong’s colleagues and friends, many of whom have cherished his friendship and mentorship over the past five decades.

Activities

Venue

IMS Executive Seminar Room

Block S17, Level 3
10 Lower Kent Ridge Road
Singapore 119076

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Date/Time : 09 Jan 2025 14:00
Venue : S17 #04-06 (SR1)
Speaker : Jian Ding, Peking University

I will describe various percolation models in statistical physics, with emphasis on phase transition, critical phenomenon as well as disorder effects. In particular, I will start my talk with Bernoulli percolation, and then present a few important examples of correlated percolation models. While I try to be a “messenger” communicating progress accomplished in the community as a whole, the talk is inevitably biased by my personal interests (for instance, I will spend some time surveying recent progress on the random field Ising model and Gaussian free field related percolation models).

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Date/Time : 08 Jan 2025 15:30
Venue : IMS executive seminar room (S17 Level 3)
Speaker : Jeremie Szeftel, Sorbonne Universite

I will introduce the celebrated black hole stability conjecture according to which the Kerr family of metrics are stable as solutions to the Einstein vacuum equations of general relativity. I will then discuss the history of this problem, including a recent work on the resolution of the black hole stability conjecture for small angular momentum.

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Date/Time : 08 Jan 2025 16:30
Venue : S17 #04-04 (SR3)
Speaker : Govind Menon, Brown University

We study the training dynamics of the Deep Linear Network (DLN) from the perspective of the geometric

theory of dynamical systems. Rigorous results by several authors are unified into a thermodynamic framework for deep learning. The analysis begins with a characterization of the invariant manifolds and Riemannian geometry in the DLN. This is followed by exact formulas for a Boltzmann entropy, as well as stochastic gradient descent of free energy using a Riemannian Langevin Equation. Several links between the DLN and other areas of mathematics are discussed, along with some open questions.

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