Date/Time : 30 Oct 2024 16:30
Venue : S17 #05-11 (SR5)
Speaker : Wang Yangshuai, National University of Singapore

The success of molecular simulations hinges on the accuracy and efficiency of force fields. Recently, machine-learned interatomic potentials (MLIPs) have revolutionized the field by bridging the gap between high-accuracy ab initio models and classical force fields. MLIPs have quickly become an essential tool in computational atomic simulations, leading to numerous breakthroughs across various scientific domains. This talk will provide an overview of the latest advancements in MLIPs, with a focus on their applications in materials science. I will start by discussing the Atomic Cluster Expansion (ACE) method, a linear model known for its strong predictive performance in small systems. To address the limitations of linear models, I will introduce MACE, an advanced potential based on ACE and enhanced by Message Passing Neural Networks (MPNN), tailored for complex systems with superior generalization and robustness. The focus will then shift to MACE-MP-0, a pre-trained foundation model built on MACE, highlighting its predictive accuracy and the advantages of fine-tuning across diverse materials applications. I will conclude by discussing future MLIP extensions that could further enhance molecular modeling and simulation in materials science and chemistry.

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Date/Time : 29 Oct 2024 14:00
Venue : S17 #04-06 (SR1)
Speaker : Nathan Ross, University of Melbourne

Neural networks are random parametric functions, where the parameters are chosen according to stochastic gradient descent, based on the sample of training data. It has long been known that at initialisation, a neural network with “large” width and “fixed” depth can be well-approximated by a limiting Gaussian random field. But what quantities are well-approximated, and how wide does a neural network need to be for the approximation to be good? There has been a flurry of recent work trying to answer these and related questions, by deriving rates of convergence between the distribution of the neural network and the limiting Gaussian random field in various probability metrics, including some at the process level.

The aim of these lectures is to explain a general approach that can be applied to derive such rates at the process level, which uses Stein’s method, functional smoothing inequalities, and classical Gaussian process concepts such as Karhunen-Loeve expansion and Cameron-Martin/Reproducing Kernel Hilbert Space. The target audience is PhD students planning to do research in probability or statistics. In particular, the definitions and relevant properties of the concepts above will be covered in detail. Open questions and future directions will also be discussed.

The approach is based on joint work with (A.D. Barbour, K. Balasubramanian, L. Goldstein, A. Salim, and G. Zheng).

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Date/Time : 28 Oct 2024 10:00
Venue : via Zoom
Speaker : Qijun Tan, Google DeepMind

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https://nus-sg.zoom.us/j/82351206827?pwd=L6NM7PEa9BfIlfHqeare8XkoY0IKnr.1

Meeting ID: 823 5120 6827
Passcode: 077539

In this talk, we will explain how Large Language Models (LLM) obtain their capability in solving difficult math problems. In particular, We will go over key techniques that unearth the reasoning potential of LLMs. We will also illustrate key challenges in LLM reasoning.

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Date/Time : 28 Oct 2024 16:00
Venue : S17 #04-06 (SR1)
Speaker : Nathan Ross, University of Melbourne

Neural networks are random parametric functions, where the parameters are chosen according to stochastic gradient descent, based on the sample of training data. It has long been known that at initialisation, a neural network with “large” width and “fixed” depth can be well-approximated by a limiting Gaussian random field. But what quantities are well-approximated, and how wide does a neural network need to be for the approximation to be good? There has been a flurry of recent work trying to answer these and related questions, by deriving rates of convergence between the distribution of the neural network and the limiting Gaussian random field in various probability metrics, including some at the process level.

The aim of these lectures is to explain a general approach that can be applied to derive such rates at the process level, which uses Stein’s method, functional smoothing inequalities, and classical Gaussian process concepts such as Karhunen-Loeve expansion and Cameron-Martin/Reproducing Kernel Hilbert Space. The target audience is PhD students planning to do research in probability or statistics. In particular, the definitions and relevant properties of the concepts above will be covered in detail. Open questions and future directions will also be discussed.

The approach is based on joint work with (A.D. Barbour, K. Balasubramanian, L. Goldstein, A. Salim, and G. Zheng).

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Date/Time : 24 Oct 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Jimmy He, Ohio State University

The study of quantum groups and integrable systems have long been connected through the Yang-Baxter equation. Recently, these ideas have been introduced in probability to study integrable stochastic models. I will discuss a similar story for models with boundary, which are connected to quantum symmetric spaces through the reflection equation, as well as some applications to probability. The focus will be on illustrating the connections through illustrative examples and applications for a specific model called the six vertex model.

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Date/Time : 24 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Michael Pevzner, Université de Reims-Champagne-Ardenne

Inspired by classical concepts of generating functions for orthogonal polynomials, this talk will explore “generating operators” for a family of differential operators acting between two manifolds.

We will present a formula for these generating operators associated with Rankin–Cohen brackets and discuss their connection to infinite-dimensional representation theory. Joint work with T. Kobayashi.

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Date/Time : 23 Oct 2024 17:00
Venue : S17 #04-04 (SR3)
Speaker : Ellen Hammatt, Victoria University of Wellington

In this talk we investigate what happens when we take concepts from computable structure theory and forbid the use of unbounded search. In other words, we discuss the primitive recursive content of structure theory. The central definition is that of punctual structures, introduced by Kalimullin, Melnikov and Ng in 2017. We investigate various concepts from computable structure theory in the primitive recursive case. A common theme is that new techniques are required in the primitive recursive case. In particular we will focus on topics such as finite punctual dimension, punctual 1-decidability and the punctual degrees. Where the punctual degrees is a degree structure within punctual presentations of a fixed structure which is induced by primitive recursive isomorphisms. I will present various results from my PhD thesis as well as pose some open questions in the area.

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Date/Time : 23 Oct 2024 15:00
Venue : S17 #05-11 (SR5)
Speaker : Zhou Tao, National University of Singapore

While finite-time blowup solutions have been studied in depth for the Keller-Segel equation, a fundamental model describing chemotaxis, the existence of finite-time blowup solutions to chemotaxis-fluid models remains largely unexplored. To fill this gap in the literature, we use a quantitative method to directly construct a smooth finite-time blowup solution for the Keller-Segel-Navier-Stokes system with buoyancy in 3D. The heart of the proof is to establish the non-radial finite-codimensional stability of an explicit self-similar blowup solution to 3D Keller-Segel equation with the abstract semigroup tool from [Merle-Raphaël-Rodnianski-Szeftel, 2022], which partially generalizes the radial stability result [Glogić-Schörkhuber, 2024] to the non-radial setting. Additionally, we introduce a robust localization argument to find blowup solutions with non-negative density and finite mass. This is talk is based on the joint work with Zexing Li.

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Date/Time : 23 Oct 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Jimmy He, Ohio State University

The study of quantum groups and integrable systems have long been connected through the Yang-Baxter equation. Recently, these ideas have been introduced in probability to study integrable stochastic models. I will discuss a similar story for models with boundary, which are connected to quantum symmetric spaces through the reflection equation, as well as some applications to probability. The focus will be on illustrating the connections through illustrative examples and applications for a specific model called the six vertex model.

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