Date/Time : 30 Apr 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Han Fei, National University of Singapore

Spin geometry is one of major areas of differential geometry, centered on manifolds admitting spin and spin^c structures. String geometry may be viewed as its natural refinement: by requiring higher obstructions to vanish, new invariants, most notably modular invariants, emerge, motivated by infinite-dimensional refinements of the Atiyah–Singer index theory.

In this talk, I will present some of our recent work on the theory and applications of spin and string geometry. A closely related object is the loop space of a manifold, which provides a typical and natural example of infinite-dimensional geometric object. I will also discuss our development of geometric and cohomological structures on loop spaces and their applications to string dualities.

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Date/Time : 06 Apr 2026 09:00
Venue : via Zoom
Speaker : Dilip Raghavan, National University of Singapore

Zoom: https://nus-sg.zoom.us/j/84790467054

Passcode: 547743 

There is an intimate relationship between Ramsey type theorems and ultrafilters on the natural numbers. On the one hand, ultrafilters can be used to prove Ramsey type theorems. On the other hand, Ramsey theoretic facts lead to new classes of ultrafilters. I will survey some aspects of this interplay, and present two recent consistency results involving ultrafilters with the Ramsey theoretic flavor.

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Date/Time : 08 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Yang Lei, National University of Singapore

A major challenge in homogeneous dynamics is to quantify fundamental theorems in this area, including Margulis’s non-divergence theorem and Ratner’s equidistribution theorem. Thanks to the deep connection between homogeneous dynamics and number theory, results in this direction have important consequences in number theory. In recent years, new ideas and tools have been introduced to this area, which leads to exciting developments in the study of quantitative behavior of unipotent orbits and their variants. I will give a brief summary of recent developments and explain my works in this direction.

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Date/Time : 25 Aug 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Li Qianxiao, National University of Singapore

In this talk we discuss connections between deep learning and the study of dynamical processes. We begin by examining how dynamics and control provide a natural framework for understanding how complexity emerges through composition—a hallmark of modern deep learning architectures, including both feed forward and recurrent models. In the reverse direction, we highlight how deep learning techniques can advance the modelling and simulation of dynamical processes in science and engineering.

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Date/Time : 18 Feb 2025 15:00
Venue : S17 #04-06 (SR1)
Speaker : Bao Huanchen, National University of Singapore

Let G be a connected reductive group over an algebraically closed field, e.g. the general linear group. Such groups are classified via root data and can be parameterised via Chevalley group schemes over integers. Let K be the fixed point subgroup of an involution of G. For example, when G is the general linear group, then K could be the group of orthogonal matrices.

In this talk, I shall discuss the construction of integral models of the symmetric pair (G, K) and the symmetric space G/K. I will also mention various applications of our new constructions, e.g., Frobenius splittings, canonical bases, spherical embeddings, etc.. This is based on several joint works with Jinfeng Song (NUS).

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Date/Time : 03 Dec 2024 14:00
Venue : S17 #04-06 (SR1)
Speaker : An Xinliang, National University of Singapore

In this talk, I will give an overview of my recent research. We prove a series of mathematical theorems that rigorously describe the entire process of black hole formation. With scale-critical short-pulse initial data, we solve Einstein’s equations and show that: “in the course of gravitational collapse, a whole trapped region and its boundary (apparent horizon) emerge from a singular spacetime point. The apparent horizon then expands as the spacetime evolves. Passing through a transition period, the spacetime later enters a regime, close to a slowly-rotating Kerr black hole solution. Nonlinear Kerr stability then comes into play and the spacetime metric eventually settles into the Kerr solution with small angular momentum.”

Meanwhile, I also introduce a new framework for proving the high co-dimensional nonlinear instability of naked-singularities. Specifically, I study the censorship of Christodoulou’s naked singularity and show that even a tiny anisotropic perturbation can trigger the formation of an anisotropic apparent horizon, thereby covering and censoring the naked singularity.

If time permits, sharp low-regularity illposedness and wellposedness results for nonlinear wave systems will also be presented.

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Date/Time : 14 Aug 2024 14:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Tengren, National University of Singapore

Anosov subgroups are a special class of discrete subgroups of a non-compact semisimple Lie group. This notion was first discovered by Labourie, who used it to prove the discreteness of Hitchin representations. In this talk, I will discuss my recent contributions to our understanding of Anosov subgroups and their various generalizations, as well as some applications to studying character varieties.

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Date/Time : 11 Jun 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Subhroshekhar Ghosh, National University of Singapore

The goal of this talk is to give an overview of my research over the past few years. Much of this talk is going to be devoted to the theory and applications of negative association. Two random variables are said to be negatively associated if an increase in one leads to a decrease in the other, in an appropriate stochastic sense. In statistical physics terms, it is a mathematical model that captures the phenomenon of repulsion between charged particles such as electrons. On the theoretical side, we will discuss the phenomena of rigidity and hyperuniformity, and their consequences for the behaviour of large scale particle systems. We will also discuss applications of such strongly correlated stochastic models in machine learning, and how these applications in turn naturally lead to phenomena and questions of interest in theoretical probability. Time permitting, we will also explore other recent results that, strictly speaking, fall outside the ambit of negative associations; a key direction being that of learning under latent group actions.

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Date/Time : 17 Nov 2023 16:15
Venue : via Zoom
Speaker : Chen Ying, National University of Singapore

Join Zoom Meeting
https://nus-sg.zoom.us/j/83899499647?pwd=U2EvRVBPZXpxeXNmV3lsVi95Z2FTQT09

Meeting ID: 838 9949 9647
Passcode: math

In the digital era, complex data has emerged across various disciplines, characterized by high dimensions, nonlinear temporal and spatial dependencies, and irregular dynamic changes (non-stationarity). Understanding and effectively analyzing such complex temporal structures and achieving high-precision forecasting have become pressing challenges. Additionally, comprehending the stochastic behaviors of forecasting is paramount for executives and managers, aiding them in making resilient and robust decisions in real-life scenarios. In my presentation, I will introduce my research on advancing time series modeling and methodologies. These approaches leverage the power of data science, machine learning, and deep neural networks, all tailored to address the complexities of modern data. Some of the innovative techniques I will discuss include functional neural tangent kernel estimators, mixed-frequency spatio-temporal models, and deep switching state space models. Together, these methods offer insights and tools for tackling the challenges posed by high-dimensional, nonlinear, and nonstationary data in the contemporary landscape.

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