Date/Time : 03 Mar 2025 16:00
Venue : S16 #03-06
Speaker : Li Zhuoyuan, Peking University

Data assimilation, as a key technique for merging physical models with observational to estimate state variables, has been widely explored in the fields of weather forecasting, oceanography, and ecology. However, conventional assimilation frameworks, such as variational methods (3D/4DVar) and sequential methods (EnKF), often struggle with the high dimensionality and pronounced nonlinearity inherent in both physical and observational models. In this talk, I will introduce our recent work on leveraging deep learning to address these challenges, focusing on data-driven reduced-order modeling and deep generative modeling.

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Date/Time : 26 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course explores the fundamental aspects of local theta correspondence. The series consists of 5 lectures covering the following topics:

1. Models of the Heisenberg-Weil representation and the Metaplectic group
2. Dual pairs and general properties of theta correspondences
3. Theta correspondences over real fields
4. Theta correspondences over finite fields and p-adic fields
5. Geometric aspects of theta correspondence

This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream. Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 24 Feb 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Shota Osada, Kagoshima University

In this talk, we will consider the construction of $\mu$-reversible diffusion processes for a given point process $\mu$ on  $\mathbb{R}^d$. Specifically, we will discuss the Dirichlet form method to construct distorted Brownian motion on configuration spaces. For Poisson point processes, this corresponds to an infinite number of independent Brownian motions on $\mathbb{R}^d$. For correlated point processes, the interaction between particles is characterized by a function called the log-derivative, which describes the force exerted on one particle by the others. In previous results, the construction of diffusion processes using Dirichlet forms and their characterization using log-derivatives have been treated separately. In this talk, I will introduce that the existence of a logarithmic derivative implies the closability of the Dirichlet form. 

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Date/Time : 24 Feb 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Shuhei Shibata, Kyushu University

We study the classical law of iterated logarithm for centered continuous Gaussian processes. Also, we introduce one of the asymptotic behavior of a non-Markovian stochastic process called elephant random walk as an application.

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Date/Time : 21 Feb 2025 13:00
Venue : S17 #04-04 (SR3)
Speaker : Weikun He, AMSS, Chinese Academy of Sciences

On homogeneous spaces such as SL_2(R)/SL_2(Z), there are interesting random walks which are driven by group action. We focus on asymptotic behaviour of such random walk, especially on the property of equidistribution in law. In this talk, I will present a method developed in a joint work with Timothée Bénard to estimate the rate of convergence of such equidistribution. It involves ideas from fractal geometry and it constitutes a crucial ingredient in the study of Diophantine approximation on fractal sets, presented in the YMLS talk.

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Date/Time : 21 Feb 2025 11:00
Venue : S17 #04-04 (SR3)
Speaker : Wang Yutong, National University of Singapore

In the third lecture, we will learn how to construct new mathematics objects in Lean. Although Mathlib4 has provide numerous amount of objects and definitions, we always need to build our own infrastractures when formalizing a new aspect. In this course, we will use examples in undergraduate calculus and Gaokao to demonstrate how to properly design the infrastracture. Specifically, we will together explore the usage of class, structure, as well as their combination with definitions and theorems to compose a reasonable formalization project.

This mini-course will live stream. Here are the zoom ID and the link:
https://nus-sg.zoom.us/j/81322620719?pwd=Wg8FVTZbfX4QpZ7vbiYwaBN3n1MO7A.1

Meeting ID: 813 2262 0719
Passcode: 359631

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Date/Time : 19 Feb 2025 15:00
Venue : S17 #04-06 (SR1)
Speaker : He Weikun, AMSS, Chinese Academy of Sciences

Diophantine approximation studies how well a real number can be approximated by rational numbers. Following a question asked by Mahler in 1984, we are interested in Diophantine properties of points in the middle third Cantor set or more generally fractal sets. I will survey briefly this topic and present a recent joint work with Timothée Bénard and Han Zhang, where we obtained a Khintchine dichotomy for the middle third Cantor set.

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Date/Time : 19 Feb 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Ma Jiajun, Xiamen University and Xiamen University Malaysia

This mini-course explores the fundamental aspects of local theta correspondence. The series consists of 5 lectures covering the following topics:

1. Models of the Heisenberg-Weil representation and the Metaplectic group
2. Dual pairs and general properties of theta correspondences
3. Theta correspondences over real fields
4. Theta correspondences over finite fields and p-adic fields
5. Geometric aspects of theta correspondence

This mini-course is designed for senior undergraduate students and graduate students.

This mini-course will live stream. Here is the zoom ID:
Meeting ID: 848 8485 0855
Passcode: 226224

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Date/Time : 19 Feb 2025 15:00
Venue : S17 #05-12 (SR4)
Speaker : Yue Xie, University of Hong Kong

The two-metric projection method is a simple yet elegant algorithm proposed by Bertsekas to address bound/box-constrained optimization problems. The algorithm’s low per-iteration cost and potential for using Hessian information make it a favorable computation method for this problem class. Inspired by this algorithm, we propose a two-metric adaptive projection method for solving the $\ell$_1-norm minimization problem that inherit these advantages. We demonstrate that the method is theoretically sound – it has global convergence. Furthermore, it is capable of manifold identification and has superlinear convergence rate under the error bound condition and strict complementarity. Therefore, given sparsity in the solution, the method enjoys superfast convergence in iteration while maintaining scalability, making it desirable for large-scale problems. We also equip the algorithm with competitive complexity to solve nonconvex problems. Numerical experiments are conducted to illustrate the advantages of this algorithm implied by the theory compared over other competitive methods, especially in large-scale scenarios. Compared with the two-metric projection method, our algorithm directly solves the l1-norm minimization problem without resorting to the intermediate reformulation as a bound-constrained problem, so it circumvents the issue of numerical instability.

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