Date/Time : 18 Apr 2022 15:00
Venue : S17 #04-06 (SR1)
Speaker : Matias Delgadino, University of Texas at Austin

Abstract: Weakly interacting diffusions are a go to model for a wide array of phenomena. In this talk, we will study when this model can be accurately approximated by its mean field limit. Phase transitions in the system will emerge as the natural obstruction to uniform in time propagation of chaos.

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Date/Time : 13 Apr 2022 16:00
Venue : via Zoom
Speaker : Wang Wei, Sun Yatsen University

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract: Recently, Chong, Yang and I prove that a version of Pigeonholes Principle for trees (TT^1) is Pi^0_3-conservative over RCA_0. So, TT^1 does not imply the totality of Ackermann function over RCA_0, like the instance of Ramsey’s Theorem for 2-colorings of pairs. To fit the trend of logic talks, I am not going to present many details. Instead, I will try to recall some stories about the Ackermann function and its appearance in reverse mathematics.

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Date/Time : 12 Apr 2022 14:00
Venue : via Zoom
Speaker : Yu Jun, Peking University

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https://nus-sg.zoom.us/j/89178679746?pwd=NUNjUVdTcWhLZ082di9tM0I1cDRXQT09

Meeting ID: 891 7867 9746
Passcode: 548511

Abstract: Given a quasisplit reductive linear algebraic group $\mathbb{G}$ over a number field $F$, this talk concerns the determination of the functional source group $H_{\pi}$ of an automorphic representation $\pi$ of Ramanujan type of $\mathbb{G}(\mathbb{A}_{F})$. Assuming that $\mathbb{G}$ is split, a unitary group or an orthogonal group and $\pi$ neither comes from the Eisenstein series nor comes from endoscopy, we show that $H_{\pi}$ is determined up to element-conjugacy by its dimension datum alone. We also show results concerning linear independent of dimension data of such $H_{\pi}$.

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Date/Time : 12 Apr 2022 10:00
Venue : via Zoom
Speaker : Minju Lee, Institute of Advanced Study

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract : This is joint work with Samuel Edwards and Hee Oh. Let $G$ be a connected semisimple real algebraic group, and $\Gamma<G$ be a Zariski dense Anosov subgroup with respect to a minimal parabolic subgroup. We describe the asymptotic behavior of matrix coefficients $\langle (\exp tv). f_1, f_2\rangle$ in $L^2(\Gamma\backslash G)$ as $t\to \infty$ for any $f_1, f_2\in C_c(\Gamma\backslash G)$ and any vector $v$ in the interior of the limit cone of $\Gamma$. These asymptotics involve higher rank analogues of Burger-Roblin measures which will be introduced in this talk. As an application, for an affine symmetric subgroup $H$ of $G$, we obtain a bisector counting result for $\Gamma$-orbits with respect to the corresponding generalized Cartan decomposition of $G$. Moreover, we obtain analogues of the results of Duke-Rudnick-Sarnak and Eskin-McMullen for counting discrete $\Gamma$-orbits in affine symmetric spaces $H\backslash G$.

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Date/Time : 11 Apr 2022 14:00
Venue : via Zoom
Speaker : Tong Xin, National University of Singapore

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https://nus-sg.zoom.us/j/82203277015?pwd=R1o1cHlTc1FueUM0c3ZETEtZQngzUT09

Meeting ID: 822 0327 7015
Passcode: 485328

Abstract: In many areas, stochastic algorithms are the main computational workhorses. In order to handle modern-day problems, we need these algorithms to scale well with model dimension and data size. How to design such algorithms with theoretical guarantees is important for both practical and theoretical interests.

In this talk, I will discuss how to use stochastic algorithms to solve problems in data assimilation, inverse problems and statistical machine learning. I will focus on how to exploit different problem structures to make the algorithms computationally efficient.

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Date/Time : 08 Apr 2022 09:00
Venue : via Zoom
Speaker : Konstantin Tikhomirov, Georgia Institute of Technology

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https://nus-sg.zoom.us/j/6124909748?pwd=TDFJYitzZ3ZSeUZUcTBEWnhTZWtSUT09

Meeting ID: 612 490 9748
Passcode: 007151

Abstract: The Gaussian Elimination with Partial Pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although the worst-case loss of precision in GEPP due to roundoff errors is known to be very significant, empirical evidence suggests that for a typical coefficient matrix, GEPP is numerically stable. Until recently, this phenomenon has received little theoretical justification. We make a progress on this problem by showing that, given the random $n\times n$ standard Gaussian coefficient matrix, the {\it growth factor} of the Gaussian Elimination with Partial Pivoting is at most polynomially large in $n$ with probability close to one. This implies that with high probability the GEPP results only in logarithmic (in $n$) loss of bits of precision, which improves an earlier estimate of Sankar of order $O(\log^2 n)$. This is joint work with Han Huang.

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Date/Time : 08 Apr 2022 10:00
Venue : via Zoom
Speaker : Gianmarco Mengaldo, National University of Singapore

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

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: We provide a perspective on the challenges and opportunities in computational modeling for industry-relevant applications towards the Exascale Era. As an example, we present the successful deployment of high-fidelity Large-Eddy Simulation (LES) technologies based on spectral/hp element methods to simulate the aerodynamics of a real automotive car, namely the Elemental Rp1 model. The simulation presents the common challenges of an industry-relevant problem, namely high Reynolds number and complex geometry. To the best of the authors’ knowledge, this simulation represents the first fifth-order accurate transient LES of an entire real car geometry using spectral element methods. Moreover, this constitutes a key milestone towards considerably expanding the computational design envelope currently allowed in industry, where steady-state modelling remains the standard. We also draw some parallels with other fields, namely numerical weather prediction, where large scale simulations play a central role and have been used since the 1950s.

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Date/Time : 07 Apr 2022 14:00
Venue : S17 #04-05 (SR2)
Speaker : Weiqiang Wang, University of Virginia

Abstract: Symmetric pairs over a local field admit a quantum deformation known as quantum symmetric pairs of affine type, (U, U^i). Here U is a Drinfeld-Jimbo affine quantum group (a quantum deformation of a loop algebra), and it admits a Drinfeld (loop) presentation. In this talk, we give a Drinfeld presentation for the affine i-quantum group U^i. Along the way, we shall construct various root vectors in U^i and describe their classical limits. This is based on joint work with Ming Lu (Sichuan) and Weinan Zhang (Virginia).

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Date/Time : 06 Apr 2022 16:00
Venue : via Zoom
Speaker : Frank Stephan, National University of Singapore

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract: The talk investigates which versions of the pumping lemma are matching where matching means that exactly the regular languages satisfy it. In particular it will be shown that two-sided pumping lemmas where an automatic function computes the pump tend to be matching.

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