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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Date/Time : 05 Apr 2022 14:00
Venue : S17 #06-11 (SR6)
Speaker : Huanchen Bao, National university of Singapore

Abstract:  The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this paper, we introduce a (new) J-total positivity on the full flag variety of an arbitrary Kac-Moody group, generalizing the (ordinary) total positivity.

We show that the J-totally nonnegative flag variety has a cellular decomposition into totally positive J-Richardson varieties. Moreover, each totally positive J-Richardson variety admits a favorable decomposition, called a product structure. Combined with the generalized Poincare conjecture, we prove that the closure of each totally positive J-Richardson variety is a regular CW complex homeomorphic to a closed ball. Moreover, the J-total positivity on the full flag provides a model for the (ordinary) totally nonnegative partial flag variety. As a consequence, we prove that the closure of each (ordinary) totally positive Richardson variety is a regular CW complex homeomorphic to a closed ball, confirming conjectures of Galashin, Karp and Lam.

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Date/Time : 05 Apr 2022 16:00
Venue : S17 #04-04 (SR3)
Speaker : John Loftin, Rutgers University

Abstract: Consider a Riemann surface S of genus g at least 2 equipped with a holomorphic cubic differential U. For a given g, such pairs (S,U) can be used to parametrize the Hitchin component of the space of representations of the fundamental group into PSL(3,R), and also the space of convex projective structures on S. This generalizes and extends the space Fuchsian representations into PSL(2,R) (the Teichmuller space of hyperbolic structures), which corresponds to the locus U=0. This parametrization of the Hitchin component is not explicit but involves the Hitchin system of PDEs. For nonzero U, we study the case sU as s approaches infinity. In particular, we show the geometry in this limit can be read off explicitly from U, in terms of an embedding of the universal cover of S into the real building given by the asymptotic cone of the symmetric space SL(3,R)/SO(3). We are able to provide explicit pictures for most triangle groups.

This is joint work with Andrea Tamburelli and Mike Wolf.

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Date/Time : 01 Apr 2022 10:00
Venue : via Zoom
Speaker : Rafael Peres Da Silva, National University of Singapore

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

Meeting ID: 977 560 6531
Passcode: 123321

Large-scale cancer omics studies have highlighted the diversity of patient molecular profiles and the importance of leveraging this information to deliver the right drug to the right patient at the right time. Key challenges in learning predictive models for this include the high-dimensionality of omics data and heterogeneity in biological and clinical factors affecting patient response. The use of multi-task learning techniques has been widely explored to address dataset limitations for in vitro drug response models, while domain adaptation (DA) has been employed to extend them to predict in vivo responses. In both of these transfer learning settings, noisy data for some tasks (or domains) can substantially reduce the performance for others compared to single-task (domain) learners, i.e. lead to negative transfer (NT).

This talk introduces TUGDA (ISMB 2021), a novel multi-task unsupervised DA method, that addresses these limitations in a unified framework by quantifying uncertainty in predictors and weighting their influence on shared feature representations. TUGDA’s ability to rely more on predictors with low-uncertainty allowed it to notably reduce cases of NT for in vitro models (94% overall) compared to state-of-the-art methods. For DA to in vivo settings, TUGDA improved over previous methods for patient-derived xenografts (9 out of 14 drugs) as well as patient datasets (significant associations in 9 out of 22 drugs). TUGDA’s ability to avoid NT thus provides a key capability as we try to integrate diverse drug-response datasets to build consistent predictive models with in-vivo utility.

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