Date/Time : 06 Oct 2021 16:00
Venue : via Zoom
Speaker : Purvi Gupta, Indian Institute of Science, Bangalore

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

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: A compact subset of $\mathbb{C^n}$ is said to be polynomially convex if it is defined by a family of polynomial inequalities. Polynomial convexity grants certain approximation-theoretic properties to the underlying set. When the set is a real submanifold of $\mathbb{C^n}$, its convexity properties are partly influenced by its topology, and the local and global structure of its CR (complex-real) singularities. The minimum complex dimension into which all compact real manifolds of a fixed dimension admit smooth polynomially convex embeddings is not known (although there are some obvious bounds). In this talk, we will discuss some recent improvements on the previously known bounds, especially focusing on the odd-dimensional case, where the embeddings cannot be produced by classical (local) perturbation techniques. This is joint work with R. Shafikov.

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Date/Time : 01 Oct 2021 10:00
Venue : via Zoom
Speaker : Li Cheng, University of Alberta

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

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Recent advancement of visual behavior analysis has opened door to many interesting applications. In this talk, I will discuss our research efforts toward addressing the related tasks of 3-D pose and shape estimation, action quality assessment, and motion synthesis of humans and beyond, from images and videos. Looking forward, our results could be applied to everyday life scenarios such as natural user interface, AR/VR, robotics, and gaming, among others.

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Date/Time : 30 Sep 2021 10:00
Venue : via Zoom
Speaker : Brian Collier, University of California Riverside

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

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract:  In this talk, we will define a special class of nilpotent elements of complex semisimple Lie algebra and describe how a Slodowy slice construction defines connected components of moduli spaces of G-Higgs bundles on a compact Riemann surface for specific real groups G. Through the nonabelian Hodge correspondence, these components define connected components of the G-character variety with many nice features. We will then describe how these nice features, together with recent work of Guichard-Labourie-Wienhard on positive representations imply that such components are higher Teichmuller spaces, that is, they consist entirely of discrete and faithful representations. In the remaining time, we will describe what remains to be proven to finish the classification of higher Teichmuller spaces.

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Date/Time : 29 Sep 2021 14:00
Venue : via Zoom
Speaker : Shunsuke Yamana, Osaka City University

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https://nus-sg.zoom.us/j/86263979122?pwd=WXNuYUdnNXdhQkNOODJJNlB3MnRhQT09

Meeting ID: 862 6397 9122
Passcode: 630599

Abstract:  p-adic L-functions involve modified p-factors which measure the discrepancy between the p-adic and complex L-values in the interpolation formula. It is a puzzling fact that this factor can vanish at the central point. Then the p-adic L-function trivially vanish at the point, and such a zero is called an exceptional zero. The p-adic L-function of an elliptic curve has an exceptional zero if and only if it has split multiplicative reduction at p, and the precise relation between derivative of the p-adic L-function and the algebraic part of the complex L-value was conjectured by Mazur-Tate-Teitelbaum and proved by Greenberg-Stevens. 　 There have been many attempts to extend this result of Greenberg-Stevens to more general automorphic forms.

In this talk I will consider the exceptional zeros of the cyclotomic twisted triple product p-adic L-function associated to elliptic curves over rationals and a real quadratic field, and prove an identity between derivatives of the p-adic L-function and complex L-values. I will also consider exceptional zeros of a certain p-adic L-function of degree 6 associated with two rational elliptic curves.

This is a joint work with Ming-Lun Hsieh.

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Date/Time : 27 Sep 2021 10:00
Venue : via Zoom
Speaker : Timo Sprekeler, National University of Singapore

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https://nus-sg.zoom.com.cn/j/86200274068?pwd=eHlLS0JHMWprU0VjVTN6WWtOVE95QT09

Meeting ID: 862 0027 4068
Passcode: 578977

Abstract:  This talk presents recent progress in the analysis and the finite element approximation of periodic homogenization problems of the form $A(x/\varepsilon):D^2 u_{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. In the first part of the talk, we discuss optimal rates for the convergence of $(u_{\varepsilon})$ to the solution of the homogenized problem in $L^{\infty}$ and $W^{1,p}$ norms, and we present a $W^{2,p}$ corrector estimate. These results are used in the second part of the talk to construct and analyze a finite element method for the approximation of such problems. This talk is based on work with Hung Tran (University of Wisconsin-Madison), and work with Yves Capdeboscq (Université de Paris, Sorbonne Université) and Endre Süli (University of Oxford).

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Date/Time : 24 Sep 2021 09:00
Venue : via Zoom
Speaker : Qianxiao Li, National University of Singapore

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https://nus-sg.zoom.us/j/84334390977?pwd=SXVUWm50R1RNSlY1NnplTXJJQ20xdz09

Meeting ID: 843 3439 0977
Passcode: 186685

Abstract:  In this talk, we discuss some recent work on the connections between machine learning and dynamical systems. These come broadly in three categories, namely machine learning via, for and of dynamical systems. In the first direction, we introduce a dynamical approach to deep learning theory with particular emphasis on its connections with approximation and control theory. In the second direction, we discuss the approximation and optimization theory of learning input-output temporal relationships using recurrent neural networks and variants, with the goal of highlighting key new phenomena that arise in learning in dynamic settings. In the last direction, we discuss some principled methods that learns stable and interpretable dynamical model from data arising in scientific applications. We conclude with some discussion on future directions in this rapidly developing field.

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Date/Time : 24 Sep 2021 10:00
Venue : via Zoom
Speaker : Weijie Su, University of Pennsylvania

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

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  The remarkable development of deep learning over the past decade relies heavily on sophisticated heuristics and tricks. To better exploit its potential in the coming decade, perhaps a rigorous framework for reasoning deep learning is needed, which however is not easy to build due to the intricate details of modern neural networks. For near-term purposes, a practical alternative is to develop a mathematically tractable surrogate model that yet maintains many characteristics of deep learning models.

This talk introduces a model of this kind as a tool toward understanding deep learning. The effectiveness of this model, which we term the Layer-Peeled Model, is evidenced by two use cases. First, we use this model to explain an empirical pattern of deep learning recently discovered by David Donoho and his students. Moreover, this model predicts a hitherto unknown phenomenon that we term Minority Collapse in deep learning training. This is based on joint work with Cong Fang, Hangfeng He, and Qi Long.

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Date/Time : 22 Sep 2021 14:00
Venue : via Zoom
Speaker : Hideya Watanabe, Osaka City University

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https://nus-sg.zoom.us/j/82636421526?pwd=WUhpZzJPMW1mWXJtRkhtZHRFeVBOUT09

Meeting ID: 826 3642 1526
Passcode: 189069

Abstract: In the representation theory of a quantum group $U$ of finite
type, a based module means a $U$-module with a canonical and crystal
basis. One of the most important properties of canonical bases is
cellularity. In this talk, I generalize the notion of based modules to the
representation theory of the i-quantum group of type AI, and explain that
the associated canonical bases are cellular. Taking the crystal limit of
the canonical bases, a new combinatorial model for irreducible modules
over the orthogonal group is obtained.

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Date/Time : 15 Sep 2021 14:00
Venue : via Zoom
Speaker : Kazuki Morimoto, Kobe University

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https://nus-sg.zoom.us/j/82991610093?pwd=SndoVzZzUmErbjhzV2FCZWZ3bHJ0QT09

Meeting ID: 829 9161 0093
Passcode: 131130

Abstract:  Lapid and Mao formulated a conjecture on Ichino-Ikea type formula of Whittaker periods for quasi-split reductive groups. In the unitary group case, they showed that their conjecture is reduced to a certain local identity. In my previous work, I showed this local identity for even unitary groups at non-split non-archimedean places. In this talk, I will talk about my ongoing work on this local identity at both non-archimedean and archimedean split places, If time permits, I will explain an application of this formula to Ichino-Ikea type formula of Bessel periods for (U(2n), U(1)).

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