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 16:00
Venue : via Zoom
Speaker : Bakhadyr Khoussainov, UESTC, Chengdu and The University of Auckland

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

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

Abstract: This talk belongs to the area of probabilistic logic semantics.

The first contribution of this work is the introduction of probability structures. Probability structures are the algebraic structures equipped with probability functions on the domains and the atomic predicates. These structures extend type 1 probability structures introduced by Halpern and Bacchus.

Type 1 probability structures contain probability functions on domains only. Our probability structures possess an additional statistical knowledge, – probability functions on atomic predicates.

We present a method that builds probability spaces for the first order logic formulas and prove that our semantics is sound.

The second contribution of this work is the introduction of smooth probability structures.

The smooth probability structures carefully refine probability structures so that we have a better control of the probability spaces defined by first order logic formulas. For these structures we initiate the study of first order probability logic (FOPLS), investigate axiomatizability of FOPLS, and address decidability and undecidability questions of the sets of valid formulas. We also study a few algorithmic questions on probability structures.

The work is joint with Mingyu Xiao (UESTC) and Jiamou Liu (The University of Auckland).

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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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Date/Time : 10 Sep 2021 15:00
Venue : via Zoom
Speaker : Emile Takahiro Okada, University of Oxford

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https://nus-sg.zoom.us/j/82201157603?pwd=WktRRC9hbHFsaFR6VlF6amdGNk5tZz09

Meeting ID: 822 0115 7603
Passcode: 509310

Abstract:  The wavefront set is a powerful invariant which one can attach to representations of reductive groups over both global and local fields. Notably there is a non-trivial interplay between the wavefront set of an automorphic representation and that of its local factors. In this talk we will discuss recent results computing the wavefront set for all spherical Arthur representations in the p-adic case and the new techniques used in the computation.

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Date/Time : 10 Sep 2021 09:00
Venue : via Zoom
Speaker : YanYan Li, Rutgers University

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https://nus-sg.zoom.us/j/84328425455?pwd=MXpPQWYxZ0hvQ2UzOW1sbUREUG5XZz09

Meeting ID: 843 2842 5455
Passcode: 204458

Abstract:  We will first recall the Nirenberg problem and the Yamabe problem, together with some previous results on the existence and compactness of solutions to the problems. We will then discuss the σ_k-Nirenberg problem and the σ_k-Yamabe problem, the study of which requires solving fully nonlinear elliptic equations involving Schouten tensor on Riemannian manifolds. Some recent works and open problems will be discussed.

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Date/Time : 08 Sep 2021 16:00
Venue : via Zoom
Speaker : Duc-Manh Nguyen, University of Bordeaux

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

Meeting ID: 875 1147 6637
Passcode: 468399

Since the work of Eskin-Okounkov in 2001, it has been known that in any stratum of translation surfaces, the number of square-tiled surafces constructed from at most n squares grows like $c\pi^{2g}n^d$, where $d$ is the (complex) dimension of the stratum, $g$ is the genus of the surfaces, and $c$ is a rational number. Similar phenomena also occur in strata of quadratic differentials. Counting square-tiled surfaces in a given stratum is more or less the same as counting quadrangulations of a topological surface, with some constraints on the singularities and the holonomy of the associated flat metric. More recently, Engel showed that the asymptotics of the numbers of quadrangulations and triangulations with at most $n$ tiles are of the form $\alpha n^d$, where $\alpha$ is a constant in $Q[\pi]$ or $Q[\sqrt{3}\pi]$. In this talk, we will explain how the asymptotics above is related to the volume of some moduli spaces. Moreover, in some situations they can be computed from the self-intersection number of a divisor in some complex projective varieties. This implies in particular that the constant $\alpha$ belongs actually to either $Q\cdot\pi^d$, or  $Q\cdot(\sqrt{3}\pi)^d$ in those cases. This is joint work with Vincent Koziarz.

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