Date/Time : 20 Oct 2021 16:00
Venue : via Zoom
Speaker : Yang Yue, 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:  This is a follow up of Liao Yuke’s talk last week. I will explain in detail his result which says that there exists a recursive coloring f: N -> {0,1} such that for all infinite subset X of N, if FS(X) is homogeneous for f, then X is not recursive in 0”. Here FS(X) is the set of all finite sums of distinct elements of X. Liao Yuke’s result improved Blass, Hirst and Simpson’s theorem in 1987 (from no 0′
recursive solutions to no 0” recursive ones).

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Date/Time : 20 Oct 2021 14:00
Venue : via Zoom
Speaker : Wen-Wei Li, Peking University

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https://nus-sg.zoom.us/j/81065287062?pwd=ajhROWc5MWV1RVQzQ1ZkS2NNcHp1Zz09

Meeting ID: 810 6528 7062
Passcode: 121544

Abstract:  A theory of endoscopy for the metaplectic covering Mp(2n) of Sp(2n) was proposed by the author ten years ago, and the elliptic part of the Arthur-Selberg trace formula has been stabilized since then. In this talk, I will give an overview of the stabilization of the full trace formula (arXiv:2109.06581) for these coverings, which is indispensable for global applications. This is largely inspired by the prior works of Arthur and Moeglin-Waldspurger for linear reductive groups.

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Date/Time : 20 Oct 2021 09:00
Venue : via Zoom
Speaker : Siqi He, Stony Brook University

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https://nus-sg.zoom.us/j/88336974987?pwd=SVVRVStaVTJ6STVEL1JGRSsxQjVFdz09

Meeting number：883 3697 4987
Password：132347

Abstract: Special Lagrangian submanifolds are a distinguished class of real calibrated submanifolds defined in a Calabi-Yau manifold, which are calibrated by the real part of the holomorphic volume form. Given a compact, smooth special Lagrangian submanifold, Mclean proved that the space of nearby special Lagrangian submanifolds of it could be parametrized by the harmonic 1-forms. In this talk, we will discuss some recent progress on generalizing Mclean’s result to the branched deformations. We will describe how to use multi-valued harmonic functions to construct branched nearby deformations.

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Date/Time : 18 Oct 2021 10:00
Venue : via Zoom
Speaker : Zhennan Zhou, Peking University

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https://nus-sg.zoom.us/j/85127734314?pwd=amUyZjZEdTQycEhETWNESlFDMEdoUT09

Meeting ID: 851 2773 4314
Passcode: 348196

Abstract:  In this talk, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at the microscopic level, such Fokker-Planck equations are endowed with an unconventional structure: transporting the boundary flux to a specific interior point. In the first part of the talk, we present a conservative and positivity preserving scheme for these Fokker-Planck equations, and we show that in the linear case, the semi-discrete scheme satisfies the discrete relative entropy estimate, which essentially matches the only known long time asymptotic solution property. We also provide extensive numerical tests to verify the scheme properties, and carry out several sets of numerical experiments, including finite-time blowup, convergence to equilibrium and capturing time-period solutions of the variant models. Secondly, we are concerned with a kinetic model for neuron networks. Individual neurons are characterized by their voltage and conductance, the dynamics of the voltage is influenced by the conductance and when the voltage is reaching a threshold, it is immediately reset to a lower value. By exploring a series of toy models, we aim to identify the cause of the emergence of time-periodic solutions in such Fokker-Planck equations.

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Date/Time : 15 Oct 2021 16:00
Venue : via Zoom
Speaker : Dietmar Gallistl, Universität Jena

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https://nus-sg.zoom.us/j/86885266448?pwd=TzJKSVhmZzdITEN3TFh2b0RMMTEzZz09

Meeting ID: 868 8526 6448
Passcode: 006862

Abstract:  This contribution proposes a compatible finite element discretization for the approximation of the inf-sup constant for the divergence. The new approximation replaces the $H^{-1}$ norm of a gradient by a discrete $H^{-1}$ norm which behaves monotonically under mesh-refinement. By discretizing the pressure space with piecewise polynomials, upper bounds to the inf-sup constant are obtained. The scheme enables an approximation with arbitrary polynomial degrees. It can be viewed as a Rayleigh-Ritz method and it gives monotonically decreasing approximations of the inf-sup constant under mesh refinement. In particular, the computed approximations are guaranteed upper bounds for the inf-sup constant. The novel error estimates prove convergence rates for the approximation of the inf-sup constant provided it is an isolated eigenvalue of the corresponding non-compact eigenvalue problem; otherwise, plain convergence is achieved. Numerical computations on uniform and adaptive meshes are presented.

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Date/Time : 15 Oct 2021 10:00
Venue : via Zoom
Speaker : Ju Sun, University of Minnesota

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

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Phase retrieval (PR) concerns the recovery of a signal (1D, 2D, or 3D) from its Fourier magnitudes, and is central to numerous areas of scientific imaging. Over the past decade, there have been numerous breakthroughs in understanding simplified or modified versions of the problem, but the existence of effective and robust methods for the original PR problem remains elusive and so theoretical insights are out of the question. In this talk, I will discuss why PR is difficult, the strength and limitation of conventional formulations, the promise and perils of deep learning approaches, as well as our recent methods that solve practical PR problems in an unprecedented regime.

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Date/Time : 13 Oct 2021 16:00
Venue : via Zoom
Speaker : Jonas Beyrer, University of Bonn

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

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract:  The study of higher rank Teichmüller spaces has attracted a lot of attention in the last 20 years. Those spaces are connected components of the character variety Hom(H,G)/G that consist entirely of discrete and faithful representations; here G is a Lie group and H the fundamental group of a closed surface. Those components generalize classical Teichmüller space, the case G=PSL(2,R), which also identifies with the moduli space of hyperbolic structures on the surface. Representations in higher rank Teichmüller spaces, so called „positive representations“, are not only discrete and faithful, but have many other striking properties and similarities to hyperbolizations (e.g. constant entropy, collar lemmas, etc). However surprisingly there are many representations that are not in higher rank Teichmüller spaces and still share many of this striking properties: representations that satisfy a „partial positivity“. In this talk on joint work with Beatrice Pozzetti I want to discuss partially positive representations and their main difference to representations in higher rank Teichmüller spaces: degenerations.

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Date/Time : 13 Oct 2021 14:00
Venue : via Zoom
Speaker : Hankyung Ko, Uppsala University

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https://nus-sg.zoom.us/j/86403704548?pwd=ZWFSVHpqMVd0TkNNVTM0ZEg0MzhSdz09

Meeting ID: 864 0370 4548
Passcode: 234932

Abstract:  A Coxeter system is a presentation of a group by generators and a specific form of relations, namely the braid relations and the reflection relations. The Coxeter presentation leads to, among others, a similar presentation of the (Iwahori-)Hecke algebras and the Kazhdan-Lusztig theory, which provides combinatorial answers to major problems in Lie theoretic representation theory and geometry. Extending such applications to the `singular land’ requires the singular version of the Hecke algebra. Underlying combinatorics of the singular Hecke algebra/category comes from the parabolic double cosets and is the first step in understanding the singular Hecke category. In this talk, I will present a Coxeter theory of the parabolic double cosets developed in a joint work with Ben Elias. In particular, I will explain a generalization of the reduced expressions and describe the braid and non-braid relations.

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Date/Time : 13 Oct 2021 16:00
Venue : via Zoom
Speaker : Liao Yuke,

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

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

Abstract: Hindman’s theorem is a Ramsey type theorem related to finite sum while its proof-theoretic strength still has a huge gap. One form of the question is that if any computable coloring function would have an arithmetic solution (homogeneous set). We will construct a computable coloring functions that no Pi-3 set can be homogeneous.

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