Date/Time : 30 Sep 2020 16:00
Venue : via Zoom
Speaker : Haijun Yu, Chinese Academy of Science

Join Zoom Meeting https://nus-sg.zoom.us/j/92338820026?pwd=U043L0JrWU9XRXFDUTVmMXVxNVBJdz09 Meeting ID: 923 3882 0026 Password: 936000 Abstract: Deep neural networks with rectified linear units (ReLU) are getting very popular recently.   Some theoretical progresses on deep ReLU network approximation for functions in Sobolev space and Korobov space have recently been made by several groups.   In this talk, we show that deep networks with rectified power units (RePU) can give better approximations for smooth functions than deep ReLU networks. Our analysis is based on classical polynomial approximation theory and some efficient and stable algorithms we proposed to convert polynomials into deep RePU networks of optimal size without any approximation error.  Our constructive proofs reveal clearly a relation between deep RePU networks and spectral methods.

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Date/Time : 30 Sep 2020 10:00
Venue : via Zoom
Speaker : Yu-Wei Fan, UC Berkeley

Join Zoom Meeting https://nus-sg.zoom.us/j/98579645138?pwd=cFZlc1QzZktFOFF1UEJjamlIUEFJUT09 Meeting ID: 985 7964 5138 Password: 872111 Abstract: We will start with a gentle introduction to the notions of categorical dynamical systems and their entropy, in which the latter is motivated from connections between Teichmuller theory and Bridgeland stability conditions. Then we will compare categorical entropy with the topological entropy of holomorphic dynamics. Finally, we will introduce a new canonical invariant that is complementary to the categorical entropy, and see how it is a generalization of the Poincare rotation number. Partly based on joint work with Simion Filip.

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Date/Time : 25 Sep 2020 15:00
Venue : via Zoom
Speaker : Joel Moreira , University of Warwick

Join Zoom Meeting Meeting ID: 985 3799 6193 Password: 535348 Abstract:  In this talk I will present a survey of arithmetic Ramsey theory. This fascinating subject, which focuses on patterns which arise in arbitrary finite colourings of the natural numbers, combines ideas and tools from diverse areas of mathematics, such as graph theory, Fourier analysis, geometric group theory, and ergodic theory; and has deep connections with number theory and additive combinatorics. The first half of the talk will be dedicated to the history of this subject, and the second to recent progress on a few simple looking but still open problems.

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Date/Time : 23 Sep 2020 15:00
Venue : via Zoom
Speaker : Hirotaka Kakuhama, Kyoto University

Join Zoom Meeting https://nus-sg.zoom.us/j/93822139520?pwd=SGhwZUMrWUFRRjdCcm9zQkk0U05sZz09 Meeting ID: 938 2213 9520 Password: 884511 Abstract: Let (H,G) be a reductive dual pair consisting of quaternion unitary groups over a local field. I will talk about the behavior of formal degrees under the theta correspondence for (H,G), which extends a work of Gan-Ichino for orthogonal-symplectic dual pairs and unitary dual pairs. The main ingredient is a precise analyzation of the local Siegel-Weil formula: which is a different point from Gan-Ichino’s work. Moreover, I will mention about an application to the formal degree conjecture.

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Date/Time : 22 Sep 2020 16:00
Venue : via Zoom
Speaker : Jérémy Toulisse, Université de Nice - Sophia Antipolis, France

Join Zoom Meeting https://nus-sg.zoom.us/j/94773388232?pwd=WWpGK1dHaEZLcEx6TWpVVU9jNUdhZz09 Meeting ID: 947 7338 8232 Password: 861264 Abstract: The pseudo-hyperbolic space H^{2,n} is the pseudo-Riemannian analogue of the classical hyperbolic space. In this talk, I will explain how to solve an asymptotic Plateau problem in this space: given a topological circle in the boundary at infinity of H^{2,n}, we construct a unique complete maximal surface bounded by this circle. This construction relies on Gromov’s theory of pseudo-holomorphic curves. This is a joint work with François Labourie and Mike Wolf.

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Date/Time : 17 Sep 2020 09:00
Venue : via Zoom
Speaker : Chen Wan , Rutgers University, Newark

Join Zoom Meeting https://nus-sg.zoom.us/j/94523183102?pwd=QXB4bmNhNTFGMFBaWStGRGg1S2wvZz09 Meeting ID: 945 2318 3102 Password: 908567 Abstract: In this talk, I will discuss the local multiplicity for the unitary Shalika model. By proving a local trace formula for the unitary Shalika model and a twisted local trace formula for the Shalika model, we are able to explicitly compute the multiplicity of the unitary Shalika model for all the discrete series. This is a joint work with R. Beuzart-Plessis.

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Date/Time : 16 Sep 2020 16:00
Venue : va Zoom
Speaker : Jinglai Li, University of Birmingham

Join Zoom Meeting https://nus-sg.zoom.us/j/92493981998?pwd=Q3VUR3ljUDBoT2JrNkN4N2h4YkJKZz09 Meeting ID: 924 9398 1998 Password: 186838 Abstract: The performance of Hamiltonian Monte Carlo (HMC) sampler depends critically on some algorithm parameters such as the total integration time and the numerical integration stepsize. The parameter tuning is particularly challenging when the mass matrix of the HMC sampler is adapted. We propose in this work a Kolmogorov-Sinai entropy (KSE) based design criterion to optimize these algorithm parameters, which can avoid some potential issues in the often used jumping-distance based measures. For near-Gaussian distributions, we are able to derive the optimal algorithm parameters with respect to the KSE criterion analytically. As a byproduct the KSE criterion also provides a theoretical justification for the need to adapt the mass matrix in HMC sampler. Building upon the results, we propose an adaptive HMC algorithm, and we then demonstrate the performance of the proposed algorithm with numerical examples.

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Date/Time : 16 Sep 2020 17:00
Venue : via Zoom
Speaker : Ye Jinhe,

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract: For any field K, we introduce natural topologies on K-points of varieties over K, which is defined to be the weakest topology such that etale morphisms are open. This topology turns out to be natural in a lot of settings. For example, when K is algebraically closed, it is easy to see that we have the Zariski topology and it picks up the valuation topology in many Henselian valued fields. Moreover, many topological properties correspond to the algebraic properties of the field. As an application, we will show large stable fields are separably closed, a special case of the stable fields conjecture. This is joint work with Will Johnson, Chieu-Minh Tran and Erik Walsberg.

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Date/Time : 16 Sep 2020 14:00
Venue : via Zoom
Speaker : Jialun Li , University of Zürich, Switzerland

Join Zoom Meeting https://nus-sg.zoom.us/j/96068904418?pwd=YkY1YmhEaHlvMk9TbERJSEllMFJ5UT09 Meeting ID: 960 6890 4418 Password: 788160 Abstract: Let mu be a Borel probability measure on SL2(R) with a finite exponential moment, such that the support of mu generates a Zariski dense subgroup in SL2(R). We can define a unique probability measure on the circle, which is called the mu stationary measure or Furstenberg measure. We will prove, using Bourgain’s discretized sum-product estimate, that the Fourier coefficients of this measure go to zero with a polynomial speed. Starting from this result, we can obtain a spectral gap of the transfer operator, whose properties enable us to get an exponential error term in the renewal theorem in the context of random products of matrices.

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