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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Date/Time : 11 Sep 2020 09:00
Venue : via Zoom
Speaker : Jiajun Tong, UCLA

Join Zoom Meeting  Meeting ID: 937 9128 5227 Password: 922637 Abstract: In this talk, we first consider 2-D Stokes immersed boundary problem. It models a 1-D closed elastic string immersed and moving in a 2-D Stokes flow, which features an autonomously moving boundary and singular forcing supported on it. We will discuss results on well-posedness of the string motion (joint work with Fanghua Lin). In the second part of the talk, we introduce a regularized version of the problem inspired by the numerical immersed boundary method, where a regularized delta-function is used to mollify the singular forcing and the flow field. We will show global well-posedness of the regularized string motion. As the regularization diminishes, we prove the string dynamics converges to that in the un-regularized case under certain assumptions. Viewing the latter as a benchmark, we derive error estimates under various norms. Our rigorous results not only coincide with existing numerical observations in many aspects, but also reveal a potential way of improving the (numerical) accuracy by choosing the regularization suitably.

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Date/Time : 09 Sep 2020 17:00
Venue : via Zoom
Speaker : Ming Xiao, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract:  In 1948, Horn and Tarski conjectured whether the sigma-finite chain condition and sigma-bounded chain condition are equivalent. The first counterexample was given by Thummel in 2012 and then a Borel counterexample was given by Todorvevic in 2014. Both examples belong to a class of poset called “Todorvevic ordering” T(X) over topological spaces X. In this talk, I will illustrate a satisfactory condition for a topological space X making the corresponding poset T(X) fail to have a countable Borel partition witnessing the sigma-finite chain condition, although it may still be witnessed by non-Borel partitions. The content of this talk is going to be the same as the one I gave in a seminar at the Chinese Academy of Sciences last year and is also a part of my Ph.D. dissertation.

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Date/Time : 09 Sep 2020 15:00
Venue : via Zoom
Speaker : Raphaël Beuzart-Plessis, Université d’Aix-Marseille

Join Zoom Meeting https://nus-sg.zoom.us/j/94485648813?pwd=d2pRWVJoVWdybTNhems3L2V4VkQvZz09 Meeting ID: 944 8564 8813 Password: 690359 Abstract: This talk concerns a global conjecture of Gan-Gross-Prasad relating the non-vanishing of certain automorphic periods on unitary groups to the non-vanishing of certain Rankin-Selberg L-functions at their center of symmetry. It also admits a refinement, proposed by Ichino-Ikeda, in the form of an exact identity connecting these two invariants. Following an approach initiated by Jacquet-Rallis of comparing two (relative) trace formulas, W. Zhang and more recently Y. Liu, W.Zhang, X. Zhu and myself have established both of these conjectures for cuspidal representations that are “stable” i.e. whose quadratic base-change is again cuspidal. In this talk, I will explain how to deal with the remaining cuspidal representations, sometimes called “endoscopic”, to which the conjectures apply through a fine spectral expansion of parts of the Jacquet-Rallis trace formula for general linear groups. This is joint work with Pierre-Henri Chaudouard and Michal Zydor..

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