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 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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Date/Time : 09 Sep 2020 11:00
Venue : via Zoom
Speaker : Hsueh-Yung Lin, Kavli-IPMU, Japan

Join Zoom Meeting https://nus-sg.zoom.us/j/95748660096?pwd=M2Y1eVJvb01iTzQrZ29CNGZuREM4UT09 Meeting ID: 957 4866 0096 Password: 871058 Abstract: Let X be a compact Kähler manifold. The celebrated Kodaira embedding theorem asserts that if the Kähler cone of X contains a rational cohomology class, then X is projective. Instead of considering Kähler classes, we will study the algebraicity of X when X carries a 1-dimensional positive rational Hodge class. We will first discuss and formulate some precise problems (depending on the notion of positivity) then focus on the following results: 1) If the interior of the dual Kähler cone of X contains a rational class, then the Picard variety of X is projective. 2) If the interior of the dual pseudoeffective cone of a compact Kähler threefold X contains a rational class, then X is projective.

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Date/Time : 09 Sep 2020 16:00
Venue : via Zoom
Speaker : Zhu Zhanxing, Peking University

Join Zoom Meeting https://nus-sg.zoom.us/j/93325963781?pwd=VVhBWkljeGQycExSOVVBdU10UW40Zz09 Meeting ID: 933 2596 3781 Password: 300023 Abstract: Iit has been a long-standing debate that “Is deep learning alchemy or science? ”, since the success of deep learning mostly relies on various engineering design and tricks, lack of  theoretical foundation. Unfortunately, the underlying mechanism of deep learning is still mysterious, which severely limits its further development from both theoretical and application aspects. In this talk, I will introduce some of our attempts on theoretically understanding deep learning, mainly focusing on analyzing its training methods and tricks, including stochastic gradient descent, batch normalization and knowledge distillation.  (1) We analyze the implicit regularization property of stochastic gradient descent (SGD), i.e. interpreting why SGD could find well generalizing minima compared with other alternatives; (2) We comprehensively reveal the learning dynamics of batch normalization and weight decay, and show its benefits on avoiding vanishing/exploding gradients, not being trapped into sharp minima and loss drop when decaying learning rate. (3) We also show the underlying mechanism of knowledge distillation, including its transfer risk bound, data efficiency and imperfect teacher distillation.  These new findings shed some light on understanding the  deep learning towards opening this black-box and also inspires new algorithmic design.

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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 : 02 Sep 2020 10:00
Venue : via Zoom
Speaker : Hongtaek Jung , Institute for Basic Science - South Korea

Join Zoom Meeting https://nus-sg.zoom.us/j/94193089627?pwd=SGZ6cUtXNnp6ejFpZUpGWHFkalM5dz09 Meeting ID: 941 9308 9627 Password: 788615 Abstract: It is known that the PSL(n,R)- Hitchin components of closed surfaces of negative Euler characteristic admit global Darboux coordinates with respect to the Goldman symplectic form. I will discuss an analogous result for the “PSL(3,R)-Hitchin components”  or the deformation spaces C(O) of convex projective structures of closed orbifolds O of negative Euler characteristic.  For this, I will present how to construct the Goldman type symplectic form on C(O).  Then I will introduce two ingredients to construct the global Darboux coordinates: a decomposition theorem that splits C(O) into simpler symplectic manifolds and an action-angle principle. This is joint work with Suhyoung Choi.

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Date/Time : 02 Sep 2020 15:00
Venue : via Zoom
Speaker : Sug Woo Shin, University of California, Berkeley

Zoom link: https://nus-sg.zoom.us/j/99468790870?pwd=SHIveFFOalkvdTczNTVteWdJbmMzdz09 Meeting ID: 994 6879 0870 Password: 374233 I will present my joint work with Arno Kret, where we construct a GSpin(2n)-valued ell-adic Galois representation attached to a cuspidal cohomological automorphic representation pi of a suitable quasi-split form of GSO(2n) over a totally real field, under the hypothesis that pi has a Steinberg component at a finite place. This uses input from the cohomology of certain Shimura varieties for GSO(2n); as such we need to take a suitable form of GSO(2n) depending on the parity of n. (We take the split form if and only if n is even.) The relevant preprint is available at https://math.berkeley.edu/~swshin/GSO.pdf.      

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Date/Time : 02 Sep 2020 16:00
Venue : via Zoom
Speaker : Sonoda Sho, RIKEN AIP, Japan

Join Zoom Meeting https://nus-sg.zoom.us/j/99186202215?pwd=ZFp5S21NVGVJclphVU82cm54TlpGQT09 Meeting ID: 991 8620 2215 Password: 026907 Abstract: Neural networks are known to be a black box due to the high-dimensionality, non-linearity, and non-convexity of parameters. In the so-called `integral representation’, at the cost of lifting up the parameters to infinite-dimensional function space, the parameter becomes linear and convex. The presenter aims to turn the black box into a white box by using integral representation. In this talk, he describes the integral representation first, then introduces recent application results for analyzing the parameters acquired through several learning algorithms.

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Date/Time : 28 Aug 2020 09:00
Venue : via Zoom
Speaker : Ying Cui , University of Minnesota

Join Zoom Meeting Meeting ID: 972 8455 8347 Password: 733806 Many modern statistical estimation problems are defined by  three major components: a statistical model that postulates the dependence of an output variable on the input features; a loss function measuring the error between the observed output and the model predicted output; and a regularizer that controls the overfitting and/or variable selection in the model.  We study the sampled version of this generic statistical estimation problem where the model parameters are estimated by empirical risk minimization, which involves the minimization of the empirical average of the loss function at the data points weighted by the model regularizer.  In our setup we allow all three component functions to be of the difference-of-convex type and illustrate them with a host of commonly used examples, including those in continuous piecewise affine regression and in deep learning with piecewise affine activation functions.  We describe a non-monotone majorization-minimization (MM) algorithm for solving the unified nonconvex, nondifferentiable optimization problem which is formulated as a specially structured composite dc program of the pointwise max type.  Numerical results are presented to demonstrate the effectiveness of the proposed algorithm and the superiority of continuous piecewise affine regression over the standard linear model. 

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