Date/Time : 18 Mar 2021 14:30
Venue : via Zoom
Speaker : Hao Liu, University of Hong Kong

Join Zoom Meeting https://nus-sg.zoom.us/j/81674259454?pwd=MmtaT2ZWUWlCeDQ1UE5oWXByeUpxZz09&from=addon Meeting ID: 816 7425 9454 Password: 778322 Abstract:  In this talk, we are going to talk about the global weak solutions to the gmCH equations which are constructed through peakons. We use a double mollification to the ODE system for trajectories of N-peakon weak solutions which has the crucial weak consistency property. With the global N-peakon weak solutions, we can use the mean-field approximation method to obtain global weak solutions for general initial data.

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Date/Time : 17 Mar 2021 15:00
Venue : via Zoom
Speaker : Gaetan Chenevier, Université Paris-Sud

Join Zoom Meeting https://nus-sg.zoom.us/j/89926187213?pwd=eGZ5M2gybnMvZWhCVGJHdnRSYWJqUT09 Meeting ID: 899 2618 7213 Password: 003341 Abstract: I will explain a method allowing to classify the isometry classes of unimodular integral lattices in all dimensions <= 28. This method has computational aspects, but also theoretical ones, involving automorphic representations of orthogonal groups. The talk should (hopefully) be accessible to a general number theorists audience.

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Date/Time : 17 Mar 2021 16:30
Venue : via Zoom
Speaker : Te Li, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/83795761997?pwd=ZFdUTXBIVGlHMHZhZlpjRmlFYnRDQT09 Meeting ID: 837 9576 1997 Password: 483694 Abstract:  We study the incompressible Navier-Stokes equations in dimensions d = 2 or 3 and address the hydrodynamic stability problem at high Reynolds. Our talk will mainly focus on the stability of laminar equilibria, around which the fluid moves in well-ordered layers. In joint works with Dongyi Wei and Zhifei Zhang, we established the (nonlinear) stability of Oseen vortices, Kolmogorov flow and Couette flow. In particular, our work on Oseen vortices confirmed Gallay’s conjecture. Pseudospectral bound and wave-operator method play crucial roles in our proofs.

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Date/Time : 11 Mar 2021 16:00
Venue : via Zoom
Speaker : Vaibhav Rajan, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Abstract:  The increasing availability of digitized clinical and genomic data presents an unprecedented opportunity to study and gain deeper understanding of diseases, develop new treatments and improve healthcare ecosystems. However, clinical data also poses modelling challenges due to the heterogeneity of data sources, e.g., structured demographic variables, text in clinical notes, images in MRI scans etc. In this talk, I’ll describe a deep multi-view learning technique, developed in my group, for unsupervised learning of representations from arbitrary collections of matrices. I’ll outline how our technique can be used for predicting gene-disease associations and drug targets in cancer.

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Date/Time : 10 Mar 2021 16:00
Venue : via Zoom
Speaker : Nicolas Gillis, Université de Mons

Join Zoom Meeting https://nus-sg.zoom.us/j/83074965403?pwd=dDZPUGltdXp0aStTUDV4UjBPeGxqdz09&from=addon Meeting ID: 830 7496 5403 Password: 366990 Abstract:  Given a nonnegative matrix X and a factorization rank r, nonnegative matrix factorization (NMF) approximates the matrix X as the product of a nonnegative matrix W with r columns and a nonnegative matrix H with r rows. NMF has become a standard linear dimensionality reduction technique in data mining and machine learning. In this talk, we address the issue of non-uniqueness of NMF decompositions, also known as the identifiability issue, which is crucial in many applications. We discuss three key NMF models that allow us to obtain unique NMFs, namely, separable NMF, minimum-volume NMF, and sparse NMF. We also discuss how the factors (W,H) in such models can be computed. We illustrate these results on facial feature extraction, blind hyperspectral unmixing, and topic modeling.

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Date/Time : 10 Mar 2021 17:00
Venue : via Zoom
Speaker : Zekun Jia,

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract: There are a lot of theorems in Ramsey theory whose proof explicitly or implicitly uses the Axiom of Choice. This talk will focus on Ramsey’s Theorem and Open Ramsey Theorem in three models of set theory where the Axiom of Choice fails (the basic Cohen model, the basic Fraenkel model, and the ordered Mostowski model), as well as some consistency and independence results that follow. Also, the usual proof of Open Ramsey Theorem on omega given by Galvin and Prikry assumes the Axiom of Dependent Choice, and this talk will sketch an improvement on that proof to make it purely constructive. This project is advised by Zach Norwood.

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Date/Time : 09 Mar 2021 14:00
Venue : via Zoom
Speaker : Shilin Yu, Xiamen University

Join Zoom Meeting https://nus-sg.zoom.us/j/83991095732?pwd=bG9Ramlwc1NGajVDUjZGQitSNUE3UT09 Meeting ID: 839 9109 5732 Password: 858523 Abstract:  The “coadjoint orbit method” philosophy of Kirillov and Kostant suggests that there is a close connection between the unitary dual of a Lie group G, which is the set of all irreducible unitary representations of G, and the set of coadjoint orbits in the dual of its Lie algebra. Roughly, one expects that the representations arise as “quantizations” of certain vector bundles on the coadjoint orbits, which are naturally symplectic manifolds. When the Lie group is a noncompact real semisimple group, both the unitary dual and the orbit method are far from being fully understood, yet a lot of deep and interesting mathematics have been developed to study this case. Vogan suggested the candidates for the vector bundles on the coadjoint orbits to be quantized, which he called admissible vector bundles. In this talk, we show that these admissible vector bundles indeed correspond to representations, with some exceptions. The tools used here are deformation quantization of symplectic varieties and their Lagrangian subvarieties. The talk is based on a joint paper with Conan Leung and an ongoing joint work with Ivan Losev.

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Date/Time : 05 Mar 2021 16:00
Venue : via Zoom
Speaker : Eric Moulines, Ecole Polytechnique

Join Zoom Meeting Meeting ID: 822 6641 6347 Password: 603563 Abstract: Statistical learning is rich in inference problems involving probability distributions (e.g. requiring to sample complex distributions, compute normalizing constants, approximate high-dimensional integrals, etc.). Examples include (Bayesian) uncertainty quantification, inference and sampling of generative models, aggregation of predictors. The classical approach to address these challenging problems in computational statistics is to use Monte Carlo techniques. Markov Chain Monte Carlo algorithms (equipped with numerus bonuses) has long provided the gold standard in this area. The situation radically changes 10 years ago with the development of deep learning: classical MCMC algorithms (Gibbs sampler, simple Metropolis-Hastings methods) fare badly for models now routinely used in today AI. This has triggered a lot of efforts in the last decade, with some initial successes, but opening new research avenues. In this talk, I will describe two approaches to raise (partially !) these issues. I will present a novel generation of methods based on non-equilibrium distributions which might be seen as a way to combine either optimization and / or normalizing flows and can be used both to sample distributions and compute normalizing constants. I will also cover new research directions allowing to enrich variational approaches with MCMC technique, a way to bridge the gap between variational inference and “plain” Monte Carlo.

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Date/Time : 04 Mar 2021 16:00
Venue : via Zoom
Speaker : Ariel Neufeld, Nanyang Technological University

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Abstract: In this talk, we first recall the mathematical concept of neural networks and its universal approximation property. Then we will show how one can combine neural networks together with tools from Stochastic Calculus, particularly the Feynman-Kac representation, to build a neural network based algorithm that can approximately solve high-dimensional nonlinear PDEs in up to 10’000 dimensions with short run times. We apply this algorithm to price high-dimensional financial derivatives under default risk.

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