Date/Time : 19 Mar 2021 09:00
Venue : via Zoom
Speaker : Dongyi Wei, Peking University

Join Zoom Meeting Meeting ID: 852 5313 6061 Password: 863217 Abstract: We study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number $Re$ in a finite or an infinite channel. It was proved that if the perturbation of the initial velocity from the Couette flow is within $c_0{Re}^{-1}$ in the $H^2$ norm, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow, and rapidly converges to a streak solution for $t >> {Re}^{1/3}$ due to the mixing-enhanced dissipation effect. This result confirms the transition threshold conjecture proposed by Trefethen et al. (Science, 1993). The most key ingredient of the proof is the resolvent estimates for the full linearized 3-D Navier-Stokes system around the flow close Couette.

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Date/Time : 18 Mar 2021 16:00
Venue : via Zoom
Speaker : Yifei Wang, Stanford University

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Abstract We introduce a framework for Newton’s flows in probability space with information metrics, named information Newton’s flows. Extending the relationship between overdamped Langevin dynamics and Wasserstein gradient flows of Kullback-Leibler (KL) divergence, we derive Newton’s Langevin dynamics from Wasserstein Newton’s flows. We design sampling efficient variational methods in affine models and reproducing kernel Hilbert space (RKHS) to approximate Wasserstein Newton’s directions. Convergence results of the proposed information Newton’s method with approximated directions are established. Several numerical examples from Bayesian inference problems are shown to demonstrate the effectiveness of the proposed method.

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Date/Time : 18 Mar 2021 10:00
Venue : via Zoom
Speaker : Ko Liling,

oin Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Given a finite lattice L that can be embedded in the recursively enumerable (r.e.) Turing degrees (R,<) we do not in general know how to characterize the degrees d in R below which L can be bounded. The important characterizations known so far are of the L_7 and 1-3-1 lattices, where the former is bounded exactly by the degrees with fickleness strictly above omega and the latter is bounded exactly by the degrees containing sets of fickleness greater equal omega^omega. Given that the fickleness hierarchy collapses exactly to the powers of omega with the first few levels being 0,omega,omega^2,…,omega^omega, we want to find a lattice that characterizes the levels strictly above omega^2. We begin by exhausting the lattices L that are as “small” as L_7 and 1-3-1, but these lattices turn out to characterize the levels strictly above omega or from omega^omega onwards, if L is not already embeddable below all non-zero r.e. degrees. We even considered small infinite lattices but they too behave like L_7 or 1-3-1. We discovered three lattices besides 1-3-1 that also characterize the levels from omega^omega onwards. Our search for a candidate characterising the levels strictly above omega^2 therefore involves the lattice-theoretic problem of finding lattices that do not contain any of the four sublattices which characterise the levels from omega^omega onwards as a sublattice. Using this criterion as a heuristic we introduce the wide diamond lattice as a candidate, though we conjecture that this lattice also behaves like 1-3-1.

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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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