Date/Time : 25 Mar 2021 16:00
Venue : via Zoom
Speaker : Joe Kileel, University of Texas at Austin

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Tensors are higher-order matrices, and decomposing tensors can reveal structure in datasets. In recent years, tensor decomposition has found applications in statistics, computational imaging, signal processing, and quantum chemistry. In this talk, we will present a new numerical method for low-rank symmetric tensor decomposition, building on the usual power method and ideas from classical algebraic geometry. The approach achieves a speed-up over the state-of-the-art by roughly one order of magnitude. We will also describe an “implicit” variant of the algorithm for the case of moment tensors which avoids the explicit formation of higher-order moments, analogously to matrix-free techniques in linear algebra. Time permitting, we will include a quantitative analysis of the non-convex optimization landscape associated with our algorithm. This is based on joint works with Joao Pereira, Tammy Kolda and Timo Klock.

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Date/Time : 24 Mar 2021 17:00
Venue : via Zoom
Speaker : Philipp Schlicht, University of Vienna

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract: While descriptive set theory studies definable sets of words of length omega, generalised descriptive set theory studies words of uncountable regular length. The talk will begin with an introduction to this field and its applications. I will then talk about how one can characterise when a definable set is small or admits a colouring with few colours with respect to an open graph. This is joint work with Dorottya Sziraki.

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Date/Time : 23 Mar 2021 16:30
Venue : via Zoom
Speaker : Jack Thorne, University of Cambridge

Join Zoom Meeting https://nus-sg.zoom.us/j/85360804573?pwd=WUZCVlQ5NU5kTW5TbWdMRmtWb09YZz09 Meeting ID: 853 6080 4573 Password: 645892 Abstract: Langlands functoriality predicts the transfer of automorphic representations along maps of L-groups. In particular, the symmetric power representation Symm^{n-1} of GL(2) should give rise to a lifting from automorphic representations of GL(2) to automorphic representations of GL(n). I will discuss joint work with James Newton proving the existence of all symmetric power lifts for those automorphic representations of GL(2, A_Q) associated to holomorphic modular forms.

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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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