Date/Time : 07 Apr 2021 16:00
Venue : via Zoom
Speaker : Guanghui HU, University of Macau

Join Zoom Meeting: https://nus-sg.zoom.us/j/82872451270?pwd=dVVtVFhacFFIc0p3eWc4TmZ2Yngzdz09&from=addon Meeting ID: 828 7245 1270 Password: 085195 In most cases the ground state would be used as an initial state in a dynamic study of a many-body electronic structure. In the numerical study with density functional theory, a complete simulation would consist of obtaining the ground state of the system by solving Kohn-Sham equation and propagating the system by solving time-dependent Kohn-Sham equation. Although there have been many libraries which can handle two processes in a unified framework, the employment of mesh adaptivity towards the efficiency of the simulation would make the realization of the algorithm much more complicated. In this talk, based on our library AFEABIC, a unified realization of the simulation of above process would be introduced. Several mathematical and technical issues, as well as our methods, would be introduced.

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Date/Time : 07 Apr 2021 14:00
Venue : via Zoom
Speaker : Shu-Yen Pan, National Tsing Hua University

Join Zoom Meeting hhttps://nus-sg.zoom.us/j/82917531325?pwd=QzVzVVdNbUZhOHlwc09MRG5nWldudz09 Meeting ID: 829 1753 1325 Password: 555209 Let $(G,G’)$ be a reductive dual pair inside a finite symplectic group. By restricting the Weil representation to the dual pair, there exists a relation (called the finite Howe correspondence) between the irreducible representations of the two groups $G,G’$. In this talk, we would like to discuss some progress on the understanding of the correspondence by using Lusztig’s classification on the representations of finite classical groups. In particular, we will focus on the following three subjects: 1. the decomposition of the uniform projection of the Weil character. 2. the commutativity between the Howe correspondence and the Lusztig correspondence. 3. the description of the Howe correspondence on unipotent characters in terms of the symbols by Lusztig.

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Date/Time : 01 Apr 2021 09:00
Venue : via Zoom
Speaker : Jayce Getz, Duke University

Join Zoom Meeting https://nus-sg.zoom.us/j/87075061185?pwd=QnNmQzNQMGxudFZ0aEIwalFTV0ZCdz09 Meeting ID: 870 7506 1185 Password: 568903 Braverman and Kazhdan proposed a conjecture, later refined by Ngo and partially set in the framework of spherical varieties by Sakellaridis, that asserts that affine spherical varieties admit Schwartz spaces, Fourier transforms, and Poisson summation formulae. In this talk I will describe explicit formulae for the Fourier transform on Braverman-Kazhdan spaces (also known as pre-flag varieties) and for certain spherical varieties that are built out of triples of quadratic spaces. Though my primary motivation comes from automorphic representation theory, these formulae should be of interest more broadly. In particular, they allow for many techniques of analytic number theory to be brought from the setting of vector spaces to the setting of spherical varieties.

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Date/Time : 01 Apr 2021 16:00
Venue : via Zoom
Speaker : Bo AN, Nanyang Technological University

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd In January 2017 CMU’s Libratus system beat a team of four top-10 headsup no-limit specialist professionals, which was the first time an AI had beaten top human players in this game. Libratus’s success is purely based on algorithms for solving large scale games and has nothing to do with deep learning! Over the last few years, algorithms for solving large scale games have also been applied to many domains such as security, sustainability, ad-word auction, and e-commerce. For some complex domains with strategic interaction, reinforcement learning is also used to learn an efficient policy. This talk will discuss key techniques behind these success and their applications in domains including games, security, e-commerce, and urban planning.

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Date/Time : 31 Mar 2021 17:00
Venue : via Zoom
Speaker : Lars Kristiansen, University of Oslo

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? We will address the following question: Do we need, or do we not need, unbounded search in order to convert one representation of an irrational number into another representation? We will consider well known representations like Cauchy sequences, Dedekind cuts, base-2 expansions, base-10 expansions and continued fractions, and maybe a few less well-know representations.

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Date/Time : 31 Mar 2021 16:00
Venue : via Zoom
Speaker : Zhou Zhennan, BICMR, Peking University

Join Zoom Meeting https://nus-sg.zoom.us/j/86252466655?pwd=Z3MxTlJIQTRBQnc1NGs3TXpDOHIzdz09&from=addon Meeting ID: 862 5246 6655 Password: 853012 We investigate the continuum limit that the number of beads goes to infinity in the ring polymer representation of thermal averages. Studying the continuum limit of the trajectory sampling equation sheds light on possible preconditioning techniques for sampling ring polymer configurations with large number of beads. In the case where the potential is quadratic, we show that the continuum limit of the preconditioned mass modified Langevin dynamics converges to its equilibrium exponentially fast, which suggests that the finite-dimensional counterpart has a dimension-independent convergence rate. An efficient sampling method, the pmmLang+RBM, is proposed to compute the quantum thermal average in the interacting quantum particle system. Benefiting from the random batch method (RBM), the pmmLang+RBM reduces the complexity due to the interaction forces per timestep from O(NP^2) to O(NP), where N is the number of beads and P is the number of particles. We also propose an extension of the pmmLang+RBM, which is based on the splitting Monte Carlo method and is applicable when the interacting potential contains a singular part.

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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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