Date/Time : 20 May 2021 16:00
Venue : via Zoom
Speaker : Yuan FANG, Singapore Management University

JJoin Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd Heterogeneous Information Networks (HIN) often model complex graph-structured data with multi-typed relationships between different types of objects. The heterogeneity gives rise to the rich semantics on HINs, such as different user interactions on social networks, and different functional associations between proteins on a biological network. Metagraphs, which model recurring subgraph structures on HINs, emerge as a powerful tool to capture the rich semantics. Compared to their simpler variant metapaths, metagraphs are higher-order structures with stronger expressiveness and can be regarded as nonlinear functions of metapaths. Not surprisingly, metagraphs can be used to derive effective graph representations on HINs, to enable various downstream tasks such as node classification and link prediction. The efficacy of metagraph-based representations can be demonstrated in various domains including social, cyberphysical and biological networks.

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Date/Time : 19 May 2021 15:00
Venue : via Zoom
Speaker : Yanlin Liu, Beijing Normal University

Join Zoom Meeting https://nus-sg.zoom.us/j/86563869492?pwd=MlRhL0k5VDhRbVFXTmFUVCtWZ0hsZz09 Meeting ID: 865 6386 9492 Passcode: 488917 We show that any unique global solution (here we do not require any smallness condition beforehand) to 3-D axisymmetric Navier-Stokes equations in some scaling invariant spaces must eventually become a small solution. In particular, we show that the limits of $\|\omega^\theta(t)/r\|_{L^1}$ and $\|u^\theta(t)/\sqrt r\|_{L^2}$ are all $0$ as $t$ tends to infinity. And by using this, we can refine some decay estimates for the axisymmetric solutions.

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Date/Time : 07 May 2021 09:00
Venue : via Zoom
Speaker : Weiqiang Wang, University of Virginia

Join Zoom Meeting https://nus-sg.zoom.us/j/82997442700?pwd=TzI5bGJEM2JMb1o0enFRMFlReEZLZz09 Meeting ID: 829 9744 2700 Passcode: 178346 The original quantum Schur duality (due to Jimbo) concerns about commuting actions on a tensor space of a quantum group and a Hecke algebra of type A. Several years ago, Huanchen Bao and I generalized this to a duality between a Hecke algebra of type B and an i-quantum group arising from quantum symmetric pairs. Both dualities are deeply connected to canonical basis, flag varieties, and Kazhdan-Lusztig theory of type ABC. In this talk, I will explain a new unification of both dualities, which leads to an unexpected generalization of Kazhdan-Lusztig construction. This is joint work with Yaolong Shen.

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Date/Time : 28 Apr 2021 15:00
Venue : via Zoom
Speaker : Chao Liu, Huazhong University of Science and Technology

Join Zoom Meeting https://nus-sg.zoom.us/j/81653239587?pwd=U2lCTS9qV01IejN3VDJ2eDB4dml2UT09 Meeting ID: 816 5323 9587 Password: 918779 Motivated by the astrophysical problems of star formations from molecular clouds, we make the first step on the possible behaviors of certain molecular clouds. This talk (1) establishes the diffuse boundary problem of Euler-Poisson system for describing the evolution of molecular clouds; (2) proves the local existence, uniqueness and continuation principle of the classical solution to the diffuse boundary problem; (3) proves the classical solution (without any symmetry condition) to the diffuse problem blows up at finite time if there is no the first class of global solution and the data is admissible (large scale, irregularly-shaped, expanding and rotational molecular clouds); (4) proves certain singularities can be removed from the boundary if the data is strongly admissible. This result partially answers Makino’s conjecture (1992) on the finite blowup of any tame solution without symmetries and gives the possibilities of star formations, fragmentation and possibilities of formations of shocks and physical vacuum boundary in perfect fluids with Newtonian self-gravity. This talk is based on the article arXiv:2102.11550.

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Date/Time : 27 Apr 2021 15:00
Venue : via Zoom
Speaker : Jinxin Xue, Tsinghua University

Join Zoom Meeting https://nus-sg.zoom.us/j/86384771548?pwd=RnMzcXJrcUtERmFrbHVXMUFrejVsZz09 Meeting ID: 863 8477 1548 Password: 244323 In this talk, we study the dynamics of geodesic flows in perturbed blackhole backgrounds using the techniques of Hamiltonian dynamics. The central object in our work is the blackhole shadow. It gives a normally hyperbolic invariant submanifold in the phase space and is robust under perturbations. We find a gap structure within the blackhole shadow and also use it to construct long chaotic orbit with large oscillation of angular momentum. Moreover, similar methodology applies to the event horizon of Kerr to give chaotic orbit skirting around the event horizon.

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Date/Time : 23 Apr 2021 16:00
Venue : via Zoom
Speaker : Jiange Li, Hebrew University of Jerusalem

Join Zoom Meeting Meeting ID: 872 8371 4051 Password: 226133 Abstract:  The balls into bins problem is a classical problem in probability theory that has many applications in computer science. It involves m balls and n bins. Each time, a ball is placed into a bin selected uniformly at random. We are interested in the following two-thinning variant. For each ball, after a random bin has been selected, we may choose to either accept it or place the ball into a new random bin. We are not aware of the secondary allocation before deciding whether accept the primary allocation. We show explicit strategies that can achieve nearly optimal maximum loads. Comparisons are also drawn between this two-thinning variant and the well-known two-choice variant, in which case one selects two random bins and places a ball into the less loaded bin and ties are broken arbitrarily. (This talk is based on joint work with Ohad Noy Feldheim and Ori Gurel-Gurevich.)

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Date/Time : 22 Apr 2021 16:00
Venue : via Zoom
Speaker : Anqi Qiu, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/88213418159?pwd=K2lPSXEvemZGSXhiVGYxTVUzQ0d3QT09 Meeting ID: 882 1341 8159 Password: pcasvd The Laplace-Beltrami operator is a generalization of the Euclidean representation of the Laplace operator to an arbitrary Riemannian manifold. It is a self-adjoint operator and its eigenfunctions form a complete set of real-valued orthonormal basis functions. In this talk, I will introduce spectral Laplace-Beltrami wavelets and its computational algorithm. I will then demonstrate its use for smoothing and classification of the data defined on smooth surfaces embedded in the 3-D Euclidean space. Furthermore, I will discuss that the spectral Laplace-Beltrami Wavelets can be used for the construction of geometric convolutional neural network (CNN) and then introduce a vertex-based geometric CNN algorithm for regular surfaces in which translation and downsampling on surfaces can be the same as those in the regular grid. I will show the use of this method for the prediction of Alzheimer’s Disease.

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Date/Time : 21 Apr 2021 15:00
Venue : via Zoom
Speaker : Andrea Granelli, Credit Suisse

Join Zoom Meeting https://nus-sg.zoom.us/j/82328711543?pwd=WEllYTc2aE1IbU5ETEk3dERKV1JHQT09 Meeting ID: 823 2871 1543 Passcode: 266585 Understanding variance risk is of key importance in mathematical finance since it affects risk management, asset allocation and derivative pricing. Variance risk is priced in financial markets by the so-called variance risk premium (VRP), which refers to the premium demanded for holding assets whose variance is exposed to stochastic shocks. This paper identifies a new modelling framework for equity indices and presents for the first time explicit analytical formulas for their VRP in a multivariate stochastic volatility setting, which includes multivariate non-Gaussian Ornstein-Uhlenbeck processes and Wishart processes. Moreover, we propose to incorporate contagion within the equity index via a multivariate Hawkes process and find that the resulting dynamics of the VRP represent a convincing alternative to the models studied in the literature up to date. We show that our new model can explain the key stylized facts of both equity indices and individual assets and their corresponding VRP, while popular (multivariate) stochastic volatility models fail. We finally prove the existence of a structure-preserving risk neutral measure for our model. In particular, we establish the class of equivalent probabilities that preserve the self-affecting structure of the Hawkes process.

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Date/Time : 21 Apr 2021 14:00
Venue : via Zoom
Speaker : Ming-Lun Hsieh, Academia Sinica

Join Zoom Meeting https://nus-sg.zoom.us/j/82234939628?pwd=TVRlLzBmS1VsaXhVZ3k5OWtXVlZYdz09 Meeting ID: 822 3493 9628 Password: 838848 Abstract: Darmon, Dasgupta and Pollack in 2011 applied the Eisenstein congruence for Hilbert modular forms to prove the rank one Gross conjecture for Deligne-Ribet p-adic L-functions under some technical assumptions. These assumptions were later lifted by Ventullo. In this talk, we will explain how to apply their ideas in the setting of CM congruence and compute the first derivative of the Katz p-adic L-functions associated with ring class characters of imaginary quadratic fields at the triviall zero. We will present a precise first derivate formula of the Katz p-adic L-functions in terms of certain Gross p-adic regulator and p-adic logarithms of elliptic units. This proves a formula proposed in a recent work of Betina and Dimitrov. This talk is based on a joint work with Masataka Chida.

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