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 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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Date/Time : 21 Apr 2021 08:00
Venue : via Zoom
Speaker : Yudong Chen, Cornell University

Join Zoom Meeting https://nus-sg.zoom.us/j/83859343651?pwd=Yy9pTWRiZ1N1SGs5dVVNbHpaRTBaQT09 Meeting ID: 838 5934 3651 Password: 685719 Estimation of mixture models is a fundamental problems in machine learning and statistics. This problem is inherently nonconvex, and may possess spurious local minimizers that are not globally optimal, both in theory and in practice. In this talk, we will present three positive results for mixture problems in the lens of nonconvex optimization. For a mixture of two components, we show that all local minima are globally optimal, and EM converges to a global optimum from random initialization. This result applies to a broad class of log-concave mixture problems including mixtures of Gaussians and linear regressions. For more than two components, spurious local minima provably exist. One such local minimizer puts multiple centers at one true component, and another center in the middle of multiple true components. We prove that this is essentially the only type of spurious local minima under certain conditions. Consequently, standard algorithms such as gradient descent and EM are guaranteed to converge to a solution that partially identifies the true model. Leveraging the above structural results, we will discuss several algorithmic ideas for avoiding local minima and finding the global optimum. Over-parametrization, in which one over-specifies the number of components, stands out as a promising approach. We characterize the benefit and price of over-parametrization in terms of its computational and statistical efficiency.

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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 : 14 Apr 2021 17:00
Venue : via Zoom
Speaker : Karen Seidel, University of Potsdam

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Learning from positive and negative information, so called informant, is one of the models for human and machine learning introduced by Gold. We review existing classical and recent results regarding the learning power of associated settings.

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Date/Time : 14 Apr 2021 16:00
Venue : via Zoom
Speaker : Chaithanya Bandi, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/86983811912?pwd=NDdLMmlEUE1sSWJ0bnVFc3dNSUJ6UT09&from=addon Meeting ID: 869 8381 1912 Password: 628006 We consider the problem faced by an e-retailer that needs to display a limited set of products to a customer with no prior information. In this context, the e-retailer is allowed to query preferences in order to inform its display. A standard approach to this problem follows a two-step approach: First, estimate the preferences of the customer using a choice model, and then optimize the product display. While this approach is applicable to many settings with stationary customer preferences, this is not applicable to scenarios with changing customer preferences. In this paper, we develop a novel product-driven online framework for efficiently learning customer preferences using a structured questionnaire design. We demonstrate that our approach provably outperforms state-of-the-art methods which focus on eliciting the preference vector. Further, we formulate a robust algorithm for eliciting the optimal display set when the customer responses are noisy.   We establish theoretical foundations for our question-design mechanism and develop efficiency guarantees for our product-driven algorithm. We also present results of our implementation on a real data set obtained from a major fashion retailer.  We demonstrate that we are able to efficiently and customer preferences to inform the optimal product display, and outperform existing approaches based on “estimate, then optimize”. Joint work with Yam Huo (NU), and based on work with Jonathan Amar and Nikos Trichakis (MIT).

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