Date/Time : 18 Sep 2019 16:00
Venue : S16 #03-09
Speaker : Chen Haoyang, Fudan University

Date/Time:18 Sep 2019 16:00 Venue: S16 #03-09 Speaker: Chen Haoyang, Fudan University Global regularity for Einstein-Klein-Gordon system with $U(1) \times \mathbb{R}$ isometry group In this paper we prove the global regularity of the 3+1 dimensional Einstein-Klein-Gordon system with a $U(1)\times \mathbb{R}$ isometry group. We reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2+1 dimensional system. We prove that the energy of this system cannot concentrate near the first possible singularity, and hence is small. Then, we show that the global regularity holds for the reduced 2+1 dimensional system with initial data of small energy. Add to calendar: 

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Date/Time : 02 May 2019 16:00
Venue : S17 #06-11
Speaker : Zhang Shuangjian, École Nationale de la Statistique et de l'Administration Économique, Paris, France

Date/Time:02 May 2019 16:00 Venue: S17 #06-11 Speaker: Zhang Shuangjian, École Nationale de la Statistique et de l’Administration Économique, Paris, France On concavity of the principal’s profit maximization facing agents who respond nonliearly to prices A monopolist wishes to maximize her profits by finding an optimal price policy. After she announces a menu of products and prices, each agent will choose to buy that product which maximizes his own utility, if positive. The principal’s profits are the sum of the net earnings produced by each product sold. These are determined by the costs of production and the distribution of products sold, which in turn are based on the distribution of anonymous agents and the choices they make in response to the principal’s price menu. In this talk, we describe a necessary and sufficient condition for the convexity or concavity of the principal’s problem, assuming each agent’s disutility is a strictly increasing but not necessarily affine (i.e. quasilinear) function of the price paid. Concavity when present, makes the problem more amenable to computational and theoretical analysis; it is key to obtaining uniqueness and stability results for the principal’s strategy in particular. Even in the quasilinear case, our analysis goes beyond previous work by addressing convexity as well as concavity, by establishing conditions which are not only sufficient but necessary, and by requiring fewer hypotheses on the agents’ preferences. Moreover, the analytic and geometric interpretations of a specific condition relevant to the concavity of the problem have been explored. This talk represents joint work with Robert McCann. Add to calendar: 

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Date/Time : 18 Apr 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Tian Fangyang, National University of Singapore

Date/Time:18 Apr 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Tian Fangyang, National University of Singapore Laplacian Equations from a Representation-Theoretic Point of View The classical Laplacian equation and wave equation are the basic examples of second order PDE. The fundamental solutions of them, which have been well studied, play an important role in the theory of these equations. A nice feature of these two equations is that the differential operator is invariant under certain classical group, hence one may expect a representation theoretic explanation of these equations. The (indefinite) Laplacian equations serve as a natural generalization of classical Laplacian equation and wave equation. In this talk, I will follow Howe and Tan’s exposition to discuss the (indefinite) Laplacian equation from a representation-theoretic point of view. We will cover some basic representation theory of (sl(2,R), so(2))-module, Weil representation of \tilde{SL(2,R)}, and the fundamental solutions of the indefinite Laplacian Equation. Add to calendar: 

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Date/Time : 15 Apr 2019 16:00
Venue : S17 #06-11
Speaker : Deng Changsong, Wuhan University

Date/Time:15 Apr 2019 16:00 Venue: S17 #06-11 Speaker: Deng Changsong, Wuhan University Space and Time-Fractional Equations: a Random Time-Change Approach I will talk about a class of non-local equations with fractional operators in time and space from the point of view of the probability theory. In particular, we establish the exact asymptotic formulas for the fundamental solution to the $n$-dimensional fractional heat equations in both time and space. Add to calendar: 

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Date/Time : 15 Apr 2019 17:00
Venue : S17 #06-11
Speaker : Lin Wayne, Lu Jianlong, Lim Zhan Feng, An X, National University of Singapore

Date/Time:15 Apr 2019 17:00 Venue: S17 #06-11 Speaker: Lin Wayne, Lu Jianlong, Lim Zhan Feng, An X, National University of Singapore Black Hole Quartet We will present four 15-minute introductory talks on black holes: i) An introduction to black hole (by Lin Wayne) ii) Frozen star paradox (by Lu Jianlong) iii) Gravitational collapse under spherical symmetry (by Lim Zhan Feng) iv) What’s inside a black hole? (by An Xinliang) Add to calendar: 

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Date/Time : 11 Apr 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Jiang Meiyue, Peking University

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Date/Time : 04 Apr 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Subhroshekhar Ghosh, National University of Singapore

Date/Time:04 Apr 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Subhroshekhar Ghosh, National University of Singapore Two manifestations of rigidity in point sets : forbidden regions and maximal degeneracy A point process is said to be “rigid” if its local observables are completely determined (as deterministic functions of) the point configuration outside a local neighbourhood. For example, it has been shown in earlier work that, in the Ginibre ensemble (a.k.a. the 2D Coulomb gas at inverse temperature beta=2), the point configuration outside any bounded domain determines, almost surely, the number of points in the domain. In this talk, we will explore two recent manifestations of such rigidity phenomena. For the zeros of the planar Gaussian analytic function, we show that outside every large “hole”, there is a “forbidden region” which contains a vanishing density of points. This should be seen in contrast with the corresponding situation for classically understood models (e.g. random matrix ensembles), where no such effects are known to occur. In the second part of the talk, we will consider “stealthy” hyperuniform systems, which are systems whose structure function (i.e., the Fourier transform of the two-point correlation) vanishes near the origin. We show that such systems exhibit “maximal degeneracy”, namely the points outside a bounded domain determine, almost surely, the entire point configuration inside the domain. En route, we establish a conjecture of Zhang, Stillinger and Torquato that such systems have (deterministically) bounded holes. Based on joint works with Joel Lebowitz and Alon Nishry. Add to calendar: 

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Date/Time : 19 Mar 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Dejan Gajic, University of Cambridge

Date/Time:28 Mar 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Dejan Gajic, University of Cambridge Quasinormal modes on black hole spacetimes A fundamental problem in the context of Einstein’s equations of general relativity is to understand the evolution of small perturbations of stationary black hole solutions. It is expected that there is a discrete set of characteristic frequencies that play a dominant role at late times and carry information about the nature of the black hole, similar to the normal frequencies of a vibrating guitar string. These frequencies are called quasinormal frequencies and they are closely related to scattering resonances in the study of Schrödinger’s equation. I will consider the linear wave equation on black hole backgrounds as a toy model for the Einstein equations and give an introduction to quasinormal frequencies in this setting. Then I will discuss a new method of defining and studying quasinormal frequencies on asymptotically flat spacetimes, developed from joint work with Claude Warnick, which interprets the frequencies as honest eigenvalues of a natural operator acting on a Hilbert space. Add to calendar: 

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Date/Time : 14 Mar 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Li Qianxiao, National University of Singapore

Date/Time:14 Mar 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Li Qianxiao, National University of Singapore A Mean-field Optimal Control Formulation of Deep Learning In this talk, we discuss formulating, through a continuous-time approximation, deep supervised learning as a mean-field optimal control problem. We prove necessary conditions for optimality in the form of a mean-field Pontryagin’s maximum principle, as well as global characterizations of optimality using Hamilton-Jacobi-Bellman equations. Interesting learning algorithms derived from this approach will also be discussed. Add to calendar: 

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