Date/Time : 14 Nov 2019 17:00
Venue : S17 #06-11
Speaker : Thilo Weinert, National University of Singapore

Date/Time:14 Nov 2019 17:00 Venue: S17 #06-11 Speaker: Thilo Weinert, National University of Singapore Partition Relations for Linear Orders in a Choiceless Context Most Partition Relations are proved for Ordinals, not general linear orders. This is due to the Axiom of Choice which I will consequently ignore during most of the lecture. Some exceptions to the rule mentioned at the beginning can be found in a 1971 paper by Erdoes, Milner and Rado and I will present some analogous results for linear orders which are given rise to by lexicographically ordered sequences of zeros and ones. I will close by discussing an open problem in this context. This is joint work (from a few years back) with Philipp Luecke and Philipp Schlicht. Add to calendar: 

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Date/Time : 13 Nov 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Li Ji, National University of Singapore

Date/Time:13 Nov 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Li Ji, National University of Singapore Numerical Algorithms of Phase Retrieval Phase retrieval is of paramount importance in a broad range of applications in engineering and imaging sciences. Mathematically, it amounts to solving a system of nonlinear quadratic equations, which is generally NP-hard. In this talk, we will give a numerical review of the problem and emphasize the different interests between the applied mathematicians and physicians. In other words, much research achievement of applied mathematicians has not intrigue the interests of physicians. One such reason is the simpler landscape of the resulting formulation. For example, the ambiguity solutions for practical phase retrieval is more complicated than phase retrieval from random sensing measurements. Thus the sound good solvers for random phase retrieval fails in locating a satisfying solution for practical phase retrieval. After we review the numerical algorithms for phase retrieval in literature, we introduce our recent work on phase retrieval, which tries its best to close the gap of random and practical phase retrieval. Our work gives some implications for designing the numerical algorithm for practical phase retrieval. Add to calendar: 

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Date/Time : 13 Nov 2019 10:00
Venue : S16 #03-09
Speaker : Wan Xiaolei,

Date/Time:13 Nov 2019 10:00 Venue: S16 #03-09 Speaker: Wan Xiaolei The formula with L-value of the spherical varieties This is the third talk of Sakellaridis’ work on Spherical Varieties and Spherical Functions. We will give a brief review of the first two talks, then we complete one of the main theorems of this talk. Namely, under some conditions, we can give an explicit formula of the eigenfunctions of the Hecke algebra in the space of spherical functions on a spherical variety. And then we can define the L-function of spherical varieties which related to the special value of the eigenfunctions. Finally we show some examples of the calculation of the L-value. The importance of the L-value lies in its relationship with the period integrals of automorphic forms. Add to calendar: 

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Date/Time : 13 Nov 2019 14:00
Venue : S17 #04-05 SR2
Speaker : Li Zimu,

Date/Time:13 Nov 2019 14:00 Venue: S17 #04-05 SR2 Speaker: Li Zimu A Global Geometric Approach to Parallel Transport of Strings in Gauge Theory In this talk, we will introduce a global geometric method to formulate the concept of parallel transport on surfaces, which first is studied in the context of higher gauge theory as an extension of the classical notion of parallel transport along paths. We will discuss a generalized 3-dimensional non-abelian Stokes’ theorem related to parallel transport on surfaces. After that, we will extend this theorem to four dimension by replacing the underlying algebraic structure: crossed module with crossed 2-module. This 4-dimensional Stokes’ theorem further yields a global formula for parallel transport on volumes, and guarantees its gauge invariance with other important properties which have been seen in the case of surfaces. Add to calendar: 

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Date/Time : 07 Nov 2019 17:00
Venue : S17 #06-11
Speaker : Chong Chi Tat, National University of Singapore

Date/Time:07 Mar 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Wu Bin On Large Games with Bio-social Traits This paper shows that, in a class of large games with traits model, distinguishing agent space and trait space via the nowhere equivalence condition is not only sufficient but also necessary for the existence of pure strategy Nash equilibrium and closed graph property. Furthermore, under the nowhere equivalence condition, we characterize Nash equilibria of large games with traits. Add to calendar: 

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Date/Time : 06 Nov 2019 10:00
Venue : S16 #03-09
Speaker : Tian Fangyang, National University of Singapore

Date/Time:06 Nov 2019 10:00 Venue: S16 #03-09 Speaker: Tian Fangyang, National University of Singapore Spherical Functions on Spherical Varieties – Explicit Formula of Eigenfunctions of Hecke Algebra This talk is a sequel of the report of Sakellaridis’ work on Spherical Varieties and Spherical Functions. Based on the geometric background which Zou Jialiang talked about last week, we will in this talk focus on the representation theoretic aspect of spherical varieties. We will start from some Bruhat-Mackey theorem on spherical varieties (distributions on orbit-spaces) and its relation with the standard interwining operators. Under a suitable normalization of these intertwining operators via the Fourier transform (of Braverman-Kazhdan), we will present Sakellaridis Theorem 1.2.1 in his 2013 paper, which provides an explicit formula for the eigenfunction of the Hecke algebra in the space of spherical functions on a spherical variety. Add to calendar: 

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Date/Time : 06 Nov 2019 14:00
Venue : S17 #04-06 SR1
Speaker : In-Jee Jeong, Korea Institute for Advanced Study

We introduce the incompressible Euler equations, which describe the dynamics of volume-preserving inviscid fluids, and describe a few open problems in relation to turbulence. Then we discuss a priori estimates, which give upper bounds on the solution in function spaces. In particular, these estimates guarantee that if the initial fluid velocity is smooth, then there is a unique smooth solution for some time interval. After that, we shall review some recent results towards the opposite direction: attempts in showing lower bounds on the solution instead, with the goal of establishing finite-time singularity formation.

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Date/Time : 06 Nov 2019 16:00
Venue : S17 #06-11
Speaker : Jonathon Teo , National University of Singapore

Date/Time:06 Nov 2019 16:00 Venue: S17 #06-11 Speaker: Jonathon Teo, National University of Singapore Branes in the moduli space of parabolic Higgs bundles In this talk, we will be looking at some constructions of families of branes in the moduli space of stable parabolic Higgs bundles. We will first be introducing the moduli space of rank 2 stable parabolic Higgs bundles over the complex projective curve, which is a hyperkahler manifold and contains the cotangent bundle of the moduli space of stable parabolic bundles. The family of branes are constructed from complex or Lagrangian submanifolds of the moduli space of stable parabolic bundles. Thus, a deformation of the submanifolds in the moduli space of stable parabolic bundles gives us a deformation of branes. We will also show that this deformation space is degenerate. Add to calendar: 

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Date/Time : 31 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Marat Arslanov, Kazan Federal University

Date/Time:31 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Marat Arslanov, Kazan Federal University n-c.e. degrees, CEA operators and fixed-point selection functions The subjects listed in the title of my talk belong to my steady scientific interest. In my talk I will speak about my recent work in these areas and list few open problems that have arisen as a result of these studies and that I can’t answer. Note: The originally planned talk by Wu Guohua for that day will be moved to the next semester. Apologies for the short notice change. Add to calendar: 

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