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 : 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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Date/Time : 30 Oct 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Luminita Danaila, University of Rouen Normandy

Date/Time:06 Nov 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Ionut Danaila, University of Rouen Normandy Numerical methods and finite-element toolboxes for the simulation of Bose-Einstein condensates We present several numerical tools using classical finite elements with mesh adaptivity for solving different models used for the study of Bose-Einstein condensates. The programs are written as toolboxes for FreeFem++ (www.freefem.org), a free finite-element software, allowing to easily implement various numerical algorithms [1]. For solving the stationary (imaginary-time) Gross-Pitaevskii equation, we use two robust and optimised numerical methods: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library IPOPT. A very recent conjugate-gradient method using concepts of Riemannian optimization is also presented [2]. For the Bogoliubov-de Gennes system, representing a linearisation of the Gross-Pitaevskii equation, a Newton method and a fast algorithm based on ARPACK for the calculation of eigenvalues are available. For the real-time Gross-Pitaevskii equation, classical splitting and relaxation methods were implemented and intensively tested. Validations and illustrations are presented for computing difficult configurations with vortices observed in physical experiments: single-line vortex, Abrikosov lattice, giant vortex, dark/anti-dark solitons in one or two-component Bose-Einstein condensates [3]. [1] G. Vergez, I. Danaila, S. Auliac, F.Hecht, A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation, Computer Physics Communications, 209, p. 144-162, 2016. [2] I. Danaila, B. Protas, Computation of Ground States of the Gross-Pitaevskii Functional via Riemannian Optimization, SIAM J. Sci. Comput. Vol. 39, No. 6, pp. B1102-B1129, 2017. [3] I. Danaila, M. A. Khamehchi, V. Gokhroo, P. Engels and P. G. Kevrekidis, Vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates, Phys. Rev. A 94, 053617, 2016. Add to calendar: 

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Date/Time : 30 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Xin Nie , Tsinghua University

Date/Time:30 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Xin Nie, Tsinghua University Planar convex domains and cubic differentials The Cheng-Yau affine sphere construction endows every properly convex domain in the real projective planar with a canonical holomorphic cubic differential. We will first explain this construction and its consequences on the moduli space of convex real projective structures, then we will talk about some recent results and open problems arising from the construction. Add to calendar: 

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Date/Time : 30 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Zou Jialiang,

Date/Time:30 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Zou Jialiang Structure of Spherical Varieties Given a spherical variety X for a group G over a non-Archimedean local field k, Sakellaridis and Venkatesh have formulated an approach to study the spectral decomposition of L^2(X) in the framework of Langlands functoriality. We will study this theory in the next few weeks. In this talk, I will present some basic knowledge of spherical variety including 1. The definition of spherical variety 2. The Luna-Vust theory about the classification of embeddings of a spherical pair H/G. Some special embeddings like toroidal embedding and wonderful compactification. 3. The knop action on spherical and the little Weyl group. 4. The dual group G_X^{\vee} of the spherical variety and the distinguished morphism. 5. Some rationality properties of the spherical variety. Reference: 1. Sakellaridis, Y. (2008). On the unramified spectrum of spherical varieties over p-adic fields. Compositio Mathematica, 144(4), 978-1016. Part 2&3. 2. Sakellaridis, Y., Venkatesh, A., & Venkatesh, A. (2017). Periods and harmonic analysis on spherical varieties. Société mathématique de France. Chapter 2. Add to calendar: 

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Date/Time : 30 Oct 2019 16:00
Venue : S17 #06-11
Speaker : Xu Binbin , University of Luxembourg

Date/Time:30 Oct 2019 16:00 Venue: S17 #06-11 Speaker: Xu Binbin, University of Luxembourg Ambartzumian-Pleijel identity in hyperbolic geometry Given a convex compact domain in Euclidean plane with C1 boundy, a measure on the space of all straight lines invariant under the isometry group of Euclidean plane induces a distribution on the positive real line, by considering the length of the intersection of straight lines with this domain. Ambartzumian-Pleijel identity is about computing the integral of any real valued C1 function on the positive real line with respect to this distribution. In this talk, we’ll introduce the counterpart of this identity in hyperbolic geometry. Then we will discuss some of its applications. In particular, it can be used to prove Croftin formula and the isoperimetric inequality in hyperbolic geometry. I’ll also discuss some of its generalizations in other context. Add to calendar: 

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Date/Time : 25 Oct 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Xiao Zhang, Guangxi University

Date/Time:25 Oct 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Xiao Zhang, Guangxi University Bondi-Sachs Spacetimes and the Bondi Energy Bondi-Sachs spacetimes were originally introduced by Bondi for axi-symmetric spacetimes, and generalized by Sachs to general asymptotically flat spacetimes for the zero cosmological constant. In this framework, Bondi defined the Bondi energy-momentum at null infinity, which represents the rest energy of spacetimes after the loss due to gravitational radiation. In this talk, we shall discuss, for zero cosmological constant, whether the Bondi energy is nonnegative? How the Bondi energy-momentum relates to the ADM energy-momentum defined at spatial infinity? We shall also discuss the natural boundary condition and the peeling property when the cosmological constant is nonzero. The talk is based on some joint works with W-l. Huang, Yau and F. Xie. Add to calendar: 

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Date/Time : 24 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Yang Yue, National University of Singapore

Date/Time:24 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Yang Yue, National University of Singapore Ramsey’s Theorem on trees and weak Koenig’s Lemma Ramsey’s Theorem for Pairs has been studied intensively in reverse mathematics. One of the major breakthroughs is Liu Lu’s 2012 result showing RT-2-2 does not imply WKL-0. Liu’s result not only answered an important question in reverse mathematics, the technique that he used turns out to have wider applications, for example, in Monin and Patey’s separation of SRT-2-2 and RT-2-2. In this talk, we generalize Liu’s result to tree. Let TT-2-k denote the combinatorial principle stating that every k-coloring of pairs of compatible nodes on the full binary tree has a homogeneous solution, i.e. an infinite perfect tree in which all pairs of compatible nodes have the same color. We show that over the base system RCA-0, TT-2-k doe not imply weak Koenig’s lemma. This is joint work with Chong Chitat, Li Wei and Liu Lu. Add to calendar: 

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Date/Time : 23 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Allan Merino, National University of Singapore

Date/Time:23 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Allan Merino, National University of Singapore Character Varieties Giving a pair (Gamma, G), where Gamma is a finitely generated group and G a complex algebraic reductive group, we define the GIT-quotient Hom(Gamma, G) // G: it’s the character variety corresponding to (Gamma, G). One can determine a set of generators when G = SL(V), Sp(V) and O(V) using results of Weyl and Procesi, and for G = SO(V) using a paper of Zhu-Aslaksen-Tan and a recent result of Sikora. In my talk, I will explain first how can we determine these generators. At the end, I will present an ongoing project, joint with Clement Guerin, concerning the character variety of Spin(n) and G2. Add to calendar: 

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