Colloquia & Seminars Archives - Page 115 of 129

Seminars: Colloquia & Seminars

Date
Time
Venue

Speaker
Affiliation
Title of Talk

22 Nov 2019
14:00
S17 #04-04 SR3

Brice Loustau
TU Darmstat
Computing harmonic maps between Riemannian manifolds

Computing harmonic maps between Riemannian manifolds

Date/Time : 22 Nov 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Brice Loustau, TU Darmstat

Date/Time:22 Nov 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Brice Loustau , TU Darmstat Computing harmonic maps between Riemannian manifolds The theory of harmonic maps between Riemannian manifolds goes back to the foundational work of Eells-Sampson and Hartman. Using the heat flow method, i.e. the gradient flow for the energy functional, they showed existence and uniqueness of harmonic maps between compact Riemannian manifolds when the target has negative sectional curvature. In order to compute such harmonic maps effectively, we discretize the theory by introducing meshes of the domain manifold, which consist of a geodesic triangulation with vertex and edge weights. By studying the convexity properties of the energy functional, we show that the discrete heat flow method converges to unique discrete harmonic maps. Moreover, under suitable assumptions, the discrete theory converges back to the smooth theory when taking finer and finer meshes. In particular, the smooth harmonic map can be obtained as the limit of discrete harmonic maps, equivalently as the double limit of the discrete heat flow when iterating both the time and space discretization steps. Time permits, we will also discuss center of mass methods to compute harmonic maps. We feature a concrete illustration of these methods withHarmony, a computer software with a graphical user interface that we developed in C++, whose main functionality is to numerically compute and display equivariant harmonic maps between hyperbolic disks. Add to calendar:

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21 Nov 2019
10:00
S17 #04-06 SR1

Yao Cheng
Institute of Mathematics, Academia Sinica
On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

Date/Time : 21 Nov 2019 10:00
Venue : S17 #04-06 SR1
Speaker : Yao Cheng, Institute of Mathematics, Academia Sinica

This is the last talk of a series of four talks on the discussion of the papers [Sak08], [Sak13] and [Sak12]. The present talk consists of two parts. In the ﬁrst part of this talk I will ﬁrst brieﬂy review some results in the previous talks and then discuss [Sak13, Part 3] on applications of the explicit formulae for spherical functions on spherical varieties. In the second part of this talk I will give an overview of the paper [Sak12] with emphasis on section 3 and section 4 which I hope it can be served as an introduction to that paper. References [Sak08] Yiannis Sakellaridis. On the unramiﬁed spectrum of spherical varieties over p-adic ﬁelds. Compositio Mathematica, 144(4):978–1016, 2008. [Sak12] Yiannis Sakellaridis. Spherical varieties and integral representations of L-functions . Algebra number theory, 6(4):611–667, 2012. [Sak13] Yiannis Sakellaridis. Spherical functions on spherical varieties. American Journal of Mathematics, 135(5):1291–1381, 2013.

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21 Nov 2019
10:00
S17 #04-06 SR1

Yao Cheng
Institute of Mathematics, Academia Sinica
On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

Date/Time : 21 Nov 2019 10:00
Venue : S17 #04-06 SR1
Speaker : Yao Cheng, Institute of Mathematics, Academia Sinica

Date/Time:21 Nov 2019 10:00 Venue: S17 #04-06 SR1 Speaker: Yao Cheng, Institute of Mathematics, Academia Sinica On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions This is the last talk of a series of four talks on the discussion of the papers [Sak08], [Sak13] and [Sak12]. The present talk consists of two parts. In the ﬁrst part of this talk I will ﬁrst brieﬂy review some results in the previous talks and then discuss [Sak13, Part 3] on applications of the explicit formulae for spherical functions on spherical varieties. In the second part of this talk I will give an overview of the paper [Sak12] with emphasis on section 3 and section 4 which I hope it can be served as an introduction to that paper. References [Sak08] Yiannis Sakellaridis. On the unramiﬁed spectrum of spherical varieties over p-adic ﬁelds. Compositio Mathematica, 144(4):978–1016, 2008. [Sak12] Yiannis Sakellaridis. Spherical varieties and integral representations of L-functions . Algebra number theory, 6(4):611–667, 2012. [Sak13] Yiannis Sakellaridis. Spherical functions on spherical varieties. American Journal of Mathematics, 135(5):1291–1381, 2013. Add to calendar:

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14 Nov 2019
17:00
S17 #06-11

Thilo Weinert
National University of Singapore
Partition Relations for Linear Orders in a Choiceless Context

Partition Relations for Linear Orders in a Choiceless Context

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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13 Nov 2019
16:00
S17 #05-11 SR5

Li Ji
National University of Singapore
Numerical Algorithms of Phase Retrieval

Numerical Algorithms of Phase Retrieval

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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13 Nov 2019
10:00
S16 #03-09

Wan Xiaolei

The formula with L-value of the spherical varieties

The formula with L-value of the spherical varieties

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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13 Nov 2019
14:00
S17 #04-05 SR2

Li Zimu

A Global Geometric Approach to Parallel Transport of Strings in Gauge Theory

A Global Geometric Approach to Parallel Transport of Strings in Gauge Theory

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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07 Nov 2019
17:00
S17 #06-11

Chong Chi Tat
National University of Singapore
The work of Gerald Sacks

The work of Gerald Sacks

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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06 Nov 2019
10:00
S16 #03-09

Tian Fangyang
National University of Singapore
Spherical Functions on Spherical Varieties – Explicit Formula of Eigenfunctions of Hecke Algebra

Spherical Functions on Spherical Varieties – Explicit Formula of Eigenfunctions of Hecke Algebra

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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