LSU  | Mathematics

# Calendar

Time interval:   Events:

Tomorrow, Wednesday, September 20, 2017

Posted August 24, 2017

3:30 pm - 4:30 pm Lockett 233

Mike Wong, Louisiana State University
TBD

Posted August 25, 2017

3:30 pm - 4:20 pm Lockett 233

Changfeng Gui, University of Texas at San Antonio
The Sphere Covering Inequality and its applications

In this talk, I will introduce a new geometric inequality: the Sphere Covering Inequality. The inequality states that the total area of two {it distinct} surfaces with Gaussian curvature less than 1, which are also conformal to the Euclidean unit disk with the same conformal factor on the boundary, must be at least $4 pi$. In other words, the areas of these surfaces must cover the whole unit sphere after a proper rearrangement. We apply the Sphere Covering Inequality to show the best constant of a Moser-Trudinger type inequality conjectured by A. Chang and P. Yang. Other applications of this inequality include the classification of certain Onsager vortices on the sphere, the radially symmetry of solutions to Gaussian curvature equation on the plane, classification of solutions for mean field equations on flat tori and the standard sphere, etc. The resolution of several open problems in these areas will be presented. The talk is based on joint work with Amir Moradifam from UC Riverside.

Thursday, September 21, 2017

Posted August 22, 2017

3:30 pm - 4:20 pm

Hongyu He, Department of Mathematics, LSU
Branching Laws and Interlacing Relation

Abstract: Let $H$ be a subgroup of a compact group $G$. Then any irreducible unitary representation of $G$, when restricted to $H$, decomposes into a direct sum of irreducible representations of $H$. A description of such a decomposition is often called a branching law. They are important in harmonic analysis, quantum mechanics and number theory. In this talk, I shall discuss the branching laws of the discrete series of the noncompact unitary groups and the recent progress towards the local Gan-Gross-Prasad conjectures. Discrete series representations were classified by Harish-Chandra in the sixties and played a fundamental role in Langland's program.

Tuesday, September 26, 2017

Posted August 22, 2017

3:30 pm - 4:30 pm 1034 Digital Media Center

Yangyang Xu, University of Alabama
Primal-dual methods for affinely constrained problems

Abstract: Optimization has been applied in many areas including engineering, statistics, finance, and data sciences. Modern applications often have rich structure information. Traditional methods like projected subgradient and the augmented Lagrangian can be used, but they do not utilize structures of the problems and thus are not so efficient. This talk will focus on convex optimization problems with affine constraints. The first part assumes two-block structure on the problem and presents the alternating direction method of multipliers (ADMM) and its accelerated variant. With strong convexity on one block variable, the ADMM can be accelerated from O(1/k) rate to O(1/k^2). Numerical results will be given to demonstrate the improved speed. In the second part, I will present a novel primal-dual block update method for a multi-block (at least three blocks) problem. Existing works have shown that directly extending two-block ADMM to multi-block problems may diverge. To guarantee convergence, either strong assumptions are made or updating order of the blocks has to be changed. Our method uses a simple randomization technique on choosing block variables, and it enjoys O(1/k) ergodic convergence rate and also global convergence in probability. In addition, by choosing a few blocks every time and using Jacobi-type update, the method enables parallel computing with guaranteed convergence. Numerical experiments will be shown to demonstrate its efficiency compared to other methods.

Wednesday, September 27, 2017

Posted August 23, 2017

10:20 am - 11:50 am Lockett 233

Yu-Chan Chang, Louisiana State University
Introduction to bounded cohomology of discrete groups

Abstract: In this introductory talk, we will focus on bounded cohomology of discrete groups with real or integer coefficient. I will talk about the bounded cohomology of Gromov hyperbolic groups and amenable groups. Also, we will discuss the comparison map, which is the map from the bounded cohomology to the usual cohomology.

Posted August 24, 2017

3:30 pm - 4:30 pm Lockett 233

John Etnyre, Georgia Institute of Technology
TBD

Thursday, September 28, 2017

Posted August 25, 2017

3:30 pm - 4:20 pm Lockett 277

John Etnyre, Georgia Institute of Technology
Curvature and contact topology

Abstract: Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it. This is joint work with Rafal Komendarczyk and Patrick Massot.

Tuesday, October 3, 2017

Posted September 14, 2017

4:15 pm - 5:00 pm 1034 Digital Media Center

Computational Mathematics Presentations

Wednesday, October 4, 2017

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Kent Vashaw, Louisiana State University
TBD

Posted August 9, 2017

3:30 pm - 4:20 pm Lockett 233

Giles Auchmuty, University of Houston
The SVD of the Poisson kernel

Tuesday, October 10, 2017

Posted August 22, 2017

3:30 pm - 4:30 pm 1034 Digital Media Center

Xiang Xu, Old Dominion University
Eigenvalue preservation for the Beris-Edwards system modeling nematic liquid crystals

Abstract: The Beris-Edward equations are a hydrodynamic system modeling nematic liquid crystals in the setting of Q-tensor order parameter. Mathematically speaking it is the incompressible Navier-Stokes equations coupled with a Q-tensor equation of parabolic type. In this talk we first consider the simplified Beris-Edward system that corresponds to the co-rotational case, and study the eigenvalue preservation property for the initial Q-tensororder parameter. Then we show that for the full system that relates to the non-rotational case, this property is not valid in general.

Wednesday, October 11, 2017

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Rima Chatterjee, Louisiana State University
TBD

Posted August 7, 2017

3:30 pm - 4:20 pm Lockett 233

Keng Deng, University of Louisiana at Lafayette
Global existence and blow-up for nonlinear diffusion equations with boundary flux governed by memory

In this talk, we introduce the study of global existence and blow-up in finite time for nonlinear diffusion equations with flux at the boundary governed by memory. Via a simple transformation, the memory term arises out of a corresponding model introduced in previous studies of tumor-induced angiogenesis. The study is also in the spirit of extending work on models of the heat equation with local, nonlocal, and delay nonlinearities present in the boundary flux. Specifically, we establish an identical set of necessary and sufficient conditions for blow-up in finite time as previously established in the case of local flux conditions at the boundary.

Wednesday, October 18, 2017

Posted August 25, 2017

10:30 am - 12:00 pm Lockett 233

Sudipta Ghosh, Louisiana State University
TBD

Posted August 25, 2017

3:30 pm - 4:20 pm Lockett 233

Ryan Hynd, University of Pennsylvania
TBA

Posted August 27, 2017

3:30 pm - 4:30 pm Lockett 233

Robin Koytcheff, University of Louisiana, Lafayette
TBD

Tuesday, October 24, 2017

Posted September 13, 2017

2:30 pm - 3:20 pm Lockett 233

Jiahong Wu, Oklahoma State University
Partial differential equations related to fluids with partial or fractional dissipation

There have been substantial recent developments on several partial differential equations from fluid dynamics with partial or fractional dissipation. This talk summarizes results on the global existence and regularity problem for the 3D Navier-Stokes equations with partial hyperdissipation, the surface quasi-geostrophic equation, the 2D Boussinesq equations with partial or fractional dissipation and the 2D magnetohydrodynamic equations with partial or fractional dissipation.

Posted August 22, 2017

3:30 pm - 4:30 pm 1034 Digital Media Center

Joscha Gedicke, Universitaet Wien
TBA

Posted August 15, 2017

3:30 pm - 4:20 pm Lockett 233

Kun Zhao, Tulane University
TBA

Wednesday, October 25, 2017

Posted September 13, 2017

3:30 pm - 4:30 pm Lockett 233

Yilong Wang, The Ohio State University
TBD

Tuesday, November 7, 2017

Posted September 9, 2017

3:00 pm - 3:50 pm

Anna Romanov, University of Utah
TBD

Posted August 23, 2017

3:30 pm - 4:30 pm 1034 Digital Media Center

Daniele Venturi, University of California Santa Cruz
TBA

Posted August 15, 2017

3:30 pm - 4:20 pm Lockett 233

Zhifu Xie, University of Southern Mississippi
TBA

Wednesday, November 8, 2017

Posted August 23, 2017

10:30 am - 12:00 pm Lockett 233

Rob Quarles, Louisiana State University
TBD

Friday, November 10, 2017

Posted August 22, 2017

11:00 am - 12:00 pm 1034 Digital Media Center

Xiao-Chuan Cai, University of Colorado Boulder
TBA

Tuesday, November 14, 2017

Posted August 31, 2017

3:00 pm - 3:50 pm

Yifan Yang, National Taiwan University
TBD

Posted September 12, 2017

3:30 pm - 4:30 pm 1034 Digital Media Center

Shawn Walker, LSU
TBA

Thursday, November 16, 2017

Posted September 1, 2017

3:30 pm - 4:20 pm Lockett 277

Yifan Yang, National Taiwan University
TBD

Tuesday, November 28, 2017

Posted August 23, 2017

3:00 pm - 3:50 pm

Li Guo, Rutgers University at Newark
TBD

Wednesday, November 29, 2017

Posted August 23, 2017