Random homogenization of $p$-Laplacian with obstacles in perforated domain

Speaker: 

Dr. Lan Tang

Institution: 

U.T. Austin

Time: 

Tuesday, January 25, 2011 - 3:00pm

Location: 

RH 306

In this talk, we will consider the homogenization of $p$-Laplacian with
obstacles in perforated domain, where the holes are periodically
distributed and have random size. And we also assume that the $p$-capacity
of each hole is stationary ergodic.

The Subset Sum Problem, I

Speaker: 

Professor Daqing Wan

Institution: 

UCI

Time: 

Thursday, January 27, 2011 - 3:00pm

Location: 

RH 306

For a subset D in an abelian group A, the subset
sum problem for D is to determine if D has a subset S which
sums to a given element of A. This is a well known NP-complete
problem, arising from diverse applications in coding theory,
cryptography and complexity theory. In this series of two
expository talks, we discuss and outline an emerging theory
of this subset sum problem by allowing D to have some
algebraic structure.

Surfaces of constant mean curvature: theory and experiments

Speaker: 

Professor Franz Pedit

Institution: 

UMass Amherst and University of Tuebingen

Time: 

Tuesday, March 8, 2011 - 4:00pm

Location: 

RH 306

Surfaces of constant mean curvature (CMC) are a prime example of an integrable system. We will focus on the classification of compact CMC surfaces and outline the complete classification in genus one. Flows on the moduli space of CMC cylinders will provide a fine structure relating CMC tori to closed curves in 3-space, another well known integrable system. Computer images and experiments will be used to demonstrate the theoretical concepts.

Homological rigidity of Schubert varieties in compact Hermitian symmetric spaces

Speaker: 

Professor Colleen Robles

Institution: 

Texas A&M

Time: 

Tuesday, March 1, 2011 - 3:00pm

Location: 

RH 306

The integral homology of a compact Hermitian symmetric spaces (CHSS) is generated by the homology classes of its Schubert varieties. Most Schubert varieties are singular. In 1961 Borel and Haefliger asked: when can the homology class [X] of a singular Schubert variety be represented by a smooth subvariety Y of the CHSS?

Remarkably, the subvarieties Y with [Y] = [X] are integrals of a (linear Pfaffian) differential system. I will discuss recent work with Dennis The in which we give a complete list of those Schubert varieties X for which there exists a first-order obstruction to the existence of a smooth Y. This extends (independent) work of M. Walters, R. Bryant and J. Hong.

The sine qua non of our analysis is a new characterization of the Schubert varieties by a non-negative integer and a marked Dynkin diagram. The description generalizes the well-known characterization of the smooth Schubert varieties by subdiagrams of the Dynkin diagram associated to the CHSS.

I will illustrate the talk with examples.

THE APPROXIMATIONS FROM BELOW FOR EIGENVALUES OF ELLIPTIC OPERATORS BY NONCONFORMING FINITE ELEMENT METHODS

Speaker: 

Professor Yunqing Huang

Institution: 

Xiangtan University, Hunan, CHINA

Time: 

Friday, February 18, 2011 - 3:00pm

Location: 

RH 306

In this talk we will present some recent progress in the analysis of the discrete eigenvalue produced by the nonconforming finite element methods for the symmetric elliptic eigenvalue problem. We obtained the principle of yielding lower bounds of eigenvalues for nonconforming finite element methods.This principle can be used as a guide to construct new nonconforming elements or modify the existing nonconforming elements to produce lower approximation. We prove the most used nonconforming element methods in the literature for various symmetric elliptic operators provide lower approximation. Some exceptions are also shown by the numerical experiments. Our analysis is valid for nonuniform grids,general elliptic operators,general boundary conditions and works for both smooth and non-smooth eigenfunctions.
This talk is based on the joint work with Hu Jun and Lin Qun.

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