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Mathematics & Statistics

# Colloquia — Spring 2011

## Friday, April 8, 2011

Title
Speaker

Time
Place
Sponsor

Developmental Computing
Przemyslaw Prusinkiewicz
Department of Computer Science
University of Calgary
Canada
3:00pm-4:00pm
PHY 120
Nagle Lecture Committeee

Abstract

L-systems, introduced by Lindenmayer in 1968, provide a useful mathematical and programming framework for modeling the development of plants. Formally, (parametric) L-systems offer a means for defining growing active cell complexes, which represent the topology and geometry of the simulated structures, but also act as a dynamic domain for self-configuring systems of equations that represent functional aspects of the models. This close coupling of topology, geometry and computation can be viewed as a paradigm for computing, pioneered by, but not restricted to, biological applications of L-systems. In my presentation, I will analyze the distinctive features of this paradigm and survey selected applications of developmental computing outside the realm of biology, with an emphasis on geometric modeling.

## Friday, March 25, 2011

Title
Speaker

Time
Place
Sponsor

On non-local generalizations of the celebrated symmetry principle
Tatiana Savin
Ohio University
Athens, OH
3:00pm-4:00pm
PHY 120
Dmitry Khavinson

Abstract

This talk is devoted to generalizations of the Schwarz symmetry principle holding for harmonic functions subject to the Dirichlet or Neumann conditions on a real-analytic curve in the plane. This celebrated point-to-point reflection almost always fails for solutions to more general elliptic equations. We will consider reflection as an integro-differential operator. In this generalized form symmetry principle holds for different elliptic equations subject to different boundary conditions.

## Friday, March 4, 2011

Title
Speaker

Time
Place
Sponsor

Quantum integrable models and Heine-Stieltjes polynomials
Vitaly Tarasov
Indiana University
3:00pm-4:00pm
PHY 120
E. A. Rakhmanov

Abstract

The history of Heine-Stieltjes polynomials is 120 years long. The history of quantum integrable models is slightly shorter, only over 80 years. And these two subjects has met more than 30 years ago. The relation of two subjects is provided by separation of variables in quantum integrable models. In the talk, I will explain this relation describing a vocabulary between two areas, and will formulate some generalizations of Heine-Stieltjes polynomials motivated by the theory of quantum integrable models.

## Friday, February 25, 2011

Title

Speaker

Time
Place
Sponsor

Loops, Quasigroups and Automated Reasoning or How I Learned To Stop Worrying and Start Letting Computers Prove Theorems
Michael Kinyon
University of Denver
Denver, CO
3:00pm-4:00pm
PHY 120
Mohamed Elhamdadi

Abstract

In the past few years, automated reasoning tools have proven to be very effective in resolving open problems in the theory of quasigroups and loops. In this talk I will survey some of these results. No background in quasigroup or loop theory is needed; what is necessary will be developed in the course of the talk.

## Friday, February 4, 2011

Title
Speaker

Time
Place
Sponsor

Differential Equations on Time Scales
Yepeng Xing
Shanghai Normal University
China
3:00pm-4:00pm
PHY 120
Yuncheng You

Abstract

Differential equations on time scales were first introduced by S. Hilger in 1990 to unify differential and difference calculus. In the past ten years, it has received a great deal of attention and hundreds of papers have been published in this area. In this talk, I will briefly summarize the idea of differential equations on time scales at first and then introduce my work on this topic.

## Friday, January 7, 2011

Title
Speaker

Time
Place
Sponsor

The existence and convergence of uniform attractors for $$3$$D Brinkman-Forchheimer equations
Caidi Zhao
Wenzhou University
China
3:00pm-4:00pm
PHY 120
Yuncheng You

Abstract

This paper discusses the three dimensional ($$3$$D) Brinkman-Forchheimer equations. The authors first prove the existence of uniform attractors for the $$3$$D Brinkman-Forchheimer equations in $$\mathbb{H}^1(\Omega)$$, and then show that the uniform attractors converges to the uniform attractor of the $$3$$D Brinkman equations as the Forchheimer coefficients tend to zero.