# Research

## Analysis

### Friday, April 15, 2005

Title: Absolute Minimizers on Carnot Groups
Speaker: Thomas Bieske
Time: 5:00pm–6:00pm
Place: PHY 120

#### Abstract

Aronsson (1967) first considered the problem of canonically extending a Lipschitz function on the boundary of a domain in $$\mathbb{R}^n$$ into the whole domain without raising the Lipschitz constant. This problem was solved by R. Jensen (1993). We consider the same problem in a class of non-abelian groups, called Carnot groups, which are also non-isotropic metric spaces.

In addition, properties of such minimizers are discussed.

### Friday, February 25, 2005

Title: Generalizations of Chebyshev Polynomials and Polynomial Mappings
Speaker: James Griffin, University of Central Florida
Time: 5:00pm–6:00pm
Place: PHY 120

#### Abstract

Generalized Chebyshev Polynomials orthogonal on two disjoint intervals have a representation in terms of elliptic functions. I will present the general case on several intervals and discuss their application to inverse images of a single interval under a polynomial mapping. I will also discuss some recent results on further generalizations of the classical orthogonal polynomials to the several interval case.

### Friday, February 18, 2005

Title: How come $$1+1=3$$?
Speaker: Wen-Xiu Ma
Time: 5:00pm–6:00pm
Place: PHY 120

### Friday, February 11, 2005

Title: Plancherel-Rotach asymptotics for $$q$$-orthogonal polynomials and a $$q$$-Airy function
Speaker: Mourad Ismail, University of Central Florida
Time: 5:00pm–6:00pm
Place: PHY 120

### Friday, February 4, 2005

Title: Algebra of Approximation: Introductory overview
Speaker: Boris Shekhtman
Time: 5:00pm–6:00pm
Place: PHY 120

#### Abstract

This seems to be a hot new topic with many possibilities for interesting discoveries in Analysis and Algebraic Geometry.