Georgia Institute of Technology College of Sciences

A teaching philosophy statement is an crucial part of your dossier. This will be a participatory workshop designed to help you write a statement of your teaching philosophy -- one that accurately reflects your personal beliefs and attitudes. We will begin with some simple exercises to help you identify what you feel is important about teaching in general and your teaching in particular. We will discuss how to translate the outcomes of these exercises into a coherent statement. With luck, there will also be plenty of time for questions. (Please bring paper and something to write with (or a laptop or tablet).)

TBA

For a nonnegative random variable Y with finite nonzero mean \mu, we say that Y^s has the Y-size bias distribution if E[Yf(Y)] = \mu E[f(Y^s)] for all bounded, measurable f. If Y can be coupled to Y^s having the Y-size bias distribution such that for some constant C we have Y^s \leq Y + C, then Y satisfies a 'Poisson tail' concentration of measure inequality. This yields concentration results for examples including urn occupancy statistics for multinomial allocation models and Germ-Grain models in stochastic geometry, which are members of a class of models with log concave marginals for which size bias couplings may be constructed more generally. Similarly, concentration bounds can be shown when one can construct a bounded zero bias coupling or a Stein pair for a mean zero random variable Y. These latter couplings can be used to demonstrate concentration in Hoeffding's permutation and doubly indexed permutations statistics. The bounds produced, which have their origin in Stein's method, offer improvements over those obtained by using other methods available in the literature. This work is joint with J. Bartroff, S. Ghosh and L. Goldstein.

In the recent past multiple orthogonal polynomials have attracted great attention. They appear in simultaneous rational approximation, simultaneous quadrature rules, number theory, and more recently in the study of certain random matrix models. These are sequences of polynomials which share orthogonality conditions with respect to a system of measures. A central role in the development of this theory is played by the so called Nikishin systems of measures for which many results of the standard theory of orthogonal polynomials has been extended. In this regard, we present some results on the convergence of type I and type II Hermite-Pade approximation for a class of meromorphic functions obtained by adding vector rational functions with real coefficients to a Nikishin system of functions (the Cauchy transforms of a Nikishin system of measures).