Georgia Institute of Technology College of Sciences

The loops on a topological space up to an equivalence relation called homotopy form a group called the fundamental group. We'll define the fundamental group and talk about two riddles whose solutions use this idea.

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.