## Women Seminars Spring 2006 Schedule

Meeting: Tuesday 5:00 pm in 343 Altgeld Hall
- January 24, 2006

**Stephanie Treneer** (UIUC Math)

**Title:**Is the whole really greater than the sum of its
parts? Exploring partitions of numbers.

**Abstract:** A partition of a positive integer n is a
sequence of positive integers that sum to n. The partition function p(n)
counts the partitions of n without regard to order. This deceptively
simple function has led to a rich theory. We'll look at two elementary
methods for analyzing partitions: Ferrers graphs and generating functions,
and then briefly discuss how the theory of modular forms has led to some
recent surprising results about p(n).

- February 7, 2006

**Jeong Ok Choi** (UIUC Math)

**Title:**Distinguishing Chromatic Number of a graph

**Abstract:** The distinguishing chromatic number of a graph
G is the least integer k such that there is a proper k-coloring of G which
is not preserved by any nontrivial automorphism of G. We will show that
the distinguishing chromatic number of G^d (the Cartesian product of G by
d times) is at most one more than the usual chromatic number of G for d at
least 6, where G is either a complete graph or a hypercube. In fact, with
a larger value of d, the generalization for any (connected) graph is true.
This is joint work with Hemanshu Kaul and Stephen Hartke.

- February 21, 2006

**Sylvia Carlisle** (UIUC Math)

**Title:**Continuous first order logic

**Abstract:** I will give an introduction to continuous first
order logic, comparing it with usual first order logic. I will give some
examples of metric structures for this setting. As time allows I will show
how to prove some theorems analogous to some of the basic theorems of
first order logic, for example, the compactness theorem or the downward
Lowenheim-Skolem theorem.

- April 11, 2006

**Zoi Rapti** (UIUC Math)

**Title:**Complexity results in Biological systems

**Title:** In this talk I'm going to review some complexity
results with applications to DNA and protein folding. I also will try to
explain how hyperbolic geometry is useful when trying to obtain fast
algorithms that solve the protein-folding and DNA-reconfiguration
problems. These ideas are based on work by V. Peterson and R. Ghrist.