Our first speaker is Robin Pemantle of the University of Pennsylvania Mathematics Department. He will talk about:

Morse theoretic deformations for evaluating integrals.

Abstract: The goal is to evaluate Talyor coefficients of a rational function

via Cauchy’s integral

formula, these series arising as multivariate generating

functions. To do so, one would like to deform the chain of integration near a critical point for a log-linear height function

on the complex hypersurface . The chain must avoid the

surface , whence there is a topological obstruction at

the critical point, but it is important to push the rest of the

chain as far beyond this as possible (this makes the integrand

decay as rapidly as possible).

In this talk I will first give the combinatorial context in

which the problem arises. The attached pictures are examples

of combinatorial limit theorems resulting from such analyses.

Next, I will give the analytic reductions to a problem that

is essentially topological. Finally, I will discuss cases

where we know how to solve this problem. These rely on some

notions such as hyperbolicity and semi-continuity that have

been around for several decades, as well as on some new tricks

that work in low-dimensional cases.

Our second speaker is

of our very own Chemistry Department. Chris will be talking about:

** Title: Toward Programmable Matter – Organic Molecules with Programmable Shapes and Functional Group Display**

Over the past nine years, my laboratory has developed a radical new approach to creating large, complex molecules that can carry out complex functions in the way that biological proteins do. Our approach is to synthesize new stereochemically pure cyclic *bis*-amino acid building blocks (*Buildomers*) that we couple through pairs of amide bonds to create large molecules with programmed shapes. The oligomers are efficiently assembled on solid support using peptide synthesis techniques to first create a flexible oligomer that is then rigidified by the simultaneous formation of a second set of amide bonds between each adjacent pair of monomers. The structure of the resulting ladder-like molecules is controlled by the sequence and stereochemistry of the component monomers. The oligomer structures made accessible by this technology range from extended molecular rods to compact structures containing small-molecule sized cavities. These oligomers can be functionalized in a variety of ways to perform different functions. We are developing a software package that will enable anyone to construct oligomer sequences with designed shapes, through automated computer searches of sequence and conformational space. Our goal is to combine this software and molecular “hardware” to create a sort of “molecular compiler” that can take a high level specification of a function (eg: “*catalyze a particular reaction*” or “*bind a target protein*”) and convert it into a molecular implementation that will carry out that function.