# Scientific

## Sequential Robust Design Strategies

The speaker introduces the formal notion of an approximately specified nonlinear regression model and investigates sequential design methodologies when the fitted model is possibly of an incorrect parametric form. He presents small-sample simulation studies which indicate that his new designs can be very successful, relative to some common competitors, in reducing mean squared error due to model misspecification and to heteroscedastic variation. His simulations also suggest that standard normal-theory inference procedures remain approximately valid under the sequential sampling schemes.

## Kirchhoff Scattering Inversion

• These lectures will introduce the theory of Kirchhoff migration and imaging from an inversion perspective

• They are intended to teach some geophysics to mathematicians and some mathematics to geophysicists

• Recommended reference: Bleistein, Cohen & Stockwell, 2001, “Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion”

## String Theory Compactification with/without Torsion

Topics:

• Geometry and Holomony

• Supersymmetry, Spinors, and Calabi-Yau

• Flux and Backreaction

• Energetics of Heterotic Flux Compactification

• Strominger System and Heterotic Flux as a Torsion

• A Supersymmetric Solution to Heterotic Flux Compactification

• Global Issues: Index Counting, Smoothness, etc

## Aperiodicity: Lessons from Various Generalizations

This is a slightly expanded version of a talk given at the Workshop on Aperiodic Order, held in Victoria, B.C. in August, 2002. The general subject of the talk was the densest packings of simple bodies, for instance spheres or polyhedra, in Euclidean or hyperbolic spaces, and describes recent joint work with Lewis Bowen. One of the main points was to report on our solution of the old problem of treating optimally dense packings of bodies in hyperbolic spaces. The other was to describe the general connection between aperiodicity and nonuniqueness in problems of optimal density.

## Random Walk in Random Scenery

In this talk we consider a random walk on a randomly colored lattice and ask what are the properties of the sequence of colors encountered by the walk.

## Phase Transitions for Interacting Diffusions

In the present talk we focus on the ergodic behavior of systems of interacting diffusions.

## Lectures on Integer Partitions

What I’d like to do in these lectures is to give, first, a review of the classical theory of integer partitions, and then to discuss some more recent developments. The latter will revolve around a chain of six papers, published since 1980, by Garsia-Milne, Jeff Remmel, Basil Gordon, Kathy O’Hara, and myself. In these papers what emerges is a unified and automated method for dealing with a large class of partition identities.

By a partition identity I will mean a theorem of the form “there are the same number of partitions of n such that . . . as there are such that . . ..” A great deal of human ingenuity has been expended on finding bijective and analytical proofs of such identities over the years, but, as with some other parts of mathematics, computers can now produce these bijections by themselves. What’s more, it seems that what the computers discover are the very same bijections that we humans had so proudly been discovering for all of those years.

These lectures are intended to be accessible to graduate students in mathematics and computer science.

## Torsion invariants of 3-manifolds

This series of six lectures is intended for a general audience. The aim of the lectures is to survey the theory of torsions of 3-dimensional manifolds. The torsions were introduced by Kurt Reidemeister in 1935 to give a topological classification of lens spaces. Recent interest in torsions is due to their connections with the Seiberg-Witten invariants of 4-manifolds and the Floer-type homology of 3-manifolds. The lectures will cover the above topics.

## Algebraic Z^d-actions

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## Entropy and Orbit Equivalence

In these notes we first offer an overview of two core areas in the dynamics of probability measure preserving systems, the Kolmogorov-Sinai theory of entropy and the theory of orbit equivalence. Entropy is a nontrivial invariant that, said simply, measures the exponential growth rate of the number of orbits in a dynamical system, a very rough measure of the complexity of the orbit structure. On the other hand, the core theorem of the orbit theory of these systems, due to Henry Dye, says that any two free and ergodic systems are orbit equivalent, that is to say can be regarded as sitting on the same set of orbits. The goal we set out to reach now is to explain and understand the seeming conflict between these two notions.