# Mathematical Physics

## From the Adinkras of Supersymmetry to the Music of Arnold Schoenberg

The concept of supersymmetry, though never observed in Nature, has been one of the primary drivers of investigations in theoretical physics for several decades. Through all of this time, there have remained questions that are unsolved. This presentation will describe how looking at such questions one can be led to the 'Dodecaphony Technique' of Austrian composer Schoenberg.

Jim Gates is a theoretical physicist known for work on supersymmetry, supergravity and superstring theory. He is currently a Professor of Physics at the University of Maryland, College Park, a University of Maryland Regents Professor and serves on President Barack Obama’s Council of Advisors on Science and Technology.

Gates was nominated by the US Department of Energy to present his work and career to middle and high school students in October 2010. He is on the board of trustees of Society for Science & the Public, he was a Martin Luther King Jr. Visiting Scholar at MIT (2010-11) and was a Residential Scholar at MIT’s Simmons Hall. On February 1, 2013, Gates received the National Medal of Science.

## Gauge Theory and Khovanov Homology

## A Functional Integral Representation for Many Boson Systems

## Introduction to Marsden & Symmetry

## Self-Interacting Walk and Functional Integration

These lectures are directed at analysts who are interested in learning some of the standard tools of theoretical physics, including functional integrals, the Feynman expansion, supersymmetry and the Renormalization Group. These lectures are centered on the problem of determining the asymptotics of the end-to-end distance of a self-avoiding walk on a *TeX Embedding failed!*-dimensional simple cubic lattice as the number of steps grows. When *TeX Embedding failed!* the end-to-end distance has been conjectured to grow as Const. *TeX Embedding failed!* where *TeX Embedding failed!* is the number of steps. We include a theorem, obtained in joint work with John Imbrie, that validates the *TeX Embedding failed!* conjecture in the simplified setting known as the ``Hierarchial Lattice.''