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.
After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology with the gauge group taken to be a complex Lie group (rather than a compact group as assumed by Floer), and how this is expected to be related to the Jones polynomial of knots and Khovanov homology.
Alan Weinstein is a Professor of the Graduate School in the Department of Mathematics at the University of California, Berkeley. He was a colleague of Jerry Marsden throughout Jerry’s career at Berkeley, and their joint papers on “Reduction of symplectic manifolds with symmetry” and “The Hamiltonian structure of the Maxwell-Vlasov equations” were fundamental contributions to geometric mechanics.
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.''