The Mathematics of Quantum Theory

University Of California-Davis, Davis CA

Investigators

Abstract

The Mathematics of Quantum Theory, 05/01/14-12/01/15, University of California, Davis An international conference focusing on recent developments in topological quantum field theory (TQFT) and topological field theory will be held on May 23-26, 2014 at the University of California, Davis: http://indico.cern.ch/conferenceDisplay.py?confId=276011 The event will be attended by leading mathematicians and theoretical physicists and dovetails with a U.C. Davis Department of Mathematics celebration of sixty years of spectacular contributions to mathematics and physics by Professor Albert Schwarz. Indeed TQFTs were first constructed by Schwarz in the 1970s. Witten's solution of Chern--Simons TQFTs then laid the foundation for rapid progress connecting quantum field theory to rigorous mathematics, especially in the arena of the topological string theories that lie at the heart of unified String and M-Theory models. Concurrently, these ideas have led to profound advances in the mathematics of low dimensional topology; enumerative, symplectic and algebraic geometry; knot theory and even non-commutative geometry. The conference will be a unique opportunity for researchers to disseminate their latest results in these areas as well as for graduate students to see scientists of the highest calibre in action. To understand the fundamental importance of this type of research, one can begin by considering the latest results coming from collider experiments. The discovery of the Higgs particle (and Nobel Prizes for its prediction) confirms once again that quantum field theory correctly describes our universe at the very largest and smallest scales. Members of the public might be surprised to learn that such an important theory as quantum field theory can still not be exactly defined mathematically. In fact, the main progress in this direction has been in special cases of topological theories that depend on the global shape of space and time (but are insensitive to small local phenomena). This conference addresses this gaping hole in our current understanding. A rigorous mathematical understanding of general quantum field theories will lead to an explosion of new mathematical and physical results likely to revolutionize science as we know it.