SM: Conference on Symmetry in Mathematics and Physics

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

Abstract Award: DMS-0753874 Principal Investigator: Donald Babbitt, Srinivasa R. Varadhan The main theme of the conference will be important recent results and outstanding problems in the fields of representation theory of finite and infinite dimensional Lie and super-Lie groups, and its applications to quantum computing, geometry, physics, and differential equations, the different areas being unified under the over-arching theme of symmetry manifested in geometric actions of groups and their representations. The speakers will be internationally recognized researchers in these fields and the audience is expected to be a mixture of senior researchers in these fields together with advanced graduate students, postdocs and junior faculty who aspire to make or already are making important contributions to these fields. There will be travel funds made available to select participants of the latter group with a special emphasis on women and underrepresented minorities. It should be pointed out that four of the twelve speakers are women. The background to the conference consists of the work on supersymmetry pioneered by the physicists such as Zumino, and Ferrara (both speakers at the conference), and the work of the mathematicians Kac, Moody, and others who brought focus to infinite dimensional Lie algebras and their applications to quantum field theory. In the 1990's the group theoretic point of view was applied successfully to the theory of meromorphic differential equations and their moduli. Very recently important new progress has been made by the development of a supersymmetric Mackey theory and its applications to super particle classification, by work on differential Galois group theory of difference equations, and by the work on the foundations of super-geometry. Symmetry is one of the most fundamental and useful notions in both mathematics and theoretical physics. For example it explains the mysteries of the periodic table of chemical elements such as why hydrogen and oxygen combine to make water. An example of symmetry is the following; consider an ordinary square made with wire, rotate it 90 degrees about its center and notice it comes back onto itself although the molecules of the wire have moved. Do it again, you still get the same square. When you do it the fourth time, i.e., you rotate it 360 degrees the molecules of the wire come back to where they started. In mathematical language this says that “the cyclic group of order 4” is the symmetry group of the square. It is a wonder that the notion of symmetry and group can be extended and enriched to explain complicated sub-atomic physical phenomena as well as solve fundamental problems in mathematics coming from areas such as cryptography. The symmetries to be considered in this conference are part of this same story. Of perhaps particular interest is the theoretical notion of supersymmetry used in the study of sub-particle physics. The founder of this notion, B. Zumino, will speak at this conference. It is presently a theoretical hypothesis that many believe to be true but which awaits experimental verification. It is one of the main goals at the European Center for Nuclear Research (CERN) in Geneva to use its multi-billion dollar Hadron Collider which comes on line in 2008 to experimentally establish the supersymmetry hypothesis. For more information see the conference Website, www.math.ucla.edu/symmetry. This award is funded jointly by the programs in Geometric Analysis, Probability, and Algebra, Number Theory, and Combinatorics.