Principal Investigator: Philip A. Foth, Paul Bressler, Kirti N. Joshi
A powerful influx of methods and ideas from geometry into the representation theory led to significant breakthroughs and stimulated the emergence of geometric representation theory as an important area of research in modern mathematics. Geometric methods have been utilized to explore many significant problems in representation theory. The Langlands program provides an example of the synthesis of representation theory, arithmetic and geometry. In its arithmetic avatar the Langlands correspondence envisages a description of certain kinds of representations of the Galois group of a number field or a function field in terms of automorphic representations. The geometric avatar of the Langlands correspondence pioneered by Drinfel'd and Laumon has also attracted a lot of attention and has turned out to be a confluence of several areas of mathematics: representation theory, D-modules, Kac-Moody and vertex algebras and integrable systems, Hitchin maps to name a few. Representation theory has been omnipresent in theoretical physics and conversely, problems and developments in physics motivated much progress in representation theory which, in turn, was a significant input into other branches of mathematics. Conformal Field Theory led to intensive study of the representation theory of the Virasoro algebra, Kac-Moody algebras and vertex operator algebras. Results in representation theory have had a significant impact on the understanding of the structure of moduli spaces. In the theory of integrable systems it has been observed long ago in numerous examples that physically meaningful completely integrable systems as well as explicit formulas for the integrals of motion are intimately related with the geometric representation theory. All these developments serve as our motivation to organize a conference on geometric representation theory, a forum where the majority of participants will be young researchers and advanced graduate students, learning from leading specialists and further advancing their research projects.
Representation theory is a quintessential branch of modern mathematics which studies symmetries of various algebraic systems. The results and ideas from representation theory found many important applications in pure and applied mathematics as well as quantum physics, biology, economics, just to name a few. More recently a powerful merge of ideas from geometry made a significant impact on the discipline and led to important breakthroughs. The main goal of our conference is to gather leading specialists in representation theory as well as beginning researchers and advanced graduate students, to create a forum where participants can exchange new ideas, communicate recent advances and assist younger participants in developing successful research strategies. A special emphasis is made on attracting women and underrepresented minority participants, especially those at the dawn of their careers.
