Workshop on "Geometry and Representation Theory"

点击翻译按钮获取中文摘要

AbstractAward: DMS-0400785Principal Investigator: Philip A. Foth, Paul Bressler, Kirti N. JoshiA powerful influx of methods and ideas from geometry into therepresentation theory led to significant breakthroughs andstimulated the emergence of geometric representation theory as animportant area of research in modern mathematics. Geometricmethods have been utilized to explore many significant problemsin representation theory. The Langlands program provides anexample of the synthesis of representation theory, arithmetic andgeometry. In its arithmetic avatar the Langlands correspondenceenvisages a description of certain kinds of representations ofthe Galois group of a number field or a function field in termsof automorphic representations. The geometric avatar of theLanglands correspondence pioneered by Drinfel'd and Laumon hasalso attracted a lot of attention and has turned out to be aconfluence of several areas of mathematics: representationtheory, D-modules, Kac-Moody and vertex algebras and integrablesystems, Hitchin maps to name a few. Representation theory hasbeen omnipresent in theoretical physics and conversely, problemsand developments in physics motivated much progress inrepresentation theory which, in turn, was a significant inputinto other branches of mathematics. Conformal Field Theory ledto intensive study of the representation theory of the Virasoroalgebra, Kac-Moody algebras and vertex operator algebras. Resultsin representation theory have had a significant impact on theunderstanding of the structure of moduli spaces. In the theoryof integrable systems it has been observed long ago in numerousexamples that physically meaningful completely integrable systemsas well as explicit formulas for the integrals of motion areintimately related with the geometric representation theory. Allthese developments serve as our motivation to organize aconference on geometric representation theory, a forum where themajority of participants will be young researchers and advancedgraduate students, learning from leading specialists and furtheradvancing their research projects.Representation theory is a quintessential branch of modernmathematics which studies symmetries of various algebraicsystems. The results and ideas from representation theory foundmany important applications in pure and applied mathematics aswell as quantum physics, biology, economics, just to name afew. More recently a powerful merge of ideas from geometry made asignificant impact on the discipline and led to importantbreakthroughs. The main goal of our conference is to gatherleading specialists in representation theory as well as beginningresearchers and advanced graduate students, to create a forumwhere participants can exchange new ideas, communicate recentadvances and assist younger participants in developing successfulresearch strategies. A special emphasis is made on attractingwomen and underrepresented minority participants, especiallythose at the dawn of their careers.