The conference "Representation Theory and Symplectic Algebraic Geometry" will take place at the CIRM (Luminy) on the dates July 9-13, 2012. The appearance of symplectic algebraic varieties in representation theory has come primarily from two different directions. First, symplectic algebraic varieties admit quantizations, and there are many symplectic algebraic varieties whose rings of "quantized functions" are of independent algebraic interest. Second, they appear through the categorification program, also known as "higher representation theory." In many examples of categorification, the categories in questions have geometric interpretations involving sheaves on symplectic algebraic varieties. This grant will provide funding for U.S. researchers to participate in a conference that addresses both of these topics. More information about this conference can be found on the CIRM web page: <www.cirm.univ-mrs.fr/index.html/spip.php?rubrique2&EX=info_rencontre&annee=2012&id_renc=637&lang=en>.
The central theme in algebraic geometry is the rich interplay between algebraic objects (called "rings" and "modules") and geometric objects (called "varieties" and "sheaves"). One of the goals of geometric representation theory is to exploit this interplay by using geometry to prove theorems about algebra. This approach has its roots in the early 1980s when it was used to prove the Kazhdan-Lusztig conjecture, an outstanding problem in algebra that, superficially, had nothing to do with geometry. The field has experienced enormous growth in the past decade, and this conference will allow researchers from around the world to keep abreast of recent work.
" was held at the Centre International de Rencontres Mathematiques in Marseille, France, in July 2012. There were over 70 participants from around the world. Participants included graduate students, postdoctoral fellows, and leading researchers in the field. Symplectic algebraic varieties are a rich class of algebraic varieties that have received much attention from physicists, representation theorists, and algebraic geometers over the last decade. The appearance of symplectic algebraic varieties in representation theory has come primarily from two different directions. First, symplectic algebraic varieties admit quantizations, and there are many symplectic algebraic varieties whose rings of quantized functions are of independent algebraic interest. The second appearance of symplectic algebraic varieties in representation theory comes through the categorification program, also known as higher representation theory. In many examples of categorification, the categories in questions have geometric interpretations involving sheaves on algebraic symplectic varieties. The program included 21 lectures and one evening problem session. Beyond the lecture schedule, the conference afforded an opportunity for pre-existing collaborations to develop, and also for new collaborations to form. Due in part to the success of this workshop, another conference on the same theme is being planned in Boston for May, 2015.
