Future Directions in Representation Theory

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This award funds participation by US researchers in an international research conference entitled Future Directions in Representation Theory, to be held at the University of Sydney from December 4-8, 2017. Broadly speaking, the field of representation theory deals with understanding symmetries of linear systems. The notion of "symmetries" is made precise by the mathematical concept of a group; given an abstract group, one can ask how that group can be realized via linear transformations on a vector space. This subject has algebraic origins, but current developments in representation theory involve input from other areas of mathematics, such as geometry and topology, as well as ideas from physics. This conference brings together experts from diverse research backgrounds to report on new developments and exchange ideas. Many current developments at the frontiers of representation theory rely on a diverse array of tools whose origins may be geometric, categorical, or homological in nature. Conversely, questions from representation theory have motivated a number of new developments in neighboring fields of mathematics and mathematical physics. This conference features speakers whose work lies at the interface of representation theory and these neighboring subjects, and whose research programs are indicative of the directions along which representation theory may develop in the future. Specific topics include: (i) symplectic duality and mathematical physics; (ii) categorification and categorical actions; (iii) cohomological methods in representation theory; (iv) parity sheaves and Soergel bimodules. US researchers supported by this funding will have the opportunity to interact with some of the world's leading experts in the representation theory, as well as to make contacts with peer researchers from Australia and other nations. The conference webpage is: https://sites.google.com/site/ausreptheory/conference2017.