Type: Seminar

Distribution: World

Expiry: 19 Feb 2010

Auth: carberry(.pmstaff;1014.2002)@p723.pc.maths.usyd.edu.au

Speaker: Prof Tara Holm, Cornell University Title: Act globally, compute locally: Group actions, fixed points, and localization Room and time: Carslaw 273, 2:05 PM-2:55 PM There will be a joint lunch with the Algebra seminar at the Grandstand Bar, leaving from the 2nd floor of Carslaw at 12 PM. At lunch we will also host Tim Riley, our Algebra speaker that day. Anyone attending either/both talk/s is welcome to join us for lunch. So that we can give the Grandstand accurate numbers, please email James East james.east@sydney.edu.au by Thursday February 18 if you plan to attend the lunch. Abstract: Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing integrals at each of the fixed points. Or, if we know that the global integral is zero, we conclude that the sum of the local integrals is zero. This often turns topological questions into combinatorial ones and vice versa. This lecture will feature several instances of localization that occur at the crossroads of symplectic and algebraic geometry on the one hand, and combinatorics and representation theory on the other. The examples come largely from the symplectic category, with particular attention to toric varieties. No background in symplectic geometry or toric varieties will be assumed.