3:30 pm Thursday, October 17, 2002
Geometry Seminar: Extracting geometry from combinatorics by Nick Proudfoot (UC Berkeley) in RLM 9.166
Hypertoric varieties are hyperkahler (ie quaternionic) analogues of toric varieties. Like toric varieties, hypertoric varieties are combinatorially defined, and many of their elegant geometric properties can be read off from simple combinatorial diagrams. In the first hour of this talk we will discuss the different combinatorics that go into the kahler and hyperkahler settings, and relate them by considering certain circle actions on hypertoric varieties. The second hour of this talk will be on quiver varieties, another class of combinatorially defined algebraic varieties with deep connections to many different fields, such as representation theory, singularity theory, and physics. Like toric varieties, quiver varieties come in Kahler and hyperkahler flavors. I will give a bunch of examples, and discuss some questions about quiver varieties that are analogous to the questions that were asked in the first half of the talk, but much more difficult to answer. Submitted by
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