Monty McGovern (UW)

Tuesday, February 1, 2022 - 2:00pm

PDL C-38

**Preseminar 2-2:30**

**Title**: Varietie

**Abstract**: Varieties with a nontrivial action of a complex torus (NOT the same as toric varieties!) turn out to have singularities that are fairly easy (on some level) to understand. I will give a very useful criterion of Brion to determine whether such varieties are rationally smooth (i.e. have the same local cohomology as smooth varieties) at specified points and indicate how this criterion is used to study the varieties arising in the main talk.

**Seminar 2:30-3:30**

**Title**: Rational smoothness of symmetric varieties

**Abstract**: Let G be a complex semisimple Lie group and B a Borel (maximal solvable) subgroup. The flag variety G/B admits many interesting subvarieties realized as closures of suborbits under proper subgroups of G. The singularities of a number of these have deep ramifications in representation theory. I will discuss two examples in detail and give a survey of the techniques used to study these singularities.

The talk will also be available via Zoom: https://washington.zoom.us/j/689897930

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