UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

November 09, 2010

939 Evans Hall

3:30PM: (At Stanford) Loop Spaces in Derived Algebraic Geometry

David Nadler (Northwestern University)

There are many notions of the circle in algebraic geometry -- for example, the multiplicative group, the punctured formal disk, and the affine line with two points attached at a node, to name a few. Perhaps most naively, there is also the circle itself regarded as the stack (or groupoid) with one object and an integers worth of automorphisms. In this talk, we will discuss the geometry of maps from this last model of the circle into algebraic varieties and stacks. Such loop spaces are naturally objects of derived algebraic geometry, and play an important role in many contexts such as Gromov-Witten theory. We will survey some of the developing theory in this subject, and in particular, explain the relation between D-modules and rotation-equivariant quasi-coherent sheaves on loop spaces. This is joint work with D. Ben-Zvi. I

5:00PM: The birational geometry of algebraic varieties

Christopher Hacon (University of Utah)

n this talk we will survey recent developments in the birational classification of varieties of log general type and applications of these results to automorphisms of varieties of general type, moduli spaces and to Shokurov's conjecture on the ascending chain condition for log canonical thresholds.

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