WAGS / Fall 2008

Titles and Abstracts

University of Utah
8-9 November 2008

Speaker: Martin Olsson
Title: Constructing integral models for moduli spaces of G-torsor
Abstract: A very special case of Abramovich and Vistoli's theory of twisted stable maps is the case when the target stack is BG, for a finite group G (or possibly tame group scheme). In this talk I will discuss how one can define twisted stable maps spaces to BG with sources higher dimensional varieties.
Speaker: Karl Schwede
Title: F-singularities and relations with the singularities of birational geometry
Abstract: For the past 30 years, people have studied relations between singularities defined by the action of Frobenius in positive characteristic and singularities defined by a resolution in characteristic zero. I will sketch how some of these relations work, and describe recent work of my own on a positive characteristic p analogue of log canonical-centers (which it turns out have themselves been studied before). I will explain the very natural way in which Q-divisors Δ such that KX + Δ is Q-Cartier appear in the positive characteristic setting. Finally, I will also explain recent work on local versions of F-(inversion of) (sub)adjunction on F-purity in positive characteristic.
Speaker: Sebastian Casalaina-Martin
Title: Birational geometry of the moduli of cubic threefolds
Abstract: In this talk, I will discuss the relationship between various projective compactifications of the moduli space of cubic threefolds; that is smooth degree three hypersurfaces in P4. The connections between this work and the work of Hassett, Hassett-Hyeon, Hyeon-Lee, and others, on the log minimal model program for the moduli space of curves will also be discussed. This is joint work with Radu Laza.
Speaker: Arend Bayer
Title: Stability conditions in the derived category and Donaldson-Thomas type invariants on Calabi-Yau threefolds
Abstract: Bridgeland constructed a space of stability conditions for any derived category. For special corner points of Bridgeland's space, the moduli spaces of stable objects give rise to Donaldson-Thomas type invariants on threefolds; changing the underlying stability condition then leads to interesting wall-crossing phenomena for the counting invariants. This talk will illustrate this principle in example situations.
Speaker: Nick Proudfoot
Title: Symplectic duality
Abstract: Symplectic duality is a relationship between pairs of algebraic symplectic varieties (or, if you prefer, hyperkähler manifolds). I will begin by examining two cohomological phenomena expressed by dual pairs, focusing on a collection of examples. Then I will briefly indicate the categorical structure that underlies these phenomena. (This is joint work with Tom Braden, Tony Licata, and Ben Webster.)
Speaker: Kai Behrend
Title: On the holomorphic Chern-Simons functional
Abstract: We explain how the transfer theorem for L-infinity algebras together with some elementary Banach algebra techniques lead to a holomorphic function germ associated to every point in a moduli space of Donaldson-Thomas type. This gives rise to the definition of a Milnor Fibre for every Schur object in the derived category of a Calabi-Yau threefold. This may lead to a categorification of Donaldson-Thomas theory. (This is joint work in progress with Getzler.)

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