University of Minnesota Algebraic Geometry Seminar 20142015 
AnaMaria
Castravet (The Ohio State University)

Abstract: I will talk about joint work with Jenia Tevelev on the birational geometry of the GrothendieckKnudsen moduli space of stable rational curves with n markings. The main result is that for n large this space is not a Mori Dream Space, thus answering a question of Hu and Keel. 
Yujong Tzeng
(University of Minnesota)

Abstract: On smooth algebraic surfaces, the number of nodal curves in a fixed linear system is universal polynomial of Chern numbers (conjectured by Gottsche, now proven). Recently Gottsche and Shende defined a "refined" invariant which can count real and complex nodal curves and is an invariant in tropical geometry. In this talk I will define two "motivic" invariants which generalize the universal polynomials and refined invariant to the algebraic cobordism group and to the Grothendieck ring of varieties. The properties and the possible meaning of those motivic invariants will be discussed. 
Craig
Westerland (University of Minnesota)

Abstract: This talk is about the
space of relatively minimal Lefschetz fibrations over
surfaces X with at most one node in each fibre. We study
the homology of these spaces as the number of nodal fibres
tends to infinity, and relate the stable homology to the
homology of the function space of maps from X to a variant
of the DeligneMumford compactification of M_g.
Restricting our answer to H_0 yields a form of Auroux's
stable classification of Lefschetz fibrations. 
Daniel Schultheis (University of
Minnesota)

Abstract: The Quot scheme over a
smooth projective curve C offers a compactification of the
space of maps from C to a Grassmannian. Numerous
mathematicians have studied the intersection theory of these
Quot schemes, culminating in proof that the virtual count of
these maps satisfies the VafaIntriligator formula from
physics. In this talk we will explore the history of this
problem, as well as recent generalizations when C is
replaced by a del Pezzo surface. 
Amin
Gholampour (University of Maryland)

Abstract:

Ionut
CiocanFontanine (University of Minnesota)

Abstract: Quasimaps provide
compactifications, depending on a stability parameter
epsilon, for moduli spaces of maps from nonsingular
algebraic curves to a large class of GIT quotients. These
compactifications enjoy good properties and in particular
they carry virtual fundamental classes. As the parameter
epsilon varies, the resulting invariants are related by
wallcrossing formulas. I will present some of these
formulas in genus zero, and will explain why they can be
viewed as generalizations (in several directions) of
Givental's toric mirror theorems. I will also describe
extensions of wallcrossing to higher genus, and (time
permitting) to orbifold GIT targets as well. The talk is
based on joint works with Bumsig Kim, and partly also with
Daewoong Cheong and with Davesh Maulik. 
Wednesday,
September 10 and September 17 Preparation for Kisin's lectures: pcurvature and the GrothendieckKatz Conjecture I and II William Messing (University of Minnesota) 