University of Utah
Algebraic Geometry Seminar
Fall 2008: Tuesdays 3:30-4:30, LCB 222

Schedule of upcoming talks:

Click on the title of a talk for the abstract (if available).

Date Speaker Title
September 2 Jimmy Dillies
On some automorphisms of K3 surfaces
September 9
Diane Maclagan
(University of Warwick)
Combinatorial bounds on nef cones of varieties I will describe joint work with Angela Gibney describing bounds on the nef cones of varieties. These are obtained from suitable embeddings of the varieties into toric varieties and use tropical techniques. Our motivating example is the moduli space of stable rational genus zero curves with n marked points.
September 16 Emanuele Macrì
Derived categories of cubics (after A. Kuznetsov)
September 23
Jaume Amorós
(Universitat Politècnica de Catalunya)
Kaehler manifolds with locally free actions A connected complex Lie group acting locally freely on a closed Kaehler manifold must be abelian. After a review of holomorphic tangent vector fields on such manifolds, I will present joint work with M. Manjarin and M. Nicolau on the topology and classification of such manifolds.
September 30 Aaron Bertram
Points in the plane ♡ the derived category
October 7 Yunfeng Jiang
The quantum cohomology of root gerbes
October 21 Christopher Hacon
Associated centers of log canonical singularities
October 28 Enka Lakuriqi
Mirrors of Enriques Surfaces
November 8-9 WAGS / Fall 2008
November 10
3:00pm, LCB 225
Hsian-Hua Tseng
(University of Wisconsin-Madison)
Extensions of finite groups, group algebras, and decomposition of étale gerbes Let G be a finite group. A G-gerbe over a space X may be intuitively thought of as a fiber bundle over X with fibers being the classifying space (stack) BG. In particular BG itself is the G-gerbe over a point. A more interesting class of examples consist of G-gerbes over BQ, which are equivalent to extensions of the finite group Q by G. Considerations from physics have led to conjectures asserting that the geometry of a G-gerbe Y over X is equivalent to certain "twisted" geometry of a "dual" space Y'. A lot of progresses have be made recently towards proving these conjectures in general. In this talk we'll try to explain theses conjectures in the elementary concrete examples of G-gerbes over a point or BQ.
November 18 Tommaso de Fernex
Extending rationally connected fibrations from subvarieties
See also: November 21
Comm. Algebra Seminar
Maurice Rojas
(Texas A&M University)
Hilbert's Tenth Problem in Low Dimensions Hilbert's Tenth Problem (HTP) asks for an algorithm to decide the existence of integer solutions to arbitrary polynomial equations. HTP was solved in the negative by Davis, Putnam, Robinson, and Matiyasevich around 1970 and, about two decades later, Z. W. Sun proved that undecidability starts already with polynomials in 11 variables. However, while it is a simple matter to find all integer solutions for polynomials in 1 variable, the minimal number of variables where undecidability starts remains a mystery. Furthermore, effective bounds for the size of integer points on curves (when there are only finitely many) also remain unknown in complete generality. We prove a result relating integer points on curves and 3-folds that provides evidence for undecidability starting at 3 variables. We then conclude with a refined result for a p-adic analogue of HTP in 1 variable. The latter result depends subtly on the distribution of primes in arithmetic progressions. We assume no background in number theory.
November 25 Milena Hering
Positivity of toric vector bundles
December 9 Tommaso de Fernex
On the ascending chain condition for log canonical thresholds

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