University of Utah


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 

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 

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 89  WAGS / Fall 2008  


Extensions of finite groups, group algebras, and decomposition of étale gerbes
Let G be a finite group. A Ggerbe 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 Ggerbe over a
point. A more interesting class of examples consist of Ggerbes 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 Ggerbe 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 Ggerbes over a
point or BQ.


November 18  Tommaso de Fernex 
Extending rationally connected fibrations from subvarieties




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 3folds that provides evidence for undecidability starting at 3 variables. We then conclude with a refined result for a padic 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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