University of Utah
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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
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| September 9 |
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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.
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| September 16 | Emanuele Macrì |
Derived categories of cubics (after A. Kuznetsov)
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| September 23 |
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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.
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| September 30 | Aaron Bertram |
Points in the plane ♡ the derived category
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| October 7 | Yunfeng Jiang |
The quantum cohomology of root gerbes
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| October 21 | Christopher Hacon |
Associated centers of log canonical singularities
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| October 28 | Enka Lakuriqi |
Mirrors of Enriques Surfaces
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| November 8-9 | WAGS / Fall 2008 | |||||
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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.
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| November 18 | Tommaso de Fernex |
Extending rationally connected fibrations from subvarieties
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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.
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| November 25 | Milena Hering |
Positivity of toric vector bundles
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| December 9 | Tommaso de Fernex |
On the ascending chain condition for log canonical thresholds
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