University of Utah
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Click on the title of a talk for the abstract (if available).
| Date | Speaker | Title | ||||
| January 12 |
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Chiral Hecke algebra and representations of affine Kac-Moody Lie algebras
I will discuss the conjectural role that the Chiral Hecke algebra plays in the local geometric Langlands correspondence.
If time permits, I will sketch a possible approach to the unramified case using BRST reduction.
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| January 19 |
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The Universal Formulas for Counting Nodal Curves on Surfaces
The problem of counting nodal curves on algebraic surfaces
has been studied since the nineteenth century. On the projective
surface, it asks how many curves defined by homogeneous degree d
polynomials have only nodes as singularities and pass through points
in general position. On K3 surfaces, the number of rational nodal
curves was predicted by the famous Yau-Zaslow formula. Goettsche
conjectured that for sufficiently ample line bundles L on algebraic
surfaces, the numbers of nodal curves in |L| are given by universal
polynomials in four topological numbers. Furthermore, based on the
Yau-Zaslow formula he gave a conjectural generating function in terms
of quasi-modular forms. The formula is consistent with many existing
results on projective surface, K3, and curves with at most 8 nodes on
general surfaces. In this talk, I will discuss how degeneration
methods can be applied to count nodal curves and sketch my proof of
Goettsche's conjecture.
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The automorphic groups of general type varieties
(Joint with C. Hacon and J. McKernan)
In this talk, I will sketch a work-in-progress, which is aimed to show that the
order of the automorphic group of a general type varietie, which is
well-known to be finite, is linearly bounded by the volume of K_X.
This is a generalization of the classical Hurwitz's theorem in the 1 dimensional case,
and G. Xiao's theorem in the 2 dimensional case.
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| January 26 | No seminar today |
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| February 2 | Y.P. Lee |
Algebraic Cobordism of Bundles on Varieties
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| February 9 | No seminar today |
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Non-commutative desingularizations and cluster-tilting objects over Cohen-Macaulay rings
Let M be a reflexive module over a Cohen-Macaulay local ring R and A = Hom(M,M). If A has finite global dimension, then it has been proposed to serve as a non-commutative analogue of desingularizations of Spec(R). In this talk, we will survey what is known about when such module M exists, and discuss the connections with birational geometry and representation theory of commutative rings. Part of the new results are joint work with Craig Huneke.
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| February 16 | No seminar today |
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| February 23 |
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| March 2 |
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| March 9 | Ching-Jui Lai |
Varieties fibered by good minimal models
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| March 16 |
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| March 30 |
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| April 6 |
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| April 13 |
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| April 20 |
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| April 27 |
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