# Difference between revisions of "Algebraic Geometry Seminar Fall 2017"

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'''LePotier's Strange Duality and Quot Schemes''' | '''LePotier's Strange Duality and Quot Schemes''' | ||

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Finite schemes of quotients over a smooth curve are a vehicle | Finite schemes of quotients over a smooth curve are a vehicle | ||

for proving strange duality for determinant line bundles on | for proving strange duality for determinant line bundles on | ||

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'''Poincare sheaf on the stack of rank two Higgs bundles''' | '''Poincare sheaf on the stack of rank two Higgs bundles''' | ||

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It is well known that for a smooth projective curve, there exists a Poincare line bundle on the product of the Jacobian of the curve which is the universal family of topologically trivial line bundles of the Jacobian. It is natural to ask whether similar results still hold for the compactified Jacobian of singular curves. There has been a lot of work in this problem. In this talk I will sketch the construction of the Poincare sheaf for spectral curves in Hitchin fibration. The new feature is that we are able to extend the construction of Poincare sheaf to nonreduced spectral curves. | It is well known that for a smooth projective curve, there exists a Poincare line bundle on the product of the Jacobian of the curve which is the universal family of topologically trivial line bundles of the Jacobian. It is natural to ask whether similar results still hold for the compactified Jacobian of singular curves. There has been a lot of work in this problem. In this talk I will sketch the construction of the Poincare sheaf for spectral curves in Hitchin fibration. The new feature is that we are able to extend the construction of Poincare sheaf to nonreduced spectral curves. |

## Revision as of 22:37, 26 October 2017

The seminar meets on Fridays at 2:25 pm in Van Vleck B321.

Here is the schedule for the previous semester.

## Contents

## Algebraic Geometry Mailing List

- Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).

## Fall 2017 Schedule

date | speaker | title | host(s) |
---|---|---|---|

October 6 | Michael Brown (UW-Madison) | Topological K-theory of equivariant singularity categories | local |

October 9 (Monday!!, 3:30-4:30, B119) | Aaron Bertram (Utah) | LePotier's Strange Duality and Quot Schemes | Andrei |

October 27 | Mao Li (UW-Madison) | Poincare sheaf on the stack of rank two Higgs bundles | local |

November 3 | Dario Beraldo (Oxford) | tba | Dima |

December 1 | Jonathan Wang (IAS) | Dima | |

December 8 | Melody Chan (Brown)) | tba | Jordan |

## Abstracts

### Michael Brown

**Topological K-theory of equivariant singularity categories**

This is joint work with Tobias Dyckerhoff. Topological K-theory of complex-linear dg categories is a notion introduced by Blanc in his recent article "Topological K-theory of complex noncommutative spaces". In this talk, I will discuss a calculation of the topological K-theory of the dg category of graded matrix factorizations associated to a quasi-homogeneous polynomial with complex coefficients in terms of a classical topological invariant of a complex hypersurface singularity: the Milnor fiber and its monodromy.

### Aaron Bertram

**LePotier's Strange Duality and Quot Schemes**

Finite schemes of quotients over a smooth curve are a vehicle for proving strange duality for determinant line bundles on moduli spaces of vector bundles on Riemann surfaces. This was observed by Marian and Oprea. In work with Drew Johnson and Thomas Goller, we extend this idea to del Pezzo surfaces, where we are able to use it to prove cases of Le Potier's strange duality conjecture.

### Mao Li

**Poincare sheaf on the stack of rank two Higgs bundles**

It is well known that for a smooth projective curve, there exists a Poincare line bundle on the product of the Jacobian of the curve which is the universal family of topologically trivial line bundles of the Jacobian. It is natural to ask whether similar results still hold for the compactified Jacobian of singular curves. There has been a lot of work in this problem. In this talk I will sketch the construction of the Poincare sheaf for spectral curves in Hitchin fibration. The new feature is that we are able to extend the construction of Poincare sheaf to nonreduced spectral curves.