Algebraic Geometry Seminar Fall 2014: Difference between revisions
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|December 12 | |December 12 | ||
|DJ Bruce (UW) | |[http://www.math.wisc.edu/~djbruce/ DJ Bruce] (UW) | ||
| | |Betti Tables of Graph Curves | ||
|local | |local | ||
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|March 13 | |||
|[http://www3.nd.edu/~jrodri18/ Jose Rodriguez] (Notre Dame) | |||
|TBD | |||
|Daniel | |||
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===Eyal Markman=== | ===Eyal Markman=== | ||
Let S be a K3 surface, v an indivisible Mukai vector, | |||
and M(v) the moduli space of stable sheaves on S with Mukai vector v. | |||
The universal sheaf gives rise to an integral functor F from the derived category of | |||
coherent sheaves on S to that on M(v). We show that the functor F is faithful (but not full). | |||
The bounded derived category of M(v) is rather mysterious at the moment. | |||
As a first step, we provide a simple conjectural description of its full subcategory | |||
whose of objects are images of objects on S via the functor F. | |||
We verify that description whenever M(v) is the Hilbert scheme of points on S. | |||
This work is joint with Sukhendu Mehrotra. | |||
===Lars W Christensen=== | ===Lars W Christensen=== | ||
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In 2012, J.P Keating and Z. Rudnick published a paper where they resolved a function field version of the Montgomery-Goldston pair correlation conjecture. Their proof relies on a recent equidistribution result of N. Katz. In joint work with Daniel Hast, we reprove their result by counting points on a certain variety using a twisted Grothendieck-Lefschetz formula and obtain also information about higher moments. | In 2012, J.P Keating and Z. Rudnick published a paper where they resolved a function field version of the Montgomery-Goldston pair correlation conjecture. Their proof relies on a recent equidistribution result of N. Katz. In joint work with Daniel Hast, we reprove their result by counting points on a certain variety using a twisted Grothendieck-Lefschetz formula and obtain also information about higher moments. | ||
Moreover our method allows us to also give a proof of the autocorrelation of the Mobius function on average in the function field setting, also known as the Chowla conjecture. | Moreover our method allows us to also give a proof of the autocorrelation of the Mobius function on average in the function field setting, also known as the Chowla conjecture. | ||
===DJ Bruce=== | |||
Given a graph one may obtain a reducible algebraic curve by associating a P^1 to each vertex with two P^1’s intersecting if there is an edge between the associated vertices. Such curve are called graph curves, or line arrangements, and were introduced by Bayer and Eisenbud in studying Green’s conjecture. I will discuss how the combinatorics of the graph affect the Betti table of its associated curve. In particular, I will present formulas for the Betti table for all graph curves of genus zero and one. Additionally, I will give formulas for the graded Betti numbers for a class of curves of higher genus. This talk is based on joint work with Pete Vermeire, Evan Nash, Ben Perez, and Pin-Hung Kao. | |||
Latest revision as of 18:26, 19 December 2014
The seminar meets on Fridays at 2:25 pm in Van Vleck B131.
The schedule for the previous semester is here.
Algebraic Geometry Mailing List
- Please join the Algebraic Geometry 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 2014 Schedule
| date | speaker | title | host(s) |
|---|---|---|---|
| September 12 | Andrei Caldararu (UW) | Geometric and algebraic significance of the Bridgeland differential | (local) |
| September 19 | Greg G. Smith (Queen's University) | Toric vector bundles | (Daniel) |
| October 3 | Daniel Erman (UW) | Tate resolutions for products of projective spaces | (local) |
| October 10 | Lars Winther Christensen (Texas Tech University) | Beyond Tate (co)homology | Daniel |
| October 17 | Claudiu Raicu (Notre Dame University) | TBA | Daniel |
| October 31 | Anatoly Libgober (UIC) | Landau-Ginzburg/Calabi-Yau and McKay correspondences for elliptic genus | Max |
| November 7 | Vlad Matei (UW) | Moments of arithmetic functions in short intervals | Local |
| November 14 | No seminar (room will be used for a specialty exam) | ||
| December 5 | Eyal Markman (UMass Amherst) | Integral transforms from a K3 surface to a moduli space of stable sheaves on it | Andrei |
| December 12 | DJ Bruce (UW) | Betti Tables of Graph Curves | local |
| March 13 | Jose Rodriguez (Notre Dame) | TBD | Daniel |
Abstracts
Andrei Caldararu
Several years ago Tom Bridgeland suggested that there should exist interesting chain maps C_*(M_{g,n}) -> C_{*+2}(M_{g,n+1}) and he conjectured some applications of these maps to mirror symmetry. I shall present a precise definition of these maps using techniques from the theory of ribbon graphs, and discuss a recent result (joint with Dima Arinkin) about the homology of the total complex associated to the bicomplex obtained from these maps. Then I shall speculate (wildly) about applications to mirror symmetry.
Eyal Markman
Let S be a K3 surface, v an indivisible Mukai vector, and M(v) the moduli space of stable sheaves on S with Mukai vector v. The universal sheaf gives rise to an integral functor F from the derived category of coherent sheaves on S to that on M(v). We show that the functor F is faithful (but not full). The bounded derived category of M(v) is rather mysterious at the moment. As a first step, we provide a simple conjectural description of its full subcategory whose of objects are images of objects on S via the functor F. We verify that description whenever M(v) is the Hilbert scheme of points on S. This work is joint with Sukhendu Mehrotra.
Lars W Christensen
Tate (co)homology was originally defined for modules over group algebras. The cohomological theory has a very satisfactory generalization---Tate--Vogel cohomology or stable cohomology---to the setting of associative rings. The properties of the corresponding generalization of the homological theory are, perhaps, less straightforward and have, in any event, been poorly understood. I will report on recent progress in this direction. The talk is based on joint work with Olgur Celikbas, Li Liang, and Grep Piepmeyer.
Anatoly Libgober
I will discuss elliptic genus of singular varieties and its extension to Witten's phases of N=2 theories. In particular McKay correspondence for elliptic genus will be described. As one of applications I will show how to derive relations between elliptic genera of Calabi Yau manifolds and related Witten phases using equivariant McKay correspondence for elliptic genus.
Vlad Matei
In 2012, J.P Keating and Z. Rudnick published a paper where they resolved a function field version of the Montgomery-Goldston pair correlation conjecture. Their proof relies on a recent equidistribution result of N. Katz. In joint work with Daniel Hast, we reprove their result by counting points on a certain variety using a twisted Grothendieck-Lefschetz formula and obtain also information about higher moments. Moreover our method allows us to also give a proof of the autocorrelation of the Mobius function on average in the function field setting, also known as the Chowla conjecture.
DJ Bruce
Given a graph one may obtain a reducible algebraic curve by associating a P^1 to each vertex with two P^1’s intersecting if there is an edge between the associated vertices. Such curve are called graph curves, or line arrangements, and were introduced by Bayer and Eisenbud in studying Green’s conjecture. I will discuss how the combinatorics of the graph affect the Betti table of its associated curve. In particular, I will present formulas for the Betti table for all graph curves of genus zero and one. Additionally, I will give formulas for the graded Betti numbers for a class of curves of higher genus. This talk is based on joint work with Pete Vermeire, Evan Nash, Ben Perez, and Pin-Hung Kao.