Algebraic Geometry Seminar Fall 2016: Difference between revisions
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== Abstracts == | == Abstracts == | ||
===Alexander Pavlov=== | |||
''Betti Tables of MCM Modules over the Cones of Plane Cubics'' | |||
Graded Betti numbers are classical invariants of finitely generated modules over graded rings describing the shape of a minimal free resolution. We show that for maximal Cohen-Macaulay (MCM) modules over a homogeneous coordinate rings of smooth Calabi-Yau varieties X computation of Betti numbers can be reduced to computations of dimensions of certain Hom groups in the bounded derived category D(X). In the simplest case of a smooth elliptic curve embedded into projective plane as a cubic we use our formula to get explicit answers for Betti numbers. In this case we show that there are only four possible shapes of the Betti tables up to a shifts in internal degree, and two possible shapes up to a shift in internal degree and taking syzygies. | |||
===PhilSang Yoo=== | ===PhilSang Yoo=== | ||
Revision as of 19:45, 12 September 2016
The seminar meets on Fridays at 2:25 pm in Van Vleck B305.
Here is the schedule for the previous semester.
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 2016 Schedule
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| September 16 | Alexander Pavlov (Wisconsin) | Betti Tables of MCM Modules over the Cones of Plane Cubics | local | |
| September 23 | PhilSang Yoo (Northwestern) | Classical Field Theories for Quantum Geometric Langlands | Dima | |
| October 14 | Luke Oeding (Auburn) | TBA | Steven | |
| October 28 | Adam Boocher (Utah) | TBA | Daniel | |
| November 4 | Reserved | TBA | Daniel | |
| November 11 | Daniel Litt (Columbia) | TBA | Jordan | |
| November 18 | David Stapleton (Stony Brook) | TBA | Daniel | |
| December 2 | Rohini Ramadas (Michigan) | TBA | Daniel and Jordan |
Abstracts
Alexander Pavlov
Betti Tables of MCM Modules over the Cones of Plane Cubics
Graded Betti numbers are classical invariants of finitely generated modules over graded rings describing the shape of a minimal free resolution. We show that for maximal Cohen-Macaulay (MCM) modules over a homogeneous coordinate rings of smooth Calabi-Yau varieties X computation of Betti numbers can be reduced to computations of dimensions of certain Hom groups in the bounded derived category D(X). In the simplest case of a smooth elliptic curve embedded into projective plane as a cubic we use our formula to get explicit answers for Betti numbers. In this case we show that there are only four possible shapes of the Betti tables up to a shifts in internal degree, and two possible shapes up to a shift in internal degree and taking syzygies.
PhilSang Yoo
Classical Field Theories for Quantum Geometric Langlands
One can study a class of classical field theories in a purely algebraic manner, thanks to the recent development of derived symplectic geometry. After reviewing the basics of derived symplectic geometry, I will discuss some interesting examples of classical field theories, including B-model, Chern-Simons theory, and Kapustin-Witten theory. Time permitting, I will make a proposal to understand quantum geometric Langlands and other related Langlands dualities in a unified way from the perspective of field theory.
Luke Oeding
TBA