Harvard/MIT Algebraic Geometry Seminar
Spring 2018
Tuesdays at 3 pm
The Harvard/MIT Algebraic Geometry Seminar will alternate between MIT
(4153) and Harvard (Science Center 507).

Feb 62018
4153 MIT
Bhargav Bhatt, Michigan
Prisms and deformations of de Rham cohomology
abstract±
In arithmetic geometry, there are multiple instances where the de Rham cohomology of a smooth variety admits a natural deformation (such as crystalline cohomology or the recently constructed A_{inf}cohomology). I will explain a general sitetheoretic approach, relying on a notion we call prisms, that produces such deformations. In addition to recovering the known deformations in a new and simple way, this framework also constructs some previously conjectural ones (qdeformations of de Rham cohomology, cohomological BreuilKisin or Wach modules). This is a report on work in progress with Peter Scholze.

Feb 132018
SC 507 Harvard
Jesse Kass, University of South Carolina
How to count lines on a cubic surface arithmetically
abstract±
Salmon and Cayley proved the celebrated 19th century result that a smooth cubic surface over the complex numbers contains exactly 27 lines. By contrast, the count over the real numbers depends on the surface, and these possible counts were classified by Segre. Benedetti–Silhol, Finashin–Kharlamov and Okonek––Teleman made the striking observation that Segre’s work shows a certain signed count is always 3. In my talk, I will explain how to extend this result to an arbitrary field. Although I will not use any homotopy, I will draw motivation from A1homotopy theory. This is joint work with Kirsten Wickelgren.

Feb 202018
4153 MIT
Angela Gibney, Rutgers
Vector bundles of conformal blocks on the moduli space of curves
abstract±
In this talk I will give a tour of recent results and open problems about vector bundles of conformal blocks on the moduli space of curves. I will discuss how these results fit into the context of some of the open problems about the birational geometry of the moduli space.

Feb 272018
SC 507Harvard
Nick Salter, Harvard
Vanishing cycles for linear systems on toric surfaces
abstract±
Given a linear system on a smooth complex toric surface (eg the projective plane or P^1 \times P^1), it is very natural to ask about the set of all possible vanishing cycles. That is, for a fixed identification of a smooth fiber with a topological surface, which simple closed curves can be shrunk to a point via a nodal degeneration of curves in the linear system? Recent work of mine gives a complete answer to this question. It turns out that the essential invariant that determines whether a simple closed curve is a vanishing cycle is an ``rspin structure’’ of the sort studied by Witten and others in the context of cohomological field theory. The techniques are essentially topological, and are based on a reformulation of the problem in terms of the mapping class groupvalued monodromy representation of the linear system.

Mar 62018
4153MIT
Michael Kemeny
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Mar 132018
SC 507Harvard
Ariyan Javanpeykar
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Mar 202018
4153MIT
Tathagata Basak
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Mar 272018
SC 507Harvard
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Apr 32018
4153MIT
Curt McMullen, Harvard
Billiards, quadrilaterals and moduli spaces
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Apr 102018
SC 507Harvard
Eric Larson, MIT
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Apr 172018
4153MIT
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Apr 242018
SC 507Harvard
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May 12018
4153MIT
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May 82018
SC 507Harvard
Renzo Cavalieri
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This seminar is organized by Joe Harris (Harvard), Davesh Maulik (MIT), Brooke Ullery (Harvard), Philip Engel (Harvard), Dhruv Ranganathan (MIT), Rohini Ramadas (Harvard). This seminar is supported in part by grants from the NSF. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.