Algebra and Algebraic Geometry Seminar Fall 2021

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Revision as of 13:21, 27 September 2021 by Derman (talk | contribs) (Michael Kemeny)
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The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.

Algebra and Algebraic Geometry Mailing List

  • Please join the AGS mailing list by sending an email to 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).

COVID-19 Update

As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is (sometimes we will have to use a different meeting link, if Michael K cannot host that day).

Fall 2021 Schedule

date speaker title host/link to talk
September 24 Michael Kemeny (local, in person) The Rank of Syzygies
October 1 Michael K Brown (Auburn University) Tate resolutions as noncommutative Fourier-Mukai transforms Daniel
October 8 Peter Wei (local) TBD (talk will be about results of Ogus on K3 surfaces in char p and syzygies) Michael
October 15
October 22 Ritvik Ramkumar (UC Berkeley) Something about Hilbert schemes, probably Daniel
October 29
November 5 Eric Ramos Equivariant log-concavity
November 12
November 19
November 26 Thanksgiving
December 3
December 10


Speaker Name

Michael Kemeny

Title: The Rank of Syzygies

Abstract: I will explain a notion of rank for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank four.

Michael Brown

Title: Tate resolutions as noncommutative Fourier-Mukai transforms

Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.