This is the homepage of the University of Illinois Urbana-Champaign Algebraic Geometry Seminar, organized by Deniz Genlik and Sheldon Katz. We meet Tuesdays at 3-3:50pm.
Other algebraic geometry activities at Illinois: AG lunch (Tu 12:30-1:30pm), AG preprint seminar (Tu 2-2:50pm). For more information, join our mailing list, either by visiting here or emailing Chris Dodd, Felix Janda, or Sheldon Katz.
Fall 2025 schedule:
September 2: Lena Ji (University of Illinois Urbana-Champaign)
Title: Finite order birational automorphisms of Fano hypersurfaces
Abstract: The birational automorphism group of an algebraic variety is an interesting birational invariant. For general type varieties this group is always finite, but for Fano varieties the situation is more complicated; for example, for P^n, the birational automorphism group is the mysterious Cremona group. In this talk, we study Fano hypersurfaces. We prove that there exist Fano hypersurfaces of arbitrarily high Fano index (in sufficiently high dimension) that admit no finite order birational automorphisms. A key input is the study of a specialization homomorphism for the birational automorphism group, which was defined by Matsusaka and Mumford. This work is joint with Nathan Chen and David Stapleton.
September 9: Ravi Fernando (University of Illinois Urbana-Champaign)
Title: Dimensional vanishing of the saturated de Rham-Witt complex
Abstract: The saturated de Rham-Witt complex, introduced by Bhatt-Lurie-Mathew, is a variant of the classical de Rham-Witt complex which is expected to behave better for singular schemes. We provide partial justification for this expectation by showing that the saturated de Rham-Witt complex satisfies dimensional vanishing even in the presence of singularities—like étale cohomology, but unlike any of de Rham, classical de Rham-Witt, and crystalline cohomology.
September 16: Christopher Dodd (University of Illinois Urbana-Champaign)
Title: Differential Operators, Gauges, and Mazur’s Theorem for Hodge Modules
Abstract: In this talk, I will explain how Mazur’s theorem about Frobenius and the Hodge filtration (from the early 1970’s) can be put into the context of filtered D-module theory. Along the way, I’ll explain the notion of a gauge, discuss Berthelot’s arithmetic differential operators, and explain how the Hodge filtration on a mixed Hodge module of geometric origin fits into the picture. I’ll give at least the basic background on all of the objects that appear in the title of the talk.
September 23: Ian Cavey (University of Illinois Urbana-Champaign)
Title: TBA
Abstract: TBA
September 30: Joshua Enwright (UCLA)
Title: TBA
Abstract: TBA
October 7: David Zureick-Brown (Amherst College)
Title: TBA
Abstract: TBA
Octover 14: Eric Zaslow (Northwestern University)
Title: TBA
Abstract: TBA
October 21
October 28
November 4
November 11
November 18
December 2
December 9