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 at Transportation Building 204.
Other algebraic geometry activities at Illinois: AG lunch (Tu 12:30-1:30pm, Harker Hall 201), AG preprint seminar (Tu 2-2:50pm, Transportation Building 204). For more information, join our mailing list, either by visiting here or emailing Felix Janda, or Sheldon Katz.
Spring 2026 Schedule:
Feb 17: Ruoxi Li (University of Illinois Urbana-Champaign)
Title: Towards derived Log GLSM: log cosections
Abstract: In Log Gauged Linear Sigma Models (log GLSM), two types of reduced perfect obstruction theories play crucial roles in computation of higher genus Gromov-Witten invariants. In this talk, I will present derived geometric constructions of these reduced perfect obstruction theories using log cosections, an approach which eliminates certain technical conditions required in the classical setting. I will also provide local models to illustrate this approach. If time permitting, I will sketch the construction of the derived moduli stack for a prototype of derived Log GLSM. This is joint work with Felix Janda.
Feb 24: Philip Engel (University of Illinois Chicago)
Title: Matroids and the integral Hodge conjecture for abelian varieties
Abstract: We will discuss a proof that the integral Hodge conjecture is false for a very general abelian variety of dimension ≥ 4. Associated to any regular matroid is a degeneration of principally polarized abelian varieties. We introduce a new combinatorial invariant of regular matroids, which obstructs the algebraicity of the minimal curve class, on the very general fiber of the associated degeneration. In concert with a result of Voisin, one deduces (via the intermediate Jacobian) the stable irrationality of a very general cubic threefold. This is joint work with Olivier de Gaay Fortman and Stefan Schreieder.
March 3: Leo Herr (Virginia Tech)
Title: (Partial) cohomological field theories in log Gromov-Witten theory
Abstract: Abramovich, Chen, Gross, and Siebert introduced punctured curves to describe log stable maps with negative contact orders. Using these, they construct an intrinsic mirror to a variety with log structure. We introduce a new formalism of “pierced maps” for negative contact orders in log geometry. We are able to prove new gluing formulas for these pierced maps and comparison results for our curve counts with theirs.
We have two events on March 10.
March 10: William Newman (The Ohio State University) Different than usual seminar time. Seminar starts at 2:00 pm (Transportation Building 204).
Title: Chow rings of moduli spaces of genus 0 curves with collisions
Abstract: Simplicially stable spaces are alternative compactifications of M_{g,n} generalizing Hassett’s moduli spaces of weighted stable curves. We give presentations of the Chow rings of these spaces in genus 0. When considering the special case of \bar M_{0,n}, this gives a new proof of Keel’s presentation of CH(\bar M_{0,n}).
March 10: Tondeur Lectures by June Huh (Princeton University)
For more details click here!
March 24: Rob Silversmith (Emory University)
Title: Counting configurations of points in projective space
Abstract: The cross-ratio degree problem is a combinatorial problem in algebraic geometry: it counts configurations of points in P^1 such that specified subsets have fixed cross-ratio. No combinatorial answer is known, though we do know various constraints involving the theory of matchings of bipartite graphs. I’ll discuss what is known about this problem, some interesting special cases and equivalent characterizations, and the natural generalization to higher dimensions.
March 31: Ajith Urundolil Kumaran (Massachusetts Institute of Technology)
Title: Enumerative geometry of (C*)^2 and the double double ramification cycle
Abstract: We introduce the enumerative geometry of (C*)^2 and connect it with intersection numbers against the higher rank double ramification cycle. A certain all genus generating function of these enumerative/virtual invariants with top lambda class insertion can be explicitly calculated using a refined tropical correspondence theorem (joint work with Patrick Kennedy-Hunt and Qaasim Shafi). This generalizes the refined tropical correspondence theorem of Pierrick Bousseau. We will report on joint work in progress with Dylan Toh on a tropical correspondence theorem in genus 1 without a top lambda class insertion.
April 7: David Jensen (University of Kentucky)
Title: Prym-Brill-Noether Theory for Covers of Elliptic Curves
Abstract: Brill-Noether theory is the study of algebraic curves and their maps to projective space. A series of results in the 80's describe the Brill-Noether theory of sufficiently general curves. More recently, many researchers have become interested in the Brill-Noether theory of special curves -- if a curve admits one unusual map to projective space, what does that imply about the existence and behavior of other such maps? We will begin with a gentle introduction to this field of study, and then survey some of the recent results on special curves. We will conclude with recent results on etale double covers of curves -- a subject known as Prym-Brill-Noether theory -- and a surprising relation to the combinatorics of Coxeter groups.
April 14: Matt Larson (Princeton University)
Title: TBA
Abstract: TBA
April 21: Grace Chen (University of Illinois Urbana-Champaign)
Title: TBA
Abstract: TBA
April 28: Siddarth Kannan (Massachusetts Institute of Technology)M
Title: TBA
Abstract: TBA
assachusetts InMassachusetts Institute of Technologystitute of Technology
May 5: Supravat Sarkar (Princeton University)
Title: TBA
Abstract: TBA