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: The linear algebra of the decomposition theorem
Abstract: The decomposition theorem is one of the deepest known facts about the topology of complex projective varieties. Given a map X -> Y of complex projective varieties, with X smooth, it implies strong restrictions on the structure of the cohomology H*(X) as a module over H*(Y). We show that many of these restrictions are linear-algebraic consequences of classically-known properties of H*(X). This enables us to deduce these restrictions in situations where one cannot apply the decomposition theorem, such as in combinatorial Hodge theory and for Chow rings modulo numerical equivalence. Joint work with Omid Amini and June Huh.
April 21: Grace Chen (University of Illinois Urbana-Champaign)
Title: Delta-matroids and toric degenerations in the maximal orthogonal Grassmannian OG(n,2n+1)
Abstract: Let Z be a general point of the Grassmannian Gr(k,n), which has an action by T = (C*)^n. Berget and Fink proved a formula via equivariant localization that expresses the cohomology class of the torus orbit closure of Z as a sum of products of Schubert classes, indexed by partitions. In a previous work, Lian gave a new proof of the formula by constructing an explicit toric degeneration of the general orbit closure in Gr(k,n) into a union of Richardson varieties, whose moment map images form a polyhedral decomposition of that of the general orbit closure. With C. Lian, we apply this strategy to deduce a formula in the case of the maximal orthogonal Grassmannian OG(n,2n+1). I will explain the general strategy, focusing on the case of Gr(k,n), and highlight the additional difficulties in its application to OG(n,2n+1).
April 28: Siddarth Kannan (Massachusetts Institute of Technology)M
Title: Virtual Poincare polynomials of universal Jacobians and moduli spaces of maps to projective space
Abstract: I will discuss how to calculate the virtual Poincare polynomial of the universal Jacobian over the moduli space of curves, as well as that of the moduli space of maps from smooth curves to projective space. The calculations rely crucially on symmetric function theory and suggest interesting stability properties for the mixed Hodge structure on the mapping space. Time-permitting I will also discuss the dual boundary complex of the Vakil—Zinger compactification of the moduli space of genus one maps: this complex is contractible, which has implications for the cohomology of the corresponding mapping space. Based on joint work with Terry Song.
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May 5: Supravat Sarkar (Princeton University)
Title: Proof of Miyanishi's conjecture on endomorphisms of varieties
Abstract: If X is a quasi-projective variety over a field k and ϕ a birational endomorphism of X that is injective outside a closed subset of codimension ≥ 2, we prove that ϕ is an automorphism. This generalizes an old theorem of Ax and proves a conjecture of Miyanishi from 2005. A key step in our proof is a finiteness result on class groups, which is of interest in its own right.