This is the homepage of the University of Illinois Urbana-Champaign Algebraic Geometry Seminar, organized by Deniz Genlik, Felix Janda, Lena Ji, and Sheldon Katz. We meet Tuesdays at 3-3:50pm, Loomis Laboratory 136 .
Other algebraic geometry activities at Illinois: AG lunch (Tu 12:30-1:30pm, Harker Hall 201), AG preprint seminar (Tu 2-2:50pm Loomis Laboratory 136). For more information, join our mailing list, either by visiting here or emailing Felix Janda, Lena Ji, or Sheldon Katz.
Fall 2026 Schedule:
Sep 1: Orgranizational Meeting at 3:00 pm, Loomis Laboratory 136
Sep 8: Ruoxi Li (University of Illinois Urbana-Champaign)
Title: Shifted Logarithmic Functions and More
Abstract: To some extent, a perfect obstruction theory in the sense of Behrend--Fantechi is the shadow of a quasi-smooth derived Deligne--Mumford stack, while a cosection of a perfect obstruction theory in the sense of Kiem-Li is the shadow of a (-1)-shifted function on a quasi-smooth derived Deligne--Mumford stack. In this talk, I will introduce shifted logarithmic functions on derived stacks equipped with log structures of Deligne--Faltings type, and logarithmic cosections of logarithmic perfect obstruction theories. As an application, I will present a decomposition theorem for virtual cycles, after Log GLSM. Meanwhile, I will discuss another facet of shifted logarithmic functions: their derived critical loci carry shifted logarithmic symplectic structures, building on work of Calaque-Safronov. If time permits, I will mention the construction of deformation to log normal bundles.
Sep 15: William Newman (The Ohio State University)
Title: Chow motives of Enriques surfaces
Abstract: An Enriques surface is a 2-dimensional smooth projective variety whose first Betti number is 0 and whose canonical bundle is 2-torsion. There are many such varieties: the moduli space is 10-dimensional. Unlike other famous examples of surfaces with positive dimensional moduli, Enriques surfaces have trivial Hodge structures on their cohomology, so this invariant cannot be used to tell them apart. In this talk, we consider a finer invariant, the integral Chow motive of an Enriques surface, and investigate what information about the Enriques surface it remembers. This is joint work with Jake Huryn.
Sep 22: Deniz Genlik (University of Illinois Urbana-Champaign)
Title: From 3-spin relations to negative r-spin relations
Abstract: We show negative r-spin relations of Chidambaram--Garcia-Failde--Giacchetto are implied by the Pixton’s 3-spin relations. To achieve this, mainly we extend a result of Janda to generically semi-simple CohFTs with a non-flat unit and perform a detailed asymptotic analysis of shifted Chiodo CohFT under the limit of a parameter. Consequently, we prove that the negative r-spin relations hold in the tautological Chow ring. This is a joint work with Felix Janda.
Sep 29: Lena Ji (University of Illinois Urbana-Champaign)
Title: Degree two rational multisections of conic bundles
Abstract: The Enriques criterion for unirationality of conic bundles states that if X is a conic bundle over P^2 , then X is unirational if and only if the conic bundle admits a rational multisection. Furthermore, if X is unirational but not rational, then such a rational multisection necessarily has even degree. In this talk, we study non-existence of degree 2 rational multisections. This is joint work with Jeffrey Diller and Eric Riedl.
Oct 15: Hsian-Hua Tseng (The Ohio State University) -- Departmental Colloquium (Reception: Harker 300 at 3:00 pm, Talk: Noyes 165 at 4:00 pm)
Title: Points, partitions, and curve counting: The Hilbert scheme of points on the plane
Abstract: The Hilbert scheme of n points on the plane is an algebraic parameter space for n points on the plane, which records very nicely when some of the points collide. We will begin with the basic construction and properties. It turns out that these Hilbert schemes play important roles in a plethora of areas of mathematics. We will then try to explain some results involving Hilbert schemes and representation theory, combinatorics, and enumerative geometry.
Oct 17-Oct 18: Workshop on Topological Recursion and Related Topics
Oct 20: Alessandro Giacchetto (ETH Zurich)
Title: Euler characteristics of strata of k-differentials
Abstract: Strata of k-differentials are natural subvarieties of moduli spaces of curves obtained by prescribing the orders of zeros and poles of a k-differential. In this talk, I will present an explicit formula for their orbifold Euler characteristics, generalising the classical Harer–Zagier formula for the moduli space of curves. As a consequence, we show that these Euler characteristics depend polynomially on the orders of the zeros and poles. I will then present an intersection-theoretic expression in terms of tautological integrals over double ramification cycles, as well as a recursion that determines the Euler characteristics from genus zero. Based on joint work with M. Costantini, M. Möller, A. Sauvaget, and J. Schmitt.
Oct 21: Maria Monks Gillespie (Colorado State University)--Combinatorics Colloquium
Oct 27: Yun Shi (Missouri State University)
Title: Stability of tangent bundle on Del Pezzo surfaces
Abstract: Donaldson and Uhlenbeck-Yau established the classical result that on a compact Kahler manifold, an irreducible holomorphic vector bundle admits a Hermitian metric solving the Hermitian-Yang-Mills equation if and only if the vector bundle is Mumford-Takemoto stable. Motivated by a modern analogue of this result, we study the stability of certain higher-rank objects in Bridgeland stability conditions. In this talk, I will present results on the stability of tangent bundle on Del Pezzo surfaces. This is based on joint work with Tristan Collins, Jason Lo, and Shing-Tung Yau.
Nov 3: Hanlin Cai (Northwestern University)
Title: Perturbation of test ideal in mixed characteristics
Abstract: Given a normal integral scheme of finite type over a mixed characteristic complete DVR or a perfect field of characteristic p, one can define the notion of a test ideal. This sheaf is used to characterize a class of mild singularities known as +rational singularities, which are analogous to rational singularities in characteristic 0. In equal characteristics, it is a well-known result that test and multiplier ideals are stable under small perturbations. In this talk, I will explain how to extend this stability result to the mixed characteristic setting and discuss some of its applications. Time permitting, I will also outline the key ideas and tools from p-adic geometry that underlie the proof. This is based on joint work in progress with Bhargav Bhatt and Linquan Ma.
Nov 10: Tomoki Oda (UCLA)
Title: Classification of Cluster-Type Pairs on P^3
Abstract: Toric varieties are among the best-understood objects in algebraic geometry: each contains a dense algebraic torus, and its geometry is governed by combinatorics. Cluster-type pairs are a natural generalization. Roughly speaking, a log Calabi–Yau pair (X, B) is of cluster type if X contains an algebraic torus whose complement is essentially the boundary B, up to codimension two. This cluster type pairs naturally appears in the work of Gross—Hacking—Keel in their work on Mirror symmetry.
In this talk, I will outline the classification of cluster-type pairs on P^3, joint work in progress with J. Moraga. I will first review the basic definitions and the known picture for del Pezzo surfaces. I will then survey recent results of Alves da Silva, Figueroa, Moraga, and Yáñez on cluster-type Fano threefolds. Finally, I will explain how the classification on P^3 builds on earlier work of Alves da Silva, Figueroa, and Moraga and gives a complementary perspective on this framework. Instead of asking which Fano threefolds are of cluster type, we fix the ambient space P^3 and ask which boundary divisors make it so.
Nov 17: TBD
Dec 1: Lutian Zhao (Kavli Institute for the Physics and Mathematics of the Universe)
Title: Gopakumar–Vafa invariants and a support theorem for stable pairs
Abstract: The Gopakumar–Vafa/Pandharipande–Thomas correspondence relates two approaches to counting curves on Calabi–Yau threefolds, using moduli spaces of one-dimensional sheaves and stable pairs. For smooth curves, its cohomological form is suggested by the classical Macdonald formula relating symmetric powers and Jacobians. I will present the cohomological correspondence for local (\mathbb P^2) and local (\mathbb P^1\times\mathbb P^1), in every effective curve class and Euler characteristic. The main ingredient is a support theorem for the direct images of stable-pair vanishing-cycle sheaves: their strict supports are closures of loci of transverse unions of smooth connected curves. I will explain how wall-crossing and duality reduce the problem to a finite range of Euler characteristics, and how a commutation relation for point modifications excludes additional supports. Applying the family Macdonald formula on the reduced locus then gives the correspondence as an identity of semisimplified perverse direct images on the Chow variety.
Dec 8: TBD
Events with red color are algebraic geometry related events that are advertised here. They are not part of the seminar.