Ohio State University Algebraic Geometry Seminar


Ohio State University Algebraic Geometry Seminar Year 2026-2027 Time: Tuesdays 10:20-11:15am Location: MW 154 (in person) or Zoom (virtual, email the organizers for the Zoom coordinates)

Schedule of talks:


TIME	SPEAKER	TITLE
September 8 Tue, 10:20am	Angélica Cueto (OSU)	Tritangent planes to space sextic curves: a tropical viewpoint
September 15 Tue, 10:20am	John Nolan (OSU)	Functorial Classification of Toric Stacks
September 22 Tue, 10:20am	Jon Kim (UC Boulder)	The log MMP for the moduli space of cubic surfaces with a marked line
September 29 Tue, 10:20am	Dawei Chen (Boston College)	Moduli of Differentials and AI
October 6 Tue, 10:20am	Keller VandeBogert (Kentucky)	Syzygies and Stability for Grassmannian Matrix Schubert Varieties
October 13 Tue, 10:20am	Emilio Dominguez (Maryland)
October 20 Tue, 10:20am	Colin Defant (Harvard)
October 27 Tue, 10:20am	Ruoxi Li (UIUC)
November 3 Tue, 10:20am	Jingxiang Ma (OSU)
November 17 Tue, 10:20am	Ayah Almousa (Kentucky)
January 26 Tue, 10:20am	Soyeon Kim (UC Davis)

See also the Arithmetic Geometry Seminar

Abstracts

(Cueto): A classical result due to Clebsch from the mid-nineteenth century confirms that every complex space sextic curve (given as an intersection of a quadric and a cubic surface in projective 3-space) has exactly 120 tritangent planes. In this talk we will show how to use combinatorial methods arising from tropical geometry to revisit this classical problem and perform the analogous count over the reals and extensions thereof. This is joint work with Yoav Len, Hannah Markwig and Yue Ren (arXiv:2512.24277 and arXiv:2605.19905).

(Nolan): Toric varieties and their stack-theoretic generalizations are common objects of study in algebraic geometry and mirror symmetry. It is well-known that toric varieties are classified by combinatorial objects known as "fans," and conventional wisdom tells us that toric stacks (whatever they are) should also be classified by more general "stacky fans." In 2011, Geraschenko and Satriano (henceforth GS) proposed a definition of stacky fans, giving a combinatorial construction of a large class of toric Artin stacks. Gillam and Molcho later observed that the GS construction is not essentially surjective, i.e. there exist objects which deserve to be called "toric stacks" but do not arise via the GS construction. Our goal in this talk is to introduce a new, more general notion of "stacky fan" and explain how to construct an equivalence between our 2-category of stacky fans and a suitable 2-category of toric stacks. (We will also include a brief review of stack theory for the uninitiated.)

(J. Kim): The moduli space of cubic surfaces with a marked line lies naturally between the moduli space of fully marked and unmarked cubic surfaces and comes equipped with a $W(D_5)$-action corresponding to the stabilizer of the marked line. Hodge theoretic compactifications of these moduli spaces have been extensively studied by many, including Allcock—Carlson—Toledo, Dolgachev—van Geemen—Kondo, and Casalaina-Martin—Grushevsky—Hulek. In previous work, by using KSBA wall crossing, we described many different birational models of this moduli space via KSBA stable pairs. In this talk, we will discuss recent results regarding the $W(D_5)$-invariant birational geometry of these KSBA moduli spaces and ongoing work on the log minimal model program for these KSBA moduli spaces with respect to their log canonical divisor.

(Chen): Differentials on Riemann surfaces correspond to translation surfaces with cone points, where the zero orders of differentials determine the cone angles of translation surfaces. Affine transformations act on translation surfaces and preserve the zero type. These perspectives make differentials and their moduli spaces extensively studied in many areas. In this talk, I’ll first introduce the background of differentials and their moduli spaces. Then I’ll explain several recent AI-assisted works relevant to moduli spaces of differentials, which include elementary number theory, automorphisms of Riemann surfaces, topology of hyperplane arrangements, and special generating functions. These AI works were not prompted by me, and they are not as fancy as the million-dollar problems. However, the related questions naturally arose in my research field, and I did think about them before the era of AI. Both parts of the talk should be accessible to a general audience.

(VandeBogert): Matrix Schubert varieties naturally generalize determinantal varieties by allowing one to impose rank conditions on specified submatrices. Knutson–Miller identify their equivariant K-polynomials, which record alternating sums of syzygy characters, with double Grothendieck polynomials. A recent conjecture of Price–Stelzer–Yong predicts stability in the Schur supports of these polynomials as the underlying permutations are enlarged. In this talk, I’ll discuss a stronger phenomenon for Grassmannian matrix Schubert varieties: the individual syzygy representations stabilize, with multiplicities and homological degrees unchanged, under a simple operation on Young diagrams called Durfee stabilization. I’ll explain how the geometry of their desingularizations allows us to prove this through vector bundle cohomology on flag varieties and determine the sharp stability range. This is based on joint work with Sasha Pevzner, Steven V Sam, and Linus Setiabrata.