About 

This is a one day algebraic geometry event, happening on Saturday, March 14, 2026 at Michigan State University. 

Schedule

All talks will take place in Wells C304 and all breaks  and lunch will happen in Wells D101.

9:30-10:00 Refreshments 

10:00-11:00 Freudenburg

11:20-12:20 Plenary 1: Riedl

12:20-1:20 Lunch

1:20-2:20 Pietromonaco

2:20-2:50 Refreshments 

2:50-3:20 Kurama

3:30-4:00 Sgallova

4:20-5:20 Plenary 2: Elmanto

6:00 Dinner 

Speakers and Abstracts

• Elden Elmanto: Formal GAGA for zero cycle

GAGA theorems, in the style of Serre and SGA1, states that under certain properness hypothesis a coherent sheaf on a scheme is equivalent to one on an analytic object. In particular, if X is a noetherian scheme, proper over an I-adically complete ring A then the Picard group of X is the same thing as a compatible system of line bundles on X/I^n. Motivated by conjectures of Bloch-Beilinson and Colliot-Thélène in arithmetic geometry, and work of Saito and Sato, we conjecture variants of such GAGA statements for zero cycles. In this talk, we will formulate this conjecture using joint work with Matthew Morrow and work of Bouis, explain how it implies a conjecture of Colliot-Thélène and discuss the proof of a perfectoid variant of this conjecture. All of this is work done in the Scarborough Institute of Motives (Annala, Rafiei and Shin) and Bouis. 

• Gene Freudenburg: Presentations, embeddings and automorphisms of homogeneous spaces for SL_2(C )

For an algebraically closed field k of characteristic zero and a linear algebraic k-group G, it is well known that every affine G variety admits a G-equivariant closed embedding into a finite-dimensional G-module. Such an embedding is a presentation of the G varietiey, and a minimal presentation is one for which the dimension of teh G-module is minimal. The problem of finding a minimal presentation generlizes the problem of determining whetehr a group action on affine space is linearizable. In this talk, a homogeneous space for SL_2(k) is an affine k-variety equipped with a transitive action of LS_2(k) by algebraic automorphisms. We give a minimal presentation for each homogeneous space for SL_2(k). This constitutes our main result. Of particular interest are the surfaces Y=SL_2(k)/T and X=SL_2(k)/N where T is the one-dimensional torus and N is its normalizer. We show that the minimal presentation of X has dimension 5, the embedding dimension of X is 4, and there does not exist a closed SL_2-equivariant embedding of X in A_k^4. Thus, the SL_2-action on X is absolutely nonextendabl to A_k^4. In addition, X is noncancelative, that is, there exists a surface \tilde{X} such that X\times \A_k^1\cong_k\tilde{X}\times\A_k^1 and X\not\cong_k\tilde{X}. Finally, we settle the long-standing open question of whether there exist inequivalent closed embeddings of Y in A_k^ by constructing inequivalent embeddings.

• Riku Kurama: Flops, derived categories, and liftability of threefolds

Using mixed characteristic minimal model program for fourfolds (under an assumption on mixed characteristic resolution of singularities), Hacon and Witaszek proved that liftability of Calabi-Yau threefolds in characteristic p > 5 is preserved under birational equivalence. In this talk, I will explain the joint work in progress with Perry where we unconditionally prove this result for smooth Calabi-Yau threefolds with characteristic p > 3 by extending Bridgeland’s work on threefold flops. This celebrated work of Bridgeland describes threefold flops over the complex numbers as moduli spaces of certain complexes of sheaves, and our work generalizes this description to a relative setting.

• Stephen Pietromonaco: Counting Hyperelliptic Curves in Nikulin K3 Surfaces

A Nikulin K3 surface is a K3 surface together with a symplectic involution. I will consider a general member of a family of Picard rank 9 Nikulin K3 surfaces. Within a fixed linear system, there are a finite number of invariant curves whose induced quotient under the involution is rational. In this talk, I will introduce a conjecture that the actual number of such curves with a specified geometric genus and degree is encoded into a modular object called a Jacobi form with a very simple expression as an infinite product. The conjecture can be checked explicitly in low degree. I will discuss some interesting special cases, as well as an avenue towards a proof involving Lagrangian fibrations and compactified Jacobians. 

• Eric Riedl: An improved Bend-and-Break

Since its introduction almost fifty years ago, Mori's Bend-and-Break lemma has been an important tool in birational geometry and the study of curves. There are several different versions, but roughly speaking, the result guarantees the existence of a rational curve of somewhat low degree under certain assumptions on the variety. It has been used in all sorts of contexts, from concretely studying the geometry of specific varieties to the MMP and the classification of Fano varieties. However, the result used up until now is off by a factor of two from the optimal bound we might hope for. In this talk, we describe an improved degeneration technique using the Kontsevich space that allows us to achieve the optimal bound for Bend-and-Break. We then discuss several applications of the stronger bound, including the study of lengths of extremal rays and characterizations of projective space. This is joint work with Eric Jovinelly and Brian Lehmann.

• Ester Sgallová: Torsion points on family of elliptic curves over local base

Understanding how special points behave under degeneration is a central theme in the study of families of algebraic curves. In the case of elliptic curves, torsion points exhibit interesting geometric behavior as the fibers approach a singular limit. Let E → Δ be a family of elliptic curves over the disc Δ with smooth total space such that the central fiber E₀ is singular. For each n ≥ 1, let Tₙ denote the closure of the union of n-torsion points on the smooth fibers. In this talk, we describe the geometry of the intersection of Tₙ with the central fiber E₀. In particular, we determine the intersection numbers of Tₙ with each irreducible component of E₀ and describe the irreducible components of Tₙ.

Registration 

If you would like to attend, please fill out the registration form, where you can indicate whether you would like to attend the conference dinner or be considered for travel funding. 

The registration deadline is March 4, 2026 --- this is especially important for those who wish to attend the conference dinner. 

Contact

Please send any questions to flapanla@msu.edu, greerfra@msu.edu, or waldro51@msu.edu.