The aim of this biweekly virtual seminar is to develop and strengthen the network of algebraic geometers at predominantly undergraduate institutions. In Spring 2026, it runs on Thursday at 4 - 5 pm (Eastern), 3 - 4 pm (Central), 2 - 3 pm (Mountain), and 1 - 2 pm (Pacific). The current organizers are Han-Bom Moon, Julie Rana, and David Swinarski.
This event is open to everyone, not just faculty at PUIs. If you want to receive a biweekly announcement email, please contact Julie.
The seminar is broadcasted via zoom. Check the announcement emails for the link.
Bring a cup of coffee or tea!
Date: February 5
Speaker: Shamil Asgarli (Santa Clara University)
Title: Blocking sets and plane curves over finite fields
Abstract. Let F_q be a finite field of order q. A subset B of a projective plane over F_q is called a blocking set if every line defined over F_q intersects B. Given an algebraic plane curve C, under what conditions do the F_q-points on C form a blocking set? We show that curves of low degree do not yield blocking sets. As an example of this phenomenon, cubic plane curves do not give rise to blocking sets whenever q > 4. In contrast, we give explicit constructions of smooth plane curves of sufficiently large degree whose F_q-points do form blocking sets. Furthermore, in a precise asymptotic sense, most plane curves over finite fields are not blocking. An interesting direction left open is to determine, for each F_q, the smallest degree of an irreducible plane curve whose F_q-points form a blocking set. This is joint work with Dragos Ghioca and Chi Hoi Yip.
Date: February 26
Speaker: Elizabeth Milicevic (Haverford College)
Title: Folded Alcove Walks and their Applications
Abstract: This talk will explain the tool of folded alcove walks, which enjoy a wide range of applications throughout combinatorics, representation theory, number theory, and algebraic geometry. We will survey the construction of both finite and affine flag varieties through this lens, focusing on the problem of understanding intersections of different kinds of Schubert cells. We then highlight several applications, including computing localizations in GKM theory for flag varieties and R-polynomials in Kazhdan-Lusztig theory.
Date: March 5
Speaker: Trevor Hyde (Vassar College)
Title: A boring dynamical system and why it is so interesting.
Abstract: In this talk we discuss an endomorphism of the configuration space of three unlabeled points in the plane which arises as the composition of two natural yet exceptional maps. The resulting dynamical system turns out to be boring, but understanding why leads us on a tour of beautiful classical constructions of algebraic geometry related to elliptic curves, finite geometries, and Galois theory.
Date: March 19
Speaker: Cigole Thomas (Bates College)
Title: Dynamics on Character Varieties over Finite Fields
Abstract: Character varieties are central objects in the study of moduli spaces and connect different areas of mathematics such as algebraic geometry, dynamics, mathematical physics, number theory, and differential geometry. A character variety is a space of equivalence classes of group homomorphisms from a group F to a "nice" (reductive) algebraic group G. We look at the finite field (F_q)-points of the variety and explore the dynamics of the action of the outer automorphism group on these points. We stratify the space and count the number of points in each stratum. This count can be used to explain the asymptotic behavior of the action as the number of elements in the field, q, goes to infinity. In particular, we will consider the case when F is the free abelian group on r variables and G=SL_3(C).
Date: April 9
Speaker: Ralph Morrison (Williams College)
Title: TBA