The aim of this biweekly virtual seminar is to develop and strengthen the network of algebraic geometers at predominantly undergraduate institutions. In Fall 2025, 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: September 11
Speaker: Jessie Loucks-Tavitas (California State University, Sacramento)
Title: Algebra and geometry of camera resectioning
Abstract: Algebraic vision, lying in the intersection of computer vision and projective geometry, is the study of three-dimensional objects being photographed by multiple pinhole cameras. Three natural questions arise:
Triangulation: Given multiple images as well as (relative) camera locations, can we reconstruct the scene or object being photographed?
Resectioning: Given a 3-D object or scene and multiple images of it, can we determine the (relative) positions of the cameras in the world?
Structure-from-motion: Given only 2D images, can we recover both the camera positions and the object being imaged?
We will discuss and characterize certain algebraic varieties associated with the camera resectioning problem. As an application, we will derive and re-interpret celebrated results in computer vision due to Carlsson, Weinshall, and others related to camera-point duality. Time-permitting, we will additionally discuss ongoing work (joint with Timothy Duff) towards a stratification of the singular locus of the resectioning variety. This is joint work with Timothy Duff and Erin Connelly.
Date: September 25
Speaker: Nathan Pflueger (Amherst)
Title: (Hurwitz--)Brill--Noether general curves via permutations
Abstract: Brill--Noether theory concerns the following question: if a genus g curve is chosen at random, what sorts of maps to projective spaces should we expect it to have? Recently, this question has been refined to address not just a random genus g curve, but instead a random degree k and genus g branched cover of the projective line. In other words, we sample our curve from Hurwitz space rather than from the moduli space of curves. This refinement has recently been named Hurwitz--Brill--Noether theory. I will explain the basic statements of Hurwitz--Brill--Noether theory, and outline a new method of proving the existence of so-called Hurwitz--Brill--Noether general curves. This method is based on the combinatorics of integer permutations, and leads to some intriguing links between combinatorics and geometry.
Date: October 9
Speaker: Maggie Regan (Grand Valley State University)
Title: Equilibrium Configurations in the Planar n-Vortex Problem Using Numerical Algebraic Geometry
Abstract: The n-vortex problem, a classical topic linking fluid dynamics and celestial mechanics, examines the motion and equilibrium of point vortices in an ideal fluid. This project focuses on relative equilibria where vortices rotate uniformly while preserving their configuration. Previous work has been done to find all possible configurations for n >= 4. To confirm and expand these results, homotopy continuation methods within numerical algebraic geometry can be applied to these nonlinear systems. This talk will give examples for the 3- and 4-vortex cases, as well as new results. This is joint work with Gareth Roberts and Nicholas Cesario.
Date: October 23
Speaker: Jack Petok (Colby College)
Title: Cubic fourfolds, K3 surfaces, and their zeta functions over finite fields
Abstract: I will explain some projects that are of the form: enumerate all hypersurfaces of degree d in n variables over a finite field, and compute their zeta functions. Kedlaya and Sutherland give a complete census of quartic K3 surfaces and their zeta functions over the finite field with two elements. In joint work with Auel, Kulkarni, and Weinbaum, we enumerated all cubic fourfolds and their zeta functions over F2. I will discuss the novel algorithmic speedups we used to complete our census, which came from an undergraduate's thesis project. Then I'll explain how we used this census in a more recent paper with Auel, where we give some new results about the arithmetic of cubic fourfolds and their associated K3 surfaces, and define the zeta function of a K3 category.
Date: Nov 6
Speaker: Aaron Wooton (University of Portland)
Title: Groups that act with almost all signatures
Abstract: The topological data associated with a group action on a compact Riemann surface of genus $g\geq 2$ can be described by a tuple of integers $(h;m_1, ...,m_s)$, known as the signature of the action. For a tuple to be a signature, it is necessary that $h\geq 0$, and that each $m_i$ corresponds to the order of a non-trivial element of the group. A group is said to act with almost all signatures (or to be AAS) if, outside of a small number of well-known exceptions, all but finitely many tuples satisfying these conditions actually arise as signatures of group actions. We derive necessary and sufficient conditions for when a group $G$ is AAS, and apply these conditions to provide a full classification of AAS groups that are quasisimple.
Date: Nov 20
Speaker: Caitlyn Booms (Mount Mary University)
Title: TBA
Date: Dec 4
Speaker: Dustin Ross (San Francisco State University)
Title: TBA