AG@PUI virtual seminar
This is a biweekly virtual seminar for algebraic geometers at primarily undergraduate institutions. In Spring 2024, it runs on Tuesdays at 3 - 4 pm (Eastern), 2 - 3 pm (Central), 1 - 2 pm (Mountain), and 12 - 1 pm (Pacific). The current organizers are Han-Bom Moon, Julie Rana, and David Swinarski.
This event is open to everyone, not only to the faculty at PUI. 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!
Spring 2024
Date: Feb. 6.
Speaker: David Swinarski (Fordham University)
Title: Some singular curves in Mukai's model of $\overline{M}_7$
Abstract: In the 1990s Mukai introduced birational models of the moduli spaces $\overline{M}_g$ for $g = 7, 8, 9$. For example, the GIT quotient Gr(7,16)//Spin(10) is a birational model of the moduli space of Deligne-Mumford stable genus 7 curves $\overline{M}_7$. The key observation is that a general smooth genus 7 curve can be realized as the intersection of the orthogonal Grassmannian OG(5,10) in $\mathbb{P}^{15}$ with a six-dimensional projective linear subspace. In this AG@PUI talk, I will discuss many of the background ideas in Mukai's construction. This is a warmup to my recent preprint arXiv:2304.12936, where I give examples of singular curves that are GIT semistable in Mukai's construction.
Date: Feb. 20.
Speaker: Dagan Karp (Harvey Mudd College)
Title: Tropical Linear Series
Abstract: In this talk I'll attempt to give a friendly and example-driven introduction to the theory of linear series on tropical curves. While in some respects mirroring the classical study of linear series, in the tropical setting there are many surprises and even basic questions remain open. This work is joint with Chang Chih-Wei, Hernan Iriarte, David Jensen, Sam Payne, and Jidong Wang.
Date: Mar. 5.
Speaker: Harpreet Bedi (Alfred University)
Title: Modulo p equivalence of categories
Abstract: An equivalence between categories of Char 0 and Char p is constructed via a modulo p map. No Witt vectors or perfectoid spaces will be harmed, but the constructions will be similar.
Date: Mar. 19.
Speaker: Javier Gonzalez Anaya (Harvey Mudd College)
Title: Higher-dimensional Losev-Manin spaces and their geometry
Abstract: The classical Losev-Manin space can be interpreted as a toric compactification of the moduli space of points in the affine line modulo translation and scaling. In this talk, we will discuss the geometry of higher-dimensional analogs of these moduli spaces, referred to as higher-dimensional Losev-Manin spaces. These varieties emerge as toric compactifications of the moduli space of distinct labeled points in affine space modulo translation and scaling, and possess their fair share of interesting geometric properties. For instance, they are locally trivial fibrations over a product of projective spaces, with fibers isomorphic to the Losev-Manin space. Additionally, they are isomorphic to the normalization of a Chow quotient. This is joint work with Patricio Gallardo, Jose Gonzalez, and Evangelos Routis.
Date: Apr. 2.
Speaker: Jessica Sidman (Amherst College)
Title: Line arrangements, parallel redrawings, and syzygies
Abstract: Let A = {L_1, . . . , L_n} ⊂ P^2 be an arrangement of distinct lines. To what extent do the algebraic structures associated to A depend only on the matroid on the lines, and when are they sensitive to the geometry of the arrangement? We will see how insights from combinatorial rigidity theory can be brought to bear to study the syzygies of the module of derivations of A and produce novel examples exhibiting special behavior. This is joint work with Michael DiPasquale and Will Traves.
Date: Apr. 16.
Speaker: Sebastian Bozlee (Fordham University)
Title: A stratification of moduli of arbitrarily singular curves
Abstract: What does the space of all algebraic curves look like? One way to answer the question is to break up this gigantic, unruly space into nice pieces, called strata, and then to describe those. For stable curves such strata have long been constructed and are used throughout the theory of moduli of curves. In this talk, I will describe how to construct a similar stratification of moduli of arbitrarily singular curves, indexed by combinatorial data generalizing dual graphs. The key idea is to combine the geometry of moduli of smooth curves with moduli of subalgebras.
Date: Apr. 30.
Speaker: David Zureick-Brown (Amherst College)
Title: The Canonical Ring of a Stacky Curve
Abstract: We give a generalization to stacks of the classical theorem of Petri -- i.e., we give a presentation for the canonical ring of a stacky curve. This is motivated by the following application: we give an explicit presentation for the ring of modular forms for a Fuchsian group with cofinite area, which depends on the signature of the group. (The talk will be mostly geometric and will require little understanding of modular forms; additionally, no prior knowledge of stacks will be needed to understand the talk.)