Front Range Algebraic Geometry Day

 We are proud to announce the first

Front Range Algebraic Geometry Day Fall 2024

at Colorado State University, Weber 201

Thursday, November 21, 2024

2:00 pm - 4:50 pm

What is FRAG Day?

This day is in collaboration with the FRAGMENT seminar for algebraic geometers in the front range area to connect and discuss their research. In particular, we are committed to fostering connections among graduate students between CU and CSU

Talks and Abstracts

Erin Dawson

Title: Tropical Tevelev Degrees

Abstract: Tropical Hurwitz spaces parameterize genus g, degree d covers of the tropical line with fixed branch profiles. Since tropical curves are metric graphs, this gives us a combinatorial way to study Hurwitz spaces. Tevelev degrees are the degrees of a natural finite map from the Hurwitz space to a product M_{0,n} cross M_{g,n}. In 2021, Cela, Pandharipande and Schmitt presented this interpretation of Tevelev degrees in terms of moduli spaces of Hurwitz covers. In this talk we will explore a method to perform this calculation of Tevelev degrees using the moduli spaces of tropical Hurwitz covers.

Carl Lian

Title: Degenerations of Torus Orbits

Abstract: Let Gr(k,n) be the Grassmannian of k-planes in C^n. The standard torus action on C^n induces a torus action on Gr(k,n), whose orbits encode interesting combinatorial and geometric invariants. I will describe an explicit degeneration of the “generic” torus orbit closure into a union of Richardson varieties (intersections of two Schubert varieties). This gives a new proof of a formula of Berget-Fink for the Chow class of this subvariety of X, and the technique has further (but not yet fully realized) applications in enumerative geometry. The method also works for the variety of full flags in C^n, giving a new proof of an earlier result of Anderson-Tymoczko. Via the toric moment map, the combinatorial shadow of this degeneration is a polyhedral decomposition of the permutohedron due to Harada-Horiguchi-Masuda-Park. Time-permitting, I will mention some ongoing work with Grace Chen extending this story to type B.

Adrian Neff

Title: Residues on Curves

Abstract: Residues of meromorphic differentials on smooth curves have played a prominent role in modern algebraic geometry. In this talk, we will first briefly discuss the history of residues and generalizations on smooth curves. We will then see how to extend the definition of residues to singular curves over local artinian rings and discuss how one shows this datum is well-defined in characteristic 0. Time permitting, we may also see how one can extend these ideas to positive characteristic.  

Organized by Jon Kim, Taylor Rogers (CU), and Ross Flaxman (CSU)