Front Range Algebraic Geometry Day

We are proud to announce the

Spring 2026

at University of Colorado Boulder, MATH 350

Thursday, April 2, 2026,

1:00-5:00

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

Thank you everyone for joining!

Photo credit: Ignacio Rojas

Schedule:

1:00-1:30 Coffee
1:30-2:30 Jeongseok Oh
2:30-2:40 Break
2:40-3:10 Daniel Lyness
3:10-3:20 Break
3:20-4:20 Ruijie Yang
4:20 Closing remarks
5:00 Dinner

Talks and Abstracts

Jeongseok Oh

Title: Virtual cycles via Fulton classes

Abstract: The (-2)-shifted cotangent bundle N of a derived scheme M whose tangent complex has three terms -- arguably the mildest non-quasi-smooth case -- admits a fibrewise torus action which is not symplectic. We construct an equivariant lift of the virtual cycle of N using an equivariant version of the Fulton class of M, which may be viewed as a localisation formula for this non-symplectic action.

We also study the difference between the virtual cycle of N and the Fulton class of M via the non-equivariant analogue, which may shed light on the virtual cycle of M.

Daniel Lyness

Title: Geometric Invariant Theory for pairs of plane curves

Abstract: Geometric Invariant Theory, developed by Mumford, is a powerful tool for finding compactifications of moduli spaces. The construction involves taking a quotient of a Hilbert Scheme by a linear group, to identify isomorphic objects. I will be explaining the basics of the theory, including how to make sure that the resulting quotient is actually a variety. Then we will apply this construction to find compactifications of the moduli spaces of plane curves and pairs of plane curves.

Ruijie Yang

Title: How big is the maximal Jordan block of a monodromy matrix?

Abstract: In the study of the singularities of a complex polynomial, geometric information is often encoded in linear algebra. For example, the Milnor fibers of a singularity give rise to monodromy matrices, whose eigenvalues have long been fully understood. However, knowing the eigenvalues does not tell us the full story of the Jordan canonical form. In this talk, I will explain why the maximal size of the associated Jordan blocks has historically been difficult to determine, and present a full solution to this problem using Hodge theory and D-modules. This is based on the joint work with András Lőrincz.

Bob Kuo (Cancelled)

Title: TBA

Abstract: TBA

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

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