Front Range Algebraic Geometry Day

 We are proud to announce the

Fall 2025 

Front Range Algebraic Geometry Day

at Colorado State University, Weber 201

Thursday, October 30, 2025,

 1:00 pm - 5:00 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

Rohini Ramadas

Title: Degenerations and irreducibility problems in dynamics 

Abstract: This talk is about an application of combinatorial algebraic geometry to complex/arithmetic dynamics. The n-th Gleason polynomial G_n is a polynomial in one variable with Z-coefficients, whose roots correspond to degree-2 polynomials with an n-periodic ramification point. Per_n is an affine algebraic curve, defined over Q, parametrizing degree-2 rational maps with an n-periodic ramification point. Two long-standing open questions in complex dynamics are: (1) Is G_n is irreducible over Q? (2) Is Per_n connected? We show that if G_n is irreducible over Q, then Per_n is irreducible over C, and is therefore connected. In order to do this, we find a Q-rational smooth point on a projective completion of Per_n — this Q-rational smooth point represents a special degeneration of degree-2 self-maps. 

Ignacio Rojas

Title: 

Abstract: 

Rob Silversmith

Title: Chromatic polynomials and moduli of curves 

Abstract: The chromatic polynomial of a graph, which counts colorings of the graph, has a habit of showing up in unexpected places in geometry, e.g. in the theory of hyperplane arrangements. This sometimes has interesting purely combinatorial consequences, such as Huh's proof of Hoggar/Read's conjecture on coefficients of chromatic polynomials.

I'll discuss a new incarnation of chromatic polynomials. To a graph G, we can naturally associate a sequence of intersection numbers on moduli spaces of stable curves. Surprisingly, we prove that these recover values of the chromatic polynomial of G at negative integers.

I'll also discuss how this leads to new algebraic invariants of directed graphs.

(Joint with Bernhard Reinke)

Sandra Nair

Title: The Ekedahl-Oort and Newton stratification of the GU(3,2) Shimura variety

Abstract: Unitary Shimura varieties of $\mathrm{sgn}(a,b)$ parametrize abelian varieties in characteristic $p$ of dimension $a+b$ with an action of signature $(a,b)$ by an order in an imaginary quadratic field in which $p$ is inert. We describe the interaction of two stratifications of Shimura varieties of $\mathrm{sgn}(3,2)$: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. We identify which Ekedahl-Oort and Newton strata intersect. This is a joint collaboration with Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson, and Steven R. Groen.

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