Algebraic & Enumerative Combinatorics - Maria Gillespie-A Positive Combinatorial Rule for Psi Class Products on Multicolored Spaces

Thursday, March 5, 2026 2:30 pm - 3:30 pm EST (GMT -05:00)
Speaker: Maria Gillespie
Affiliation: Colorado State University
Location: MC 5417

Abstract: We use a new combinatorial construction and a sign-reversing involution to simplify an alternating sum that arises naturally in intersection theory on moduli spaces of curves. In particular, it is well known that a product of ψ classes on the moduli space M₀,ₙ-bar, the most commonly studied compactification of the moduli space M₀,ₙ of choices of n distinct marked points on ℙ¹, is equal to a multinomial coefficient and has many natural combinatorial interpretations.

There are similar ψ class products on other compactifications of M₀,ₙ, including the "multicolored" spaces, in which the answer is a positive integer and yet only signed summation formulas were known. We simplify the alternating sum formula in the multicolored case to give a positive combinatorial rule, and discuss some applications of the formula. This is joint work with Vance Blankers and Jake Levinson.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm in MC 5417.