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Tournaments and slide rules for $\omega$ and $\psi$ class products on $\overline{M}_{0,n}$

Algebra & Discrete Mathematics

Speaker: Sean Griffin, UC Davis
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Location: MSB 1147 + Zoom (livestream)
Start time: Mon, Oct 11 2021, 11:00AM

We present two combinatorial algorithms on trivalent trees that give rise to new geometric interpretations of the multidegrees of certain projective embeddings of the moduli space $\overline{M}_{0,n}$ of stable n-marked genus 0 curves. The first algorithm is in terms of lazy tournaments and gives a simple proof of the fact that the total degree of this moduli space under the iterated Kapranov embedding is $(2n-1)!!$. The second formula is via slide labelings and allows us to express products of omega and psi classes as positive multiplicity-free sums of boundary strata.

This is joint work with Maria Gillespie and Jake Levinson.