Abstract:

Geometric Invariant Theory (GIT) gives us a theory of how to take quotients in a way that is 'nice' in an algebraic geometry sense. In 2020, inspired by mirror symmetry, Kite-Segal conjectured the following: Given a wall in a toric Calabi-Yau GIT problem and what we call 'a minimal face of the primary polytope', the multiplicity on the A-side is equal to the multiplicity on the B-side. The theorem was proved in 2022 by Huang and Zhou. The goal of this talk is to explain all the words in this theorem and perhaps to motivate it. Fortunately for us, this doesn't require Hartshorne as a prerequisite. The statement and its proof turn out to be mostly a combinatorics problem thanks to toric geometry. Throughout the talk we will explain all the ingredients needed, including some GIT theory, toric geometry, and a refreshment on derived categories.

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