Speaker: Thomas Brazelton (Harvard University)

Title: Equivariant enumerative geometry II

Abstract: In this talk we’ll review how an Euler class valued in equivariant homotopical bordism can reveal conserved symmetries in the solutions to equivariant enumerative problems. We apply this idea in joint work with C. Bethea to compute bitangents to symmetric plane quartics, where we will see that homotopical techniques directly reveal patterns which are not obvious from a classical moduli perspective. We will also discuss ongoing work with S. Raman, in which we initiate a study of Galois groups of symmetric enumerative problems, leveraging tools from Hodge theory, hyperbolic geometry, and computational numerical analysis.