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Seminar
Counting lattices: algebraic geometry, non-algebraic geometry and modularity
Speaker
Zhiyu Zhang (Stanford)
Date
Fri, Nov 8 2024, 4:00pm
Location
384H

Counting special lattices inside the "moduli space" of all lattices with extra symmetry leads to interesting invariants e.g. L-functions and orbital integrals, and interesting questions e.g. the fundamental lemma. I will explain my related research on a generalization of this toy model to "moduli space” of algebraic varieties, with interesting questions e.g. special cycles on moduli spaces, Gross-Zagier formulas on moduli of elliptic curves, and arithmetic fundamental lemma, where we are counting “lattices” with extra symmetry of Frobenius. Finally, I will mention counting “lattices” inside non-algebraic “manifolds", the role of Fourier transform and modularity of theta series, in the framework of relative Langlands duality.