### Algebra SeminarSato-Tate Distributions And Identities Of Symplectic CharactersKyu-Hwan Lee (University Of Connecticut)

Wednesday, October 28, 2020
11:15am – 12:05pm

Storrs Campus
WebEx

The Sato$$--$$Tate distributions for genus $$2$$ curves (conjecturally) describe the statistics of numbers of rational points on the curves. In this talk, we explicitly compute the auto-correlation functions of Sato$$--$$Tate distributions for genus $$2$$ curves as sums of irreducible characters of symplectic groups. Our computations bring about families of identities involving irreducible characters of symplectic groups, which have interest in their own rights.