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Jul

10

2020

In this talk we will begin by defining elliptic curves from three perspectives. The first is as the space of solutions to certain polynomial equations in two complex variables, the second is as a parallelogram with certain sides identified by translation, and the third is as the complex numbers modulo some period lattice. There are interesting classes of functions on these surfaces called elliptic functions.

Jul

13

2020

Hypergeometric functions in various forms are ubiquitous in mathematics. Hypergeometric functions over finite fields are character sums, and they have applications to counting points of varieties over finite fields, which provide information on the corresponding Galois representations (and L-functions). Classical hypergeometric functions, and their finite fields version have parallel properties. In this talk, we give an overview of hypergeometric functions over complex field, finite fields, and their truncated version.

Jul

15

2020

Jul

17

2020

Jul

20

2020