November 3rd |
Nadir Hajouji (UCSB)
Intro to Arithmetic of Elliptic Curves
Abstract: I will give an introductory talk to the arithmetic of elliptic curves. I will briefly define elliptic curves, discuss their group structure, show how they give rise to p-adic Galois representations and explain how attempts to computing the group of rational points on an elliptic curve can be obstructed by counterexamples to the Hasse principle.
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December 1st |
The Riemann zeta function and its modern generalizations
Abstract: The classical Riemann zeta function, made famous from Riemann's 1859 memoir, "On the Number of Primes Less Than a Given Magnitude," shed tremendous light on the mysterious distribution of prime numbers. Generalization of the Riemann zeta function began with Dirichlet who used them to prove a deep result on primes in arithmetic progression. In this talk I will survey the classical Riemann zeta function, its modern generalizations, and how they relate to the Langlands conjectures.
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