Advisor: Dr. Jeff Achter

Committee:  Dr. Rachel Pries, Dr. Jamie Juul, Dr. Indrajit Ray

Title: Explicit and quantitative results for abelian varieties over finite fields

Abstract: Given an elliptic curve $E$ over a finite field, one may study the number of points of $E$, as well as the number of curves in its isogeny class. Moreover, for an elliptic curve defined over $\F_p$, one can study the statistics of these quantities after base change to $\F_{p^n}$. These statistics are controlled by the sequence of integer multiples of a certain irrational number attached to $E$. The theory of equidistribution of sequences and quasi-Monte Carlo integration provides both explicit and quantitative methods to understand the behavior of such a sequence. More generally, the theory of quasi-Monte Carlo lends itself to the study of invariants of abelian varieties over finite fields, giving both distributions and speed of convergence to the distribution.

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Meeting ID: 997 0579 9700

Passcode: 999604