Number Theory Seminar

Speaker: Patricio Andres Perez Pina

Title:  p-adic and archimedean equidistribution of arithmetic cycles.

Abstract: Let d be a fundamental discriminant. Depending on the sign of d,
one can attach to it a collection of arithmetic cycles inside the complex
points of the modular curve. When d is negative, the collection consists of
the Galois orbit formed by the CM points of discriminant d. In the positive
case, a set of closed geodesics whose length is related to d is considered.
In 1988, Duke established that these collections hold equidistribution
properties when d grows in absolute value. We will start this talk by
recalling this result. Motivated by this, we will review other
equidistribution statements for cycles of p-adic and S-arithmetic nature.
Finally, if time allows, we will explain the techniques used to prove these
statements.

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