Joint IAS/Princeton University Number Theory Seminar

Low-lying, fundamental, reciprocal geodesics

Markoff numbers give rise to extremely low-lying reciprocal geodesics on the modular surface, but it is unknown whether infinitely many of these are fundamental, that is, the corresponding binary quadratic form has fundamental discriminant. In joint work with Jean Bourgain, we unconditionally produce infinitely many low-lying (though not "extremely" so), reciprocal geodesics on the modular surface, settling a question of Einsiedler-Lindenstrauss-Michel-Venkatesh. Some ingredients are expander graphs, sieving on thin orbits, and producing a level of distribution "beyond expansion". No prior knowledge of these topics will be assumed.

Date & Time

March 24, 2016 | 4:30pm – 5:30pm

Location

S-101

Affiliation

Rutgers University; Member, School of Mathematics

Event Series

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