|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||Low-lying Fundamental Geodesics|
|Affiliation:||Yale University; Member, School of Mathematics|
|Date:||Thursday, February 6|
|Time/Room:||4:30pm - 5:30pm/Fine 214, Princeton University|
It is classical that an element of the class group of a real quadratic field corresponds to a closed geodesic on the modular surface, but not every closed geodesic arises this way; we call those that do "fundamental." Given a fixed compact subset W of (the unit tangent bundle of) the modular surface, we say a closed geodesic is "low-lying" if it is contained in W; in particular, it does not enter "high" into the cusp. In joint work with Bourgain, we exhibit a region W which contains infinitely many fundamental geodesics, answering a question of Einsiedler-Lindenstrauss-Michel-Venkatesh.