Joint IAS/Princeton University Number Theory Seminar | |

Topic: | Low-lying Fundamental Geodesics |

Speaker: | Alex Kontorovich |

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.