The conference entitled "Geometric Topology in Cortona: Interactions of quantum topology and hyperbolic geometry" will be held in Cortona, Italy, on June 3-8, 2013. This conference will focus on two areas of low-dimensional topology that have had significant overlap in recent years. In particular, the conference will concentrate on the interaction between hyperbolic geometry and quantum topology. In the last two decades, both of these areas have seen significant progress. In hyperbolic geometry, several longstanding conjectures concerning the geometric structure of 3-manifolds and their covers have been proved. On the quantum side, families of TQFTs have been constructed and shown to be related to quantum invariants such as the Jones polynomial. There is increasing evidence that many quantum invariants have connections to hyperbolic geometry, and there are several open conjectures in these directions, including the Volume Conjecture and its variants. This conference will bring together outstanding international researchers in both fields.
This conference has three central goals. First, it will stimulate dialogue among an international group of mathematicians, by bringing together leading experts from the US and other countries to discuss cutting edge research. Second, it will promote an exchange of ideas and collaboration among hyperbolic geometers and quantum topologists, leading to further integration of these two fields. Finally, it will expose graduate students and early career mathematicians to the important developments in these areas. Both junior and senior mathematicians will be given an opportunity to learn of new research and present their results to a broad audience. We expect that this will be a major international conference. More information is available on the conference website: www.dm.unipi.it/~martelli/Cortona/Cortona.html.
In June 2013, an international conference was held in Cortona, Italy, concerning interactions between quantum topology and hyperbolic geometry. Over 70 mathematicians from around the world participated in the conference. This award helped to fund the participation of U.S. based mathematicians in the conference. One of the major goals of the project under intellectual merit was to bring together outstanding researchers in two different fields, quantum topology and hyperbolic geometry, to stimulate new ideas and discussion. Both of these areas have seen significant progress in the last two decades, and there is increasing evidence that quantum invariants have connections to hyperbolic geometry. There are several active areas of research and open questions in both areas, and there are important conjectures relating the areas. By bringing together strong researchers in both fields, this conference stimulated the cross-pollination of ideas and dissemination of results. It also encouraged new collaborations by participants. In terms of broader impacts, one goal was to expose graduate students and early career mathematicians to new areas of research, and to allow them to learn of important developments in the two fields of the conference. Under the award, we were able to fund the participation of several junior mathematicians. Another goal was to encourage the participation of under-represented groups. We strived to encourage their participation by inviting a diverse group of mathematicians.
