Conference: Higher Rank Geometric Structures

This award provides support for US-based mathematicians and graduate students to participate in a school and two workshops associated to a trimester program on “Higher Rank Geometric Structures” organized by the Institute Henri Poincaré (IHP), Paris, from April to July 2025. The school will be held the at the CIRM-Centre International de Rencontres Mathématiques near Marseille, France, while the two workshops will take place at the IHP.

This school will offer an opportunity for US based graduate students and post-doctoral fellows to learn a variety of topics on higher rank geometric structures from international experts. The two workshops will bring together researchers throughout the world and give the US based attendees a venue to exchange ideas and make connections with their European and international colleagues. The primary focus of the award is to support travel for early career US-based mathematicians.

The study of discrete subgroups of Lie groups has a long history with connections to many different areas of mathematics including geometry, dynamics and number theory. Some of the earliest advances in the field (of Mostow, Margulis, Ratner) were about characterizing rigidity. For example, showing that a group is isomorphic to a unique lattice in a Lie group.

On the other hand, Teichmüller theory and Thurston’s theory of hyperbolic 3-manifolds involved studying the deformation theory of hyperbolic 2 and 3-manifolds. While Thurston developed this theory in the 70’s (depending heavily on the earlier work of the Ahlfors-Bers school) this deformation theory of flexible groups was largely undeveloped outside of these two examples.

This changed two decades ago when Labourie introduced the notion of an Anosov subgroup and Fock- Goncharov gave coordinates for studying certain discrete representations of surface groups in semi-simple Lie groups. Since then, the subject has grown immensely and attracted a multitude of researchers. This award will give the opportunity to early career mathematicians from the US to learn from and interact with experts from all over the world who are leading the field.

Further information about the school and workshops can be found at the website: https://indico.math.cnrs.fr/event/11551/

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.