Conference: A Conference on the Geometry, Topology, and Dynamics of Infinite-Type Surfaces

The purpose of this project is to provide travel and accommodation support for participants based in the United States to attend the workshop "A Conference on the Geometry, Topology, and Dynamics of Infinite-Type Surfaces", which will take place at the Casa Matemática Oaxaca in Oaxaca, Mexico from the 22nd to 27th of June, 2025. The workshop aims to create a dynamic platform where both established and emerging researchers, specializing in infinite-type surfaces and related fields, can come together.

This event's goal is twofold: first, to facilitate a comprehensive understanding of recent breakthroughs in the field, and second, to explore various avenues for future research and encourage future collaboration. Furthermore, enabling US-based scientists to attend this international meeting has two additional benefits: (1) Allowing for future long term collaborations with researchers outside of the US, and (2) Providing a means to disseminate research and results to the global mathematical community.

Infinite-type surfaces serve as a common thread connecting various areas of mathematics. An infinite-type surface is a two dimensional manifold with "infinitely much topology,'' e.g. the sphere with a Cantor set of points removed or a surface of infinite genus. They appear in the study of polygonal billiards, topological dynamics, as generic leaves of foliations on compact spaces, in the study of Thompson groups, or in 3-manifolds that fiber over the circle.

More recently, there has been a significant surge in the study of mapping class groups associated with infinite-type surfaces, also known as big mapping class groups. These are topological groups exhibiting rich phenomenology. As automorphism groups of countable structures, often endowed with well-defined large-scale geometry, they also inhabit the intersection of geometric group theory, model theory, and descriptive set theory.

While infinite-type surfaces possess this interdisciplinary nature, historically, only two workshops (in 2013 and 2019) have brought together experts from diverse fields sharing this common theme. Thus, the primary scientific objective of this workshop is to convene a diverse group of mathematicians to facilitate cross-pollination among the different areas converging on infinite-type surfaces.

More information on this workshop can be found at: https://www.birs.ca/events/2025/5-day-workshops/25w5359.

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.