Collaborative Research: Conference: Topological and Geometric Structures in Low Dimensions

This award provides partial support for US-based participants in activities related to the thematic program "Topological and Geometric Structures in Low Dimensions", which will occur July 2 through September 12, 2025 at Centre de Recherches Mathématiques, Montréal (CRM), with some activities held at Université du Québec à Montréal (UQAM). The primary purpose of the is to disseminate the most current results in low-dimensional geometry and topology and to foster interaction between researchers in some of the most active and rapidly developing areas within the field.

Participation of early-career researchers in these activities will provide opportunities to make new professional connections, collaborate with peers, establish access to experts in their field, and learn the details of distinct topics of contemporary interest through attending mini-courses, conferences, and other program activities.

One component of this collaborative project is support through the lead organization (Temple University) for participation in the thematic program, including three focused activities, each for 40 to 50 participants, consisting of a week of mini-courses followed by a week-long conference: "Topological 4-manifolds" (CRM, July 2-11), "Low-dimensional topology and Floer theory" (UQAM, Aug. 18-29), and "Hyperbolic manifolds of dimension 4 (and more)" (CRM, Sept. 2-12). The second component, through non-lead organization the University of Texas at Austin, is support for participation in the conference "Knots, groups, and manifolds" (UQAM, Aug. 11-15) centered around current developments in low dimensional topology; this conference is attached to the thematic program but organized as a separate event of a significantly larger scale, with over 150 total participants expected.

Broadly speaking, the scientific theme of the activities is contemporary classification problems in low-dimensional topology and the interplay between the algebraic, topological, geometric and analytic structures that arise in these classifications. Central focus will be on emerging areas, new progress in traditional areas, investigating conjectured connections between disparate structures on low-dimensional manifolds, and applications of these methods to the topology of manifolds of dimension 3 and 4.The workshop website is at: https://www.crmath.ca/en/activities/#/type/activity/id/3951

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.