Conference: Gauge Theory and Topology

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

This awards support participation of US-based mathematicians in the conference "Gauge Theory and Topology", which will take place at the Clay Mathematics Institute, Oxford, UK, on July 24-28, 2023.The conference will bring experts from around the world together to discuss issues of current interest in geometry and topology, focusing on the areas of Floer homology, low-dimensional topology, and gauge theory. A broad range of topics within the field will be covered, creating opportunities for interaction of researchers at different career stages and those working in different subfields. The breadth of conference topics will present an excellent training opportunity for young researchers, who would be exposed to a wealth of current knowledge and a range of long-standing and newly accessible problems in the field. The funding will primarily be used to support graduate students and young researchers, with priority given to qualified participants from underrepresented groups. Beginning with the discovery of Donaldson theory, Seiberg-Witten theory, and Floer homology several decades ago, extracting geometrical and topological meaning from equations on manifolds has been a powerful tool that led to many breakthroughs in the area, often in combination with the more classical topological techniques. These areas of mathematics, as well as newer subfields such as Heegaard Floer theory, continue to thrive, but each has grown to become a separate field, with somewhat limited interaction between them. The meeting will encompass a broad range of topics to encourage cross-fertilization of ideas and connections and collaborations of experts in different subfields. Topics of particular current interest include new developments in gauge theory and geometric partial differential equations, including instanton invariants and the family Seiberg-Witten invariants; the topology of 4-manifolds, including advances in topological 4-manifolds and the study of embedded surfaces; and Floer homology for 3-manifolds, including equivariant Floer homology, knot detection and the relations between instanton and monopole homology. The conference will focus on recent achievements and new developments in gauge theory and topology. It is expected to give rise to new questions, opening the door to further progress in the area. Webpage: https://www.claymath.org/events/gauge-theory-and-topology-celebration-peter-kronheimers-60th-birthday 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.