Gauge Theory and Floer Homology in Low Dimensional Topology: April 28 – May 2, 2025

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Organized by:

• David Auckly (Kansas State)
• Aliakbar Daemi (Washington Univ-St Louis)
• Olga Plamenevskaya (Stony Brook University)
• Daniel Ruberman (Brandeis)
• Nikolai Saveliev (University of Miami)

In the 1980s, Donaldson introduced methods of Yang–Mills gauge theory in topology, with remarkable applications. By the 1990s, research largely shifted away from Donaldson theory to Seiberg–Witten theory, and, a few years later, to Heegaard Floer theory. In dimension four, the invariants arising from these theories are either known to be equivalent, or at least there are well formed conjectures stating the same. However, it is still a challenge to understand the relationship between the invariants of 3-manifolds arising from Donaldson theory and the invariants from the other gauge theories. Attention is therefore returning to Yang–Mills theory, especially at the level of 3-manifolds and knots, where new structures are being uncovered and new invariants are being defined. The field is developing at breakneck speed in search of elusive relationships between the invariants. It is also expanding: for example, the methods of Yang–Mills and Seiberg–Witten gauge theories have recently led to breakthroughs in the study of the topology of diffeomorphism groups of 4-manifolds. The proposed five-day international workshop aims to account for all of these developments.