## Gauge Theory and Topology: in Celebration of Peter Kronheimer’s 60th Birthday

**Date:**
24 - 28 July 2023

**Location: ** Mathematical Institute, University of Oxford

**Event type:**
CMI Workshop

**Organisers: ** Andrew Lobb (Durham), Ciprian Manolescu (Stanford), Vlad Markovic (Oxford), Olga Plamenevskaya (Stony Brook), Jacob Rasmussen (Cambridge)

Beginning with the work of Donaldson and Floer, the 1980’s saw the development of a powerful circle of ideas relating gauge theory and low-dimensional topology. In the time since, this theory has grown, matured, and developed a wide range of applications. This workshop celebrates the enduring influence of Peter Kronheimer on this field.

Since the 1980’s the subject has seen many important theoretical developments: the advent of Seiberg-Witten theory, the construction of Floer homology theories for 3-manifolds, and extensions including the development of equivariant and family invariants. Along the way, it has developed connections with symplectic and contact topology, the theory of sutured manifolds, and Khovanov homology. The theory has had many remarkable geometric applications, including the proof of the Thom Conjecture, the Weinstein Conjecture, the resolution of thehigh-dimensional Triangulation Conjecture, and new insights into the structure of the concordance and homology cobordism groups.

The workshop will bring experts from around the world together to discuss issues of current interest in the areas of Floer homology, low-dimensional topology, and gauge theory. Topics of particular interest include new developments in gauge theory and geometric PDE’s, including instanton invariants and the family Seiberg-Witten invariant; 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.

**Speakers: ** Mohammed Abouzaid (Columbia), Ali Daemi (Washington, St Louis), Kristen Hendricks (Rutgers), Nigel Hitchin (Oxford), Andras Juhász (Oxford), Hokuto Konno (Tokyo), Maggie Miller (Stanford), Tomasz Mrówka (MIT), Hiraku Nakajima (Kyoto), Peter Ozsváth (Princeton), Lisa Piccirillo (MIT), Arunima Ray (MPIM Bonn), Danny Ruberman (Brandeis), Rosa Sena-Dias (Lisbon), Steven Sivek (MPIM Bonn), Zoltan Szabó (Princeton), Joshua Wang (Harvard), Yi Xie (Peking), Ian Zemke (Princeton), Raphael Zentner (Regensburg)

**Registration is now closed.**