Seiberg–Witten invariants
Spin-c structures, Dirac operators, the Seiberg–Witten equations, adjunction inequalities, Kähler surfaces, Bauer–Furuta invariants, and the 10/8 theorem.
Lectures and videos
Recorded courses and talks
Lecture series and selected talks on gauge theory, low-dimensional topology, instanton homology, knots, webs, and four-manifolds.
Courses
Lecture series
Multi-lecture courses intended for graduate students and researchers.
Instanton homology for links and webs in 3-manifolds
A Minerva mini-course on instanton Floer homology, knot and web invariants, Khovanov homology, higher-rank generalizations, and the four-color problem.
Instantons, knots and Khovanov homology
A five-day masterclass at the Centre for Quantum Geometry of Moduli Spaces, with recordings and introductory slides.
Selected talks
Conference and research lectures
Individual lectures and institutional video collections.
2025
SU(3) instanton homology for knots and webs
Gauge Theory and Floer Homology in Low Dimensional Topology, Simons Center for Geometry and Physics.
2023
Gauge theory and low-dimensional topology
Conference at the Institute of the Mathematical Sciences of the Americas, University of Miami.
2018
Knots, three-manifolds and instantons
ICM plenary lecture with Peter Kronheimer, Rio de Janeiro.
2016
An approach to the Four Color Theorem via gauge theory and three-manifold topology
Recent Developments in the Mathematical Study of Gauge Theory, Simons Center for Geometry and Physics.
2011–25
SCGP lecture archive
Six recordings, including lectures on instanton knot homology, webs and foams, four-manifolds, the four-color theorem, and SU(3) instanton homology.
Links and titles checked September 2026. Institutional course or archive pages are included when available to provide a stable reference if a video host changes its URL.