# Mathematical Sciences Research Institute

Home » [HYBRID WORKSHOP] New Four-Dimensional Gauge Theories

# Workshop

[HYBRID WORKSHOP] New Four-Dimensional Gauge Theories October 24, 2022 - October 28, 2022
 Registration Deadline: November 03, 2022 3 months ago August 31, 2022 5 months ago
Parent Program: Analytic and Geometric Aspects of Gauge Theory MSRI: Simons Auditorium
Organizers Andriy Haydys (Université Libre de Bruxelles), Lotte Hollands (Heriot-Watt University, Riccarton Campus), LEAD Eleny-Nicoleta Ionel (Stanford University), Richard Thomas (Imperial College, London), Thomas Walpuski (Humboldt-Universität)
Speaker(s)

## Show List of Speakers

Description
Image drawn by Dr. Lotte Hollands
This will be a hybrid workshop with in-person participation only available to members of the semester-long program and invited guests.  Online participation will be open to all who register. Due to limited capacity, mathematicians who have not received an official invitation will not be permitted to enter the institute. This workshop will bring together researchers working on new four-dimensional gauge theories from the perspectives of differential geometry, algebraic geometry, and physics. Over the last 25 years, physicists have made tantalizing conjectures relating the Vafa–Witten equation to modular forms and the Kapustin–Witten and Haydys–Witten equations to knot theory and the geometric Langlands programme. The analytical challenges in the way of establishing these predictions are now being pursued vigorously.  More recently, algebraic geometers have had enormous success in confirming and refining Vafa–Witten's predictions for projective surfaces. The workshop will serve as a platform for reporting on recent progress and exchanging ideas in all of these areas, with the aim of strengthening existing and fostering new interactions. Bibliography
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
• gauge theory

• Vafa–Witten

• Kapustin–Witten

• Haydys–Witten

• Khovanov homology

• geometric Langlands

• geometric PDEs

• Yang-Mills

• moduli spaces

• Z/2Z harmonic spinors

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
Oct 24, 2022
Monday
 09:15 AM - 09:30 AM Welcome 09:30 AM - 10:30 AM Overview of Some Appearances of Multivalued Solutions in Differential Geometry Simon Donaldson (State University of New York, Stony Brook) 10:30 AM - 11:00 AM Break 11:00 AM - 12:00 PM K3 Surfaces as Gauge-Theoretic Moduli Spaces Max Zimet (Stanford University) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM Vafa-Witten Invariants of Projective Surfaces - Overview Martijn Kool (Universiteit Utrecht) 03:00 PM - 03:30 PM Afternoon Tea 03:30 PM - 04:30 PM Holomorphic Floer Theory and Donaldson-Thomas Invariants Pierrick Bousseau (University of Georgia) 04:30 PM - 06:20 PM Reception
Oct 25, 2022
Tuesday
 09:30 AM - 10:30 AM All Gravitational Instantons from Monopole Moduli Spaces Sergey Cherkis 10:30 AM - 11:00 AM Break 11:00 AM - 12:00 PM Homological Link Invariants from Mirror Symmetry Mina Aganagic (University of California, Berkeley) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM Existence and Non-Existence Results of Z2 Harmonic 1-Forms Siqi He (Academy of Mathematics and Systems Science) 03:00 PM - 03:30 PM Afternoon Tea 03:30 PM - 04:30 PM Holomorphic Floer Theory and the Fueter Equation Aleksander Doan (University of Cambridge; University College London)
Oct 26, 2022
Wednesday
 09:30 AM - 10:30 AM Computations of Instanton Knot Floer Homology with Local Coefficients Tomasz Mrowka (Massachusetts Institute of Technology) 10:30 AM - 11:00 AM Break 11:00 AM - 12:00 PM Concentrating Local Solutions of the Two-Spinor Seiberg-Witten Equations Gregory Parker (Stanford University) 12:00 PM - 02:00 PM Lunch
Oct 27, 2022
Thursday
 09:30 AM - 10:30 AM Disconnected Gauge Groups and Categorical Symmetry Mathew Bullimore (University of Durham) 10:30 AM - 11:00 AM Break 11:00 AM - 12:00 PM Hyperkahler Metrics Near Semi-Flat Limits Laura Fredrickson (University of Oregon) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM Counting Solutions of Kapustin-Witten Equations on a Three-Manifold Times a Line from Physics Dualities Pavel Putrov (Abdus Salam International Centre for Theoretical Physics) 03:00 PM - 03:30 PM Afternoon Tea 03:30 PM - 04:30 PM On the Geometry of $G_2$-Monopoles and the Donaldson--Segal Program Ákos Nagy (University of California, Santa Barbara)
Oct 28, 2022
Friday
 09:30 AM - 10:30 AM Hyperkahler Mirror Symmetry Arnav Tripathy (Harvard University) 10:30 AM - 11:00 AM Break 11:00 AM - 12:00 PM Path Integral Derivations of Vafa-Witten and K-Theoretic Donaldson Invariants Jan Manschot (Trinity College) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM Some Remarks on Yang–Mills Type Equations in Higher Dimensions Richard Wentworth (University of Maryland) 03:00 PM - 03:30 PM Afternoon Tea 03:30 PM - 04:30 PM Towards a Monopole Fueter Floer Homology Saman Habibi Esfahani (Duke University; MSRI / Simons Laufer Mathematical Sciences Institute (SLMath))