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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 about 1 month ago
To apply for Funding you must register by: August 31, 2022 3 months ago
Parent Program:
Location: 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)

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Description
Msri pic crop
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
Schedule, Notes/Handouts & Videos
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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 (Trinity College; 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 (MSRI - Mathematical Sciences Research Institute)