Arrival Date: Sunday January 5, 2020. Departure Date: Saturday January 11, 2020.

All talks will be at Huxley Bldg 140.  [ click for map ]

Registration and coffee/tea are in the Huxley 5th floor common room.

Scientific Organizers: Dominic Joyce joyce@maths.ox.ac.uk, Aleksander Doan doan@math.columbia.edu.

Timetable

Speakers (click on title to see abstract and lecture slides):

• Aleksander Doan (Columbia and Cambridge), On complexification and categorification
• Sir Simon Donaldson (Simons Center, Stony Brook and Imperial College London), Gauge theory and special holonomy I,II
• Penka Georgieva (Jussieu), Real Gromov-Witten theory
• Andriy Haydys (Freiburg), On the blow up set for the Seiberg-Witten equations with two spinors
• Siqi He (Simons Center, Stony Brook), The counting problem of the Kapustin-Witten equations
• Eleny Ionel (Stanford), Counting embedded curves in 3-folds
• Dominic Joyce (Oxford), Shifted symplectic Derived Algebraic Geometry for dummies
• Yang Li (Institute for Advanced Study), Informal talk:
• Yang Li (Institute for Advanced Study), High codimension phenomena for Hermitian Yang-Mills connections
• Davesh Maulik (MIT), Stable pair invariants for Calabi-Yau 4-folds
• Tony Pantev (University of Pennsylvania), Constructing shifted symplectic structures
• Tristan Rivière (ETH, Zürich), L^p-bounded curvatures in high dimensions
• Pavel Safronov (Universität Zürich), Enumerative invariants from supersymmetric twists
• Vivek Shende (UC Berkeley), Skeins on Branes
• Song Sun (UC Berkeley), Singular Hermitian-Yang-Mills connections and reflexive sheaves
• Richard Thomas (Imperial College London), Borisov-Joyce in algebraic geometry

The workshop will have two main themes:

(A) The Donaldson-Segal programme for defining enumerative invariants of compact G2-manifolds by counting G2 instantons, with correction terms from associative 3-folds. Analysis of G2-instanton moduli spaces, singularities of G2-instantons. Analysis of Seiberg-Witten type equations on 3-manifolds used to define correction terms in Donaldson-Segal programme. Related gauge theory problems, including singularities of Hermitian-Yang Mills connections.

(B) The Pantev-Toën-Vaquié-Vezzosi theory of shifted symplectic derived algebraic geometry, giving geometric structures on Calabi-Yau moduli spaces, and its applications to generalizations of Donaldson-Thomas theory of Calabi-Yau 3- and 4-folds. One particular aim is to present the theory in a way accessible to String Theorists, to encourage communication between mathematicians and physicists on this subject, and to facilitate interpretation of the implications of the theory in String Theory terms. Algebro-geometric enumerative invariants (and Floer theories, etc), particularly of Calabi-Yau manifolds, related to the PTVV theory: Donaldson-Thomas, Gromov-Witten, and Vafa-Witten invariants, Donaldson-Thomas type invariants of Calabi-Yau 4-folds, the Gopakumar-Vafa conjecture.

Attendance at the workshop is by invitation only (except for London locals). Non-invitees wishing to attend may contact the organizers, but are likely to be disappointed, as we are already inviting as many as the lecture theatre will comfortably hold, so we can only include others if we have refusals.