The collaboration will hold a VIRTUAL meeting on 11-15 January, 2021, entitled “Donaldson-Thomas invariants and Resurgence”.
Dominic Joyce, Simon Salamon, and Sakura Schafer-Nameki.
3-Calabi-Yau triangulated categories T are a major area of research in Geometry and String Theory. Examples include derived categories Dbcoh X of coherent sheaves and the derived Fukaya category DbF(X) on a Calabi-Yau 3-fold X, where Kontsevich’s Homological Mirror Symmetry Conjecture explains mirror symmetry between Calabi-Yau 3-folds X, X* as equivalences of categories Dbcoh X = DbF(X*), DbF(X) = Dbcoh X*.
For such a 3-Calabi-Yau category T one can consider the moduli space Stab(T) of Bridgeland stability conditions on T, and for each σ in Stab(T) one can (under good conditions) define Donaldson-Thomas (D-T) invariants DTα(σ), which are rational numbers ‘counting’ σ-semistable objects in class α in Knum(T).
A nice example, which will be covered at the conference, is a class of categories T of derived representations of a quiver with superpotential (Q,W), in which Stab(T) and DTα(σ) can be described by work of Bridgeland and Smith in terms of quadratic differentials on a Riemann surface.
Recent work of Tom Bridgeland and coauthors explains how to encode D-T invariants into interesting geometric structures on Stab(T), involving Stokes phenomena and Riemann-Hilbert problems for singular flat connections, and connected (via Tom’s paper with Ian Strachan) to complex hyperkahler manifolds and twistor theory. All this is related to work of Kontsevich and Soibelman on analytic stability data and resurgence, and to a circle of ideas in String Theory, including work of Gaiotto, Moore and Neitzke, and topics such as resurgence, WKB analysis, and line operators.
The conference will explain these ideas with introductory talks, and aim to promote communication between Geometers and String Theorists, to better understand this new and fast-moving area.
The virtual meeting comes in two parts:
- Recorded lectures which can be viewed by participants at any time, and;
- “Live” lectures streamed via Zoom and YouTube, which can also be watched later. Our live sessions will also include some discussions, which may include discussions of both the live lectures and the recorded lectures. YouTube access for the lectures is available at
Our recorded lectures are as follows. Those who are unfamiliar with Bridgeland stability should endeavor to watch these recorded lectures before the live lectures by Bridgeland.
- Fabian Haiden (Oxford), Introduction to Bridgeland stability
- Dominic Joyce (Oxford), Donaldson-Thomas theory of Calabi-Yau 3-folds
Our live schedule is as follows. – All times are given in British time, in honor of the originally planned venue for the meeting, as well as in Eastern Daylight Time. (Please refer to a time zone converter if you aren’t sure what time it will be in your time zone). There will be a brief conference introduction from Robert Bryant prior to the first talk on Monday.
You can download the programme of this meeting, or consult the version below.
MON 11 JANUARY
TUE 12 JANUARY
WED 13 JANUARY
THU 14 JANUARY
FRI 15 JANUARY
|B. Pym||M. Kontsevich||G. Moore||T. Bridgeland, III||I.-A. Coman|
|T. Bridgeland, I||M. Mariño||F. Yan||S. Donaldson I||S. Donaldson II|
|Meal break||Meal break||Meal break||Meal break||Meal break|
|I. Smith||T. Bridgeland, II||Discussion, led by Maxim Kontsevich and Richard Thomas||Discussion on “complex hyperkähler manifolds”, led by Roger Bielawski||Discussion on “DT invariants and resurgence: Good questions for the future?”, led by Joerg Teschner|
|Questions/Discussion||Questions/Discussion||Discussion, con.||Discussion, con.||Discussion, con.|
Documents associated with Thursday’s discussion:
Documents associated with Friday’s discussion:
The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).
- Tom Bridgeland (Sheffield), From Donaldson-Thomas invariants to complex hyperkahler structures (3 lectures)
- Ioana-Alexandra Coman (Amsterdam), Geometric description of topological string partition functions from quantum curves and integrability
- Simon Donaldson (SCGP and Imperial College London), Deformations of singular sets and Nash-Moser theory I, II
- Maxim Kontsevich (IHES, Paris), Analyticity and resurgence
- Marcos Mariño (Geneva), From resurgence to topological strings
- Greg Moore (Rutgers), Informal Remarks Complementary To, And Preparatory For,
Fei Yan’s Talk
Andy Neitzke (Yale), Riemann-Hilbert problems, Hitchin systems and the conformal limit
- Brent Pym (McGill), Introduction to Stokes phenomena and resurgence
- Ivan Smith (Cambridge), Quadratic differentials as stability conditions
- Fei Yan (Rutgers), Line defects, UV-IR map and exact WKB