Home » Lectures » Geometry and Analysis of Moduli Spaces, Imperial College, 6-10 January 2020

Geometry and Analysis of Moduli Spaces, Imperial College, 6-10 January 2020

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.


Provisional Timetable

MON 6 JAN

TUE 7 JAN

WED 8 JAN

THU 9 JAN

FRI 10 JAN

9:00 -9:30

REGISTRATION

9:30-10:30

Joyce Donaldson 2 Doan Georgieva Li 2

10:30-11:00

Q&A / Discussion Q&A / Discussion Q&A / Discussion Q&A / Discussion Q&A / Discussion

11:00-11:30

Coffee Coffee Coffee Coffee Coffee

11:30-12:30

Thomas Sun Riviere Ionel He

12:30-14:00

Lunch Lunch Lunch Lunch Lunch

14:00-15:00

Pantev 1 Pantev 2 Maulik Haydys

15:00-15:30

Coffee Coffee Coffee Coffee

15:30-16:30

Donaldson 1 Safronov Li 1 Shende

16:30-17:00

Q&A / Discussion Q&A / Discussion Q&A / Discussion Q&A / Discussion

19:00-21:00

Social Dinner

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

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.