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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.

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.

Speakers:

  • Aleksander Doan (Columbia)
  • Simon Donaldson (Stony Brook and Imperial College London)
  • Penka Georgieva (Paris)
  • Andriy Haydys (Freiburg)
  • Eleny Ionel (Stanford)
  • Dominic Joyce (Oxford)
  • Yang Li (Institute for Advanced Study)
  • Davesh Maulik (MIT)
  • Tony Pantev (University of Pensylvania)
  • Tristan Riviere (Zurich)
  • Pavel Safronov (Zurich)
  • Vivek Shende (U. C. Berkeley)
  • Song Sun (U. C. Berkeley)
  • Richard Thomas (Imperial College London)

Progress and Open Problems 2019: September 8-11, 2019, SCGP, Stony Brook

Arrival date: Saturday, September 7.
Departure date: Wednesday afternoon, September 11, or Thursday, September 12.

Schedule:

SUN 8 SEP

MON 9 SEP

TUES 10 SEP

WED 11 SEP

8:30 -9:30

Breakfast Breakfast Breakfast Breakfast

9:30-10:30

B. Lawson A. Hanany C. Hull C. Vafa

10:30-11:00

Coffee/tea Coffee/tea Coffee/tea Coffee/tea

11:00-12:00

M. Larfors R. Conlon G. Ball A. Klemm

12:00-13:00

Lunch Lunch Lunch Lunch

13:00-14:00

D. Morrison (SCGP Weekly Talk)

13:30

Leave for NYC (from hotel)

14:00-15:00

S.-T. Yau N. Fornasin

15:30-16:00

Tea Tea Tea

16:00-17:00

A. Waldron B. Willett A. Moroianu

18:00-20:00

Conference Banquet

Speakers:

This conference will be immediately followed by our Third annual meeting held at the Simons Foundation in New York City.

Special Holonomy and Calibrated Geometry, Imperial College, 3-7 June 2019

Arrival Date: Sunday June 2, 2019. Departure Date: Saturday June 8, 2019.

All talks will take place in the Huxley Building, room 140.
Registration and coffee/tea are in the Huxley 5th floor common room.

Scientific Organizers: Mark Haskins and Dominic Joyce

Local Organizer: Mark Haskins


Schedule

MON 3 JUNE

TUE 4 JUNE

WED 5 JUNE

THU 6 JUNE

FRI 7 JUNE

9:00 -9:30

REGISTRATION

9:30-10:30

Haskins Putrov Donaldson 1 Treumann Donaldson 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

Yng-Ing Lee Imagi Bellettini 1 Zaslow Nordström

12:30-14:00

LUNCH LUNCH LUNCH LUNCH LUNCH

14:00-15:00

Lotay Abouzaid Bellettini 2 Joyce

15:00-15:30

COFFEE COFFEE COFFEE COFFEE

15:30-16:30

Solomon Lekili Discussion Yang Li

16:30-17:00

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

19:00-21:00

SOCIAL DINNER

Speakers:

Physics and Special Holonomy, KITP, 8-12 April 2019

Arrival Date: Sunday April 7, 2019. Departure Date: Saturday April 13, 2019.

All talks and discussions will be held in the Main Seminar Room at KITP on the UC Santa Barbara campus.

Shuttle service will be provided for conference participants between the Best Western South Coast Inn and KITP beginning at 7:45 a.m. each morning, with return shuttles beginning 15 minutes after the conclusion of the final event of the day.


Schedule

MON 8 APR

TUE 9 APR

WED 10 APR

THU 11 APR

FRI 12 APR

9:00 -9:50

Haskins 1 Halverson Schafer-Nameki Li Fiset

9:50-10:20

COFFEE COFFEE COFFEE COFFEE COFFEE

10:20-11:10

Kachru Del Zotto Gukov 1 Goette Heckman

11:10-12:50

LUNCH LUNCH LUNCH LUNCH LUNCH

12:50-13:40

Haskins 2 DISCUSSION Gukov 2 Kane DISCUSSION

13:40-14:30

Acharya Sun Xie Cvetic COFFEE

14:30-15:00

COFFEE COFFEE COFFEE COFFEE END OF MEETING

15:00-15:50

Lotay Braun Barbosa Kinsella

15:50-16:40

DISCUSSION DISCUSSION DISCUSSION DISCUSSION

17:30-18:00

Reception

18:00-?

Conference Banquet

Speakers:

Donaldson, Sun, & Xiu Xiong Chen awarded the Oswald Veblen prize

Collaboration Principal Investigators Sir Simon Donaldson and Song Sun, as well as their Stony Brook colleague Xiu Xiong Chen, will be awarded the Oswald Veblen Prize In Geometry by the American Mathematical Society at the Joint Math Meetings in January 2019. Read the AMS news item about the award.

Bobby Acharya awarded the Lawrence Bragg medal.

Bobby Acharya, one of our Collaboration’s Principal Investigators, has been awarded the 2018 Lawrence Bragg medal from the Institute of Physics. Congratulations, Bobby!

Progress and Open Problems 2018: September 9-12, 2018, SCGP, Stony Brook

Arrival date: Saturday, September 8.
Departure date: Wednesday afternoon, September 12, or Thursday, September 13.

Schedule:

SUN 9 SEP

MON 10 SEP

TUES 11 SEP

WED 12 SEP

8:30 -9:30

Breakfast Breakfast Breakfast Breakfast

9:30-10:30

E. Svanes S. Salamon S. Donaldson S. Gukov

10:30-11:00

Coffee/tea Coffee/tea Coffee/tea Coffee/tea

11:00-12:00

T. Walpuski Y. Tanaka Y. Zhang G. Chen

12:00-13:00

Lunch Lunch Lunch Lunch

13:00-14:00

M. Haskins (SCGP Weekly Talk)

13:30

Leave for NYC (from hotel)

14:00-15:00

A. Haydys A. Fino

15:30-16:00

Tea Tea Tea

16:00-17:00

D. Morrison H. Hein M. Upmeier

18:00-20:00

Conference Banquet

Speakers:

This conference will be immediately followed by our Second annual meeting held at the Simons Foundation in New York City.

Alex Waldron: Lectures

September 8, 2019
TITLE: G2-instantons on the 7-sphere

ABSTRACT: I’ll discuss a forthcoming paper studying families of G_2-instantons on S^7, focusing on those which are obtained by pulling back asd instantons on S^4 via the quaternionic Hopf fibration. In the charge-1 case this yields a smooth and complete 15-dimensional family. The situation for higher charge is more complicated, but we are able to compute all the infinitesimal deformations.

June 4 and June 6, 2018
TITLE: Recent developments in Yang-Mills flow

ABSTRACT: YM flow is the basic evolution equation for a connection on a vector bundle over a Riemannian manifold. It functions both as an important tool in classical gauge theory, and as a model problem for more highly nonlinear parabolic equations (such as Ricci flow or Bryant’s Laplacian flow). In the first of two talks, I will give an introduction to the subject and describe some historical results. In the second I will describe my own results in the four-dimensional case, and briefly discuss some forthcoming work with Goncalo Oliveira characterizing blowup in the exceptional holonomy scenario.

Esther Cabezas-Rivas: Lectures

June 5, 2018
TITLE: Ricci Flow, non-negative curvatures & beyond

ABSTRACT: In order to use the Ricci flow to prove classification results in geometry and control the behaviour of solutions as times goes by, it is crucial to look for properties of the manifold that are preserved under the flow. During the talk we will see that this is typically the case for a large family of non-negative curvature conditions.
In contrast, the condition of almost non-negative curvature operator (e.g. the condition that its smallest eigenvalue is larger than -1) is not preserved under Ricci flow. In this second talk we will present a work (joint with Richard Bamler and Burkhard Wilking) in which we generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an application of our almost preservation results we deduce a variety of gap and smoothing results of independent interest, including a classification for non-collapsed manifolds with almost non-negative curvature operator and a smoothing result for singular spaces coming from sequences of manifolds with lower curvature bounds. We also obtain a short-time existence result for the Ricci flow on open manifolds with almost non-negative curvature (without requiring upper curvature bounds).

June 4, 2018
TITLE: The ABC of Ricci Flow

ABSTRACT: Geometric flows have been used to address successfully key questions in Differential Geometry like isoperimetric inequalities, the Poincaré conjecture, Thurston’s geometrization conjecture, or the differentiable sphere theorem. During this talk we will give an intuitive introduction to Ricci flow, which is sort of a non-linear version of the heat equation for the Riemannian metric. The equation should be understood as a tool to canonically deform a manifold into a manifold with nicer properties, for instance, some kind of constant curvature. We will emphasize the features that convert evolution equations into a powerful tool in geometry.

Celso Viana: Lectures

June 7, 2018
TITLE: The evolution of the Whitney sphere along mean curvature flow

ABSTRACT: In this talk we will be concern with the evolution of the Whitney sphere along the Lagrangian mean curvature flow. We show that equivariant Lagrangian spheres in Cn satisfying mild geometric assumptions collapse to a point in finite time and the tangent flows converge to a Lagrangian plane with multiplicity two.