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Numerical and Geometric Methods for Ricci-flat Metrics and Flows, virtual meeting online, 24-28 May 2021

The collaboration will hold a VIRTUAL meeting on 24-28 May, 2021, entitled “Numerical and Geometric Methods for Ricci-flat Metrics and Flows”.

Scientific Organizers:
Bobby Acharya, Robert Bryant, and Jason Lotay.


Summary:
This workshop will survey some recent progress in understanding methods for constructing, analyzing, and classifying Ricci-flat metrics, Ricci solitons, and various flows. These methods include traditional geometric estimate-based methods as well as numerical approaches to approximating Ricci-flat metrics. There will talks by both mathematicians and physicists and motivations, methods, and applications in physics will be discussed as well.

We will hold two lectures per day, plus moderated discussion sessions on Tuesday and Thursday. Zoom access to the lectures is by invitation only, but YouTube access for the lectures will also be available at
https://www.youtube.com/channel/UCGw1y7VGRYGM7Wtk07JtFcA/

Our schedule is as follows. – All times are given in British Summer Time 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.

Timetable

MON 24 MAY

TUE 25 MAY

WED 26 MAY

THU 27 MAY

FRI 28 MAY

16:00-17:00 (BST)
11:00-12:00 (EDT)

S. Donaldson H.-J. Hein S. Brendle N. Kapouleas D. Knopf

18:00-19:00 (BST)
13:00-14:00 (EDT)

M. Douglas L. Anderson P. Daskalopoulos T. Ozuch R. Bamler

19:15-21:00 (BST)
14:15-16:00 (EDT)

Discussion Led by A. Ashmore (U. Chicago, physics) Discussion

Speakers:

The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).


Fabian Haiden: Lectures

Recorded lecture associated with the January 2021 meeting
TITLE: Introduction to Bridgeland stability

ABSTRACT:
The lecture provides a first introduction to triangulated categories and stability conditions on them. The motivation for such notions is discussed from the perspective of (homological) mirror symmetry.

Slides of Lecture

Donaldson-Thomas invariants and Resurgence, virtual meeting online, 11-15 January 2021

The collaboration will hold a VIRTUAL meeting on 11-15 January, 2021, entitled “Donaldson-Thomas invariants and Resurgence”.

Scientific Organizers:
Dominic Joyce, Simon Salamon, and Sakura Schafer-Nameki.


Summary:
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:

  1. Recorded lectures which can be viewed by participants at any time, and;
  2. “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
    https://www.youtube.com/channel/UCGw1y7VGRYGM7Wtk07JtFcA/


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.


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.

Timetable

MON 11 JANUARY

TUE 12 JANUARY

WED 13 JANUARY

THU 14 JANUARY

FRI 15 JANUARY

16:00-17:00 (GMT)
11:00-12:00 (EST)

B. Pym M. Kontsevich G. Moore T. Bridgeland, III I.-A. Coman

17:00-17:30 (GMT)
12:00-12:30 (EST)

Questions/Break Questions/Break Questions/Break Questions/Break Questions/Break

17:30-18:30 (GMT)
12:30-13:30 (EST)

T. Bridgeland, I M. Mariño F. Yan S. Donaldson I S. Donaldson II

18:45-20:00 (GMT)
13:45-15:00 (EST)

Meal break Meal break Meal break Meal break Meal break

20:00-21:00 (GMT)
15:00-16:00 (EST)

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

21:00-21:30 (GMT)
16:00-16:30 (EST)

Questions/Discussion Questions/Discussion Discussion, con. Discussion, con. Discussion, con.

Documents associated with Thursday’s discussion:

Slides from Lionel Mason

Documents associated with Friday’s discussion:

Questions from Greg Moore

Speakers:

The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).


Special Holonomy and Branes (AIM workshop)

The collaboration co-sponsored a workshop with the American Institute of Mathematics (AIM) on Special Holonomy and Branes on October 26-30 2020. The workshop was organized by Sergei Gukov, Rafe Mazzeo, and Sakura Schafer-Nameki.
The workshop featured extensive discussions as well as lectures; we have preserved the lectures on this website. The entire conference was held online.


The lecture schedule was as follows. (All times are given in California time.)

Timetable:

MON 26 OCTOBER

TUE 27 OCTOBER

WED 28 OCTOBER

THU 29 OCTOBER

FRI 30 OCTOBER

08:00-09:30 (PDT)

L. Anderson/
A. Braun
L. Fredrickson/
D. Pei
L. Foscolo C. Lawrie T. Walpuski

12:30-14:00 (PDT)

D. Morrison/
J. Lotay
A. Haydys/
J. Sparks
R. Barbosa

Speakers:

The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).


Sun awarded 2021 New Horizons in Mathematics Prize

Collaboration Principal Investigator Song Sun (U. C. Berkeley) has been awarded a 2021 New Horizons in Mathematics prize. The other awardees are Bhargav Bhatt (University of Michigan) and Aleksandr Logunov (Princeton University).

Sun is being recognized “for many groundbreaking contributions to complex differential geometry, including existence results for Kahler-Einstein metrics and connections with moduli questions and singularities.”

Due to the global pandemic, the award ceremony has been postponed until March 2021.

Read the news article.

Special Holonomy: Progress and Open Problems 2020, virtual meeting online, 14, 16, and 18 Sept., 2020

The collaboration will hold a VIRTUAL meeting on 14, 16, and 18 Sept., 2020, entitled “Special Holonomy: Progress and Open Problems 2020”.

Scientific Organizers:
Bobby Acharya bacharya@ictp.it,
Mirjam Cvetič cvetic@physics.upenn.edu, and
Jason Lotay jason.lotay@maths.ox.ac.uk.


Our schedule is as follows. – All times are given in British Summer Time 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).

Timetable

MON 14 SEPTEMBER

WED 16 SEPTEMBER

FRI 18 SEPTEMBER

13:00-14:00 (BST)
8:00am-9:00am (EDT)

Y. Li S. Donaldson D. Joyce

14:00-14:30 (BST)
9:00am-9:30am (EDT)

Discussion I Discussion IV Discussion VII

14:30-15:00 (BST)
9:30am-10:00am (EDT)

Break Break Break

15:00-15:30 (BST)
10:00am-10:30am (EDT)

M. Haskins/J. Nordström K. Dixon J. Lotay

15:30-16:00 (BST)
10:30am-11:00am (EDT)

Discussion II M. Cvetic/G. Zoccarato R. Bryant

16:00-16:30 (BST)
11:00am-11:30am (EDT)

Break Discussion V G. Ball

16:30-17:00 (BST)
11:30am-12:00pm (EDT)

B. Acharya Break Break

17:00-17:30 (BST)
12:00pm-12:30pm (EDT)

Discussion III T. Walpuski D. Morrison

17:30-18:00 (BST)
12:30pm-1:00pm (EDT)

Discussion III Discussion VI Discussion VIII

18:00-18:30 (BST)
1:00pm-1:30pm (EDT)

Discussion VI Discussion VIII

Discussion Sessions:

  • Discussion I: SYZ/Singular fibrations, led by Y. Li
  • Discussion II: Singularities in G2-Laplacian flow, led by M. Haskins and J. Lotay
    (with a contribution from Jason Lotay)
  • Discussion III: Constructions of G2-manifolds/Interfaces of Physics with Geometry, led by B. Acharya
  • Discussion IV: Adiabatic coassociatives/counting associatives, led by S. Donaldson
  • Discussion V: Physics of Spin(7)/G2 bundles, led by J. Heckman and M. Cvetič
  • Discussion VI: Degenerations of G2-manifolds/Topology of G2-moduli space, led by S. Goette and T. Walpuski
  • Discussion VII: Open problems on enumerative invariants/Codim>4 singularities in higher dim gauge theory, led by D. Joyce and T.Walpuski
  • Discussion VIII: Open Problems in Special Holonomy from a Physics point of view, led by S. Schafer-Nameki

Speakers:

The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures (when available).


Moduli of special holonomy metrics and their periods: virtual meeting online, 1-5 June 2020

The collaboration will hold a VIRTUAL meeting June 1-5, 2020, on the general topic of Moduli of special holonomy metrics and their periods.

Scientific Organizers:
Mark Haskins mhaskins@math.duke.edu,
Jason Lotay jason.lotay@maths.ox.ac.uk,
David Morrison drm@math.ucsb.edu,
Simon Salamon simon.salamon@kcl.ac.uk.

The virtual meeting comes in two parts:

  1. Recorded lectures which can be viewed by participants at any time, and;
  2. “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 https://www.youtube.com/playlist?list=PLEUBxKnFNbBApwGH0DJh4PlPmAio_Z_Jw

Our recorded lectures are as follows. The recorded lecture by Voisin is a pre-requisite to her subsequent live lecture, so the audience is encouraged to watch this lecture first.


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).

Timetable

MON 1 JUNE

WED 3 JUNE

FRI 5 JUNE

16:00-17:00 (England)
11:00am-12:00pm (EDT)

Joyce Neitzke Voisin

17:00-18:00 (England)
12:00pm-1:00pm (EDT)

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

18:00-19:00 (England)
1:00pm-2:00pm (EDT)

Wisniewski Saccà Szendrői

19:00-20:00 (England)
2:00pm-3:00pm (EDT)

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

Speakers:

The links will take you to abstracts, slides of lectures, and/or video recordings of the lectures.


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.


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.

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: