ICMS

Jun 14, 2010 - Jun 18, 2010

14 India Street, Edinburgh, EH3 6EZ

Organisers

Name	Institution
Freed, Dan	University of Texas at Austin
Gasparim, Elizabeth	University of Edinburgh
Pantev, Tony	University of Pennsylvania

The workshop organisers will gather about 40 mathematicians and physicists, and the scientific goal is to pursue an in-depth understanding of the interactions between Hodge theory on the one hand and QFT and string theory on the other.  This includes work relating to supersymmetric gauge theories with the geometric Langlands conjecture, the use of mixed Hodge theory to study the renormalization group flow, and the noncommutative Hodge structure uncovered in the theory of charges in boundary TQFTs.  In addition, there are plans to have a series of expository lectures on scale in QFT.

 

Arrangements

Participation
Participation is by invitation only.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and, if so, how to apply for one. If you do require a visa, ICMS can (on request) provide a signed invitation letter.

Venue
The workshop will take place at 14 India Street, Edinburgh, EH3 6EZ. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.

The ICMS travel pages contain advice on how to travel to Edinburgh. To find the location of the workshop venue follow this link to 14 India Street.

You may also find this map useful. 

If you have been invited to give a presentation, the seminar room at 14 India Street has whiteboards, 2 overhead projectors, a data projector and laptop. We ask that you use our laptop for your presentation which you may bring on a memory stick or CD. Alternatively, a pdf or PowerPoint file may be emailed to Audrey Brown by Thursday 10 June to be loaded onto the laptop in advance of the workshop.

Wireless access is available throughout the building. There are also 3 public PCs which may be used at any time for internet access and to check email.

Accommodation
ICMS will arrange en-suite rooms in hotels/guest houses nearby for those who request this. Accommodation is typically about a 20 minute walk from 14 India Street. Participants making their own arrangements may claim back the cost, with original receipts, up to a maximum of £65.00 per night bed and breakfast for a maximum of five or six nights. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.

Registration
Registration will take place from 09.00 - 09.50 on Monday 14 June in the Exhibition Room at 14 India Street. 

Minicourse Lecture Series
Professor Andrew Neitzke has kindly agreed to present a series of three talks as 'Minicourse Lectures'.  Further information can be found in the Programme Section of this website (below).

The Hardy Lecture in Edinburgh
On Friday 18 June, all participants are invited to attend The Hardy Lecture, hosted by the Edinburgh Mathematical Society, where Hiraku Nakajima will talk at 16.30.  This lecture will take place in Lecture Theatre 175, Old College, University of Edinburgh.  Coffee will be available from 16.00 outside the lecture theatre.  

Meals and Refreshments
Morning and afternoon refreshments will be provided on each day of the workshop.

On Monday 14 June and Friday 18 June, a light buffet lunch will be provided free of charge to participants in the Exhibition Room at 14 India Street. On the remaining days participants are free to explore the many cafés, sandwich shops, restaurants and bars nearby.  There will be an informal evening meal provided on Monday 14 June in Ristorante Librizzi (Sicilian), and the Workshop Dinner will take place on the evening of Thursday 17 June at The Magnum Restaurant (Scottish).  The workshop grant will cover the cost of this catering.

Financial Arrangements
Your individual financial arrangements will be laid out in your invitation email and the email received shortly before the workshop.

If we have agreed to pay some of your travel costs, you will have been informed by email. Reimbursement will take place after the workshop and will involve payment directly into your bank account. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with original receipts. It would be helpful if you could bring your bank details to the workshop. In addition to the bank account number, participants from the USA and Canada will require their bank’s routing number, those from the UK will be asked for the bank sort code, and those from Europe and the rest of the world, their IBAN and SWIFT/BIC code. We cannot reimburse any item without a signed claim form and original receipts.

Please note the registration fee has been waived for ALL participants.  We will no longer charge a registration fee for this workshop.    

 

Programme

Minicourse Lecture Series
Professor Andrew Neitzke will present a series of three talks as 'Minicourse Lectures'.  Provisional talk titles and abstracts are as follows but may yet be subject to change:

Talk 1:  Effective field theory:  or, why don't we need to know quantum chromodynamics to build a radio?
I will give a general account of what physicists mean by "effective field theory" and why it is a useful notion.

Talk 2:  Effective field theories in string theory:  or, what do strings have to do with black holes?
Practitioners of string theory frequently shift back and forth between the "microscopic" language of the string worldsheet and the "macroscopic" language of effective field theory. I will explain the distinction, with the aim of resolving the apparent contradictions between statements such as "string theory is a 2-dimensional QFT", "string theory solves the divergence problems of conventional QFT" and "string theory is described by 11-dimensional supergravity".

Talk 3:  Mathematical applications of effective field theory:  or, why don't we need to know Donaldson theory to calculate a Donaldson invariant?
Many of the deepest applications of quantum field theory to mathematics depend crucially on the notion of effective field theory.  A spectacular example is the equivalence between Seiberg-Witten and Donaldson invariants.  I will describe this example, and a few others more briefly as time permits.
 

Programme

Monday 14 June 2010

09.00-09.50	Registration & coffee
09.50-10.00	Welcome & introduction
10.00-11.00	Michael Atiyah (University of Edinburgh) Models of matter?
11.00-12.00	John Jones (University of Warwick) The Kervaire invariant
12.00-14.30	Lunch provided in the Exhibition Room, 14 India Street
14.30-15.30	Chiu-Chu Liu (Columbia University ) The coherent-constructible correspondence for toric orbifolds
15.30-16.30	Ludmil Katzarkov (University of Miami) Noncommutative Hodge theory and applications
16.30-18.45	Wine reception at 14 India Street
19.30	Informal evening meal at Ristorante Librizzi, 69 North Castle Street

Tuesday 15 June 2010

10.00-11.00	Andrew Nietzke (University of Texas at Austin) Effective field theory:  or, why don't we need to know quantum chromodynamics to build a radio?
11.00-12.00	Oren Ben Bassat (University of Haifa) Gerbes and the holomorphic Brauer group of complex tori   pdf of presentation
12.00-14.30	Lunch break
14.30-15.30	Constantin Teleman (UC Berkeley) Gauged TQFT's in 2 dimensions and the Brauer group of K-theory
15.30-16.30	Christian Saemann  (Heriot-Watt University) M2-branes ending on M5-branes

Wednesday 16 June 2010

10.00-11.00	Andrew Nietzke (University of Texas at Austin) Effective field theories in string theory:  or, what do strings have to do with black holes?
11.00-12.00	Nigel Hitchin (University of Oxford) Generalized holomorphic bundles and the B-field action
12.00-13.00	Emanuel Diaconescu (Rutgers University) Wallcrossing and cohomology of Hitchin moduli spaces
13.00	Free afternoon

Thursday 17 June 2010

10.00-11.00	Andrew Nietzke (University of Texas at Austin) Mathematical applications of effective field theory:  or, why don't we need to know Donaldson theory to calculate a Donaldson invariant?
11.00-12.00	Peter Dalakov (University of Massachusetts - Amherst) On deformations of the uniformising Higgs bundles
12.00-14.30	Lunch break
14.30-15.30	Joan Simón (University of Edinburgh) Holography: Boltzmann, Shannon & Cardy meet Bekenstein & Hawking  pdf of presentation
15.30-16.30	Philip Candelas (University of Oxford) A three-generation Calabi-Yau manifold with small Hodge numbers
19.00	Workshop dinner at Magnum Restaurant, 1 Albany Street

Friday 18 June 2010

10.00-11.00	Richard Szabo (Heriot-Watt University) Instantons on noncommutative toric varieties   pdf of presentation
11.00-12.00	Alexander Braverman A finite analog of the AGT relation
12.00-14.30	Lunch provided in the Exhibition Room, 14 India Street
14.30-15.30	Dennis Gaitsgory (Harvard University) Geometric Eisenstein series; some new developments
15.30	Close of workshop
16.30	All participants are invited to attend the Hardy Lecture, hosted by the Edinburgh Mathematical Society, where Hiraku Nakajima will talk at 16.30.  This will take place in Lecture Theatre 175, Old College, University of Edinburgh.  Coffee will be available from 16.00.

 

Presentations:

Presentation Details
Atiyah, Sir Michael
Models of matter?
View Abstract Hide Abstract
I will discuss a very speculative idea that 4-dimensional conformally self-dual manifolds might be used as classical models of matter. The signature would determine electric charge and the Euler characteristic would relate to Baryon number. Electrons would be germs of singular points. Anti-matter would correspond to reversal of orientation.
Ben Bassat, Oren
Gerbes and the holomorphic Brauer group of complex tori
View Abstract Hide Abstract
Holomorphic gerbes are certain geometric objects whose isomorphism classes form the second cohomology group of the sheaf of nowhere vanishing holomorphic functions. Locally a gerbe on a small open set should be thought of as something isomorphic to the collection of all line bundles. Actually the line bundles act on gerbes similarly to the way to functions act on sections of line bundles. In this talk, we will present some aspects of the study of gerbes on complex tori. This study is analogous to the classical study of line bundles on complex tori. Concepts such as the Appell-Humbert theorem, and the Poincare bundle and more will be presented in this new setting.
Braverman, Alexander
A finite analog of the AGT relation
View Abstract Hide Abstract
Recently Alday-Gaiotto-Tachikaw (AGT) suggested an interpretation of the so called Nekrasov partition function (defined via certain equivariant integration over the space of G-instantons on R^4 where G is a semi-simple algebraic group) for 4-dimensional super-symmetric gauge theory using the representation theory of affine W-algebras. We formulate a conjectural "finite" analog of the AGT conjecture in which the moduli spaces of instantons are replaced with certain moduli spaces of 3d monopoles and affine W-algebras are replaced by finite W-algebras (the definition will be explained during the lecture). We shall also indicate a proof of the above conjecture for G=SL(n) Joint work with M.Finkelberg.
Candelas, Philip
A three-generation Calabi-Yau manifold with small Hodge numbers
View Abstract Hide Abstract
For a Calabi-Yau manifold M let us refer to the sum h^{1,1} + h^{21} as the height of M. All known CY manifolds have height in the range 4 <= ht(M) <= 502. it is intriguing that it is possible to find a low energy effective field theory with three generations and, seemingly, with the particle content of the minimal supersymmetric standard model for a CY manifold of height 4, that lies right at the tip of the Hodge number landscape.
Dalakov, Peter
On deformations of the uniformising Higgs bundles
View Abstract Hide Abstract
I will discuss some results about the deformation theory of the uniformising Higgs bundles (on a curve of genus at least two), using DGLA/L-infinity techniques.
Diaconescu, Emanuel
Wallcrossing and cohomology of Hitchin moduli spaces
View Abstract Hide Abstract
Conjectural recursive formulas for Poincare and Hodge polynomials of moduli spaces of Hitchin pairs will be derived using wallcrossing techniques.
Gaitsgory, Dennis
Geometric Eisenstein series; some new developments
View Abstract Hide Abstract
To follow
Hitchin, Nigel
Generalized holomorphic bundles and the B-field action
View Abstract Hide Abstract
On a generalized complex manifold there is an associated definition of a generalized holomorphic bundle, introduced by Gualtieri. We investigate the moduli space in the case of an ordinary complex structure viewed in this way, and consider in particular the action of B-fields, both local and global. This makes contact with both Nahm's equations and holomorphic gerbes.
Jones, John
The Kervaire invariant
View Abstract Hide Abstract
Just over a year ago Hill, Hopkins, and Ravenel proved that the Kervaire invariant of framed manifolds is zero except in dimensions 2, 6, 14, 30, 62 and possibly 126. It is of course very interesting to look for the special topological/geometric phenomena which leads to this list of at most six special cases and this is not yet understood. In this talk I will summarise what is known about constructing examples in these special cases.
Katzarkov, Ludmil
Noncommutative Hodge theory and applications
View Abstract Hide Abstract
In this talk we will introduce new birational invariants Gaps of spectra of derived categories. We will discuss potential applications.
Liu, Chiu-Chu
The coherent-constructible correspondence for toric orbifolds
View Abstract Hide Abstract
A toric orbifold is defined by a stacky fan lying in a real vector space N_R. From the stacky fan we define a conical Lagrangian inside the cotangent of the dual vector space M_R such that torus-equivariant, coherent sheaves on the toric orbifold are equivalent to constructible sheaves on M_R with singular support in the conical Lagrangian. The equivalence intertwines the tensor product of coherent sheaves with the convolution product of constructible sheaves. This is based on joint work with Bohan Fang, David Treumann, and Eric Zaslow.
Sämann, Christian
M2-branes ending on M5-branes
View Abstract Hide Abstract
The study of M2-branes ending on M5-branes has led to many exciting results in the past two years. I will review some of these and focus in particular on 3- Lie algebras and the Bagger-Lambert-Gustavsson (BLG) model. As I will show, 3- Lie algebras are special cases of ungraded strong homotopy Lie algebras and they provide the gauge algebra structure for the BLG model. It turns out that there is essentially only one 3-Lie algebra with all the physically desirable properties, and therefore generalizations of 3-Lie algebras have been proposed. I review these generalizations and present representations of these on *-algebras. Because the BLG model is an effective description of M2-branes in the same sense that supersymmetric Yang-Mills (SYM) theories are for D- branes, it is encouraging that many of the properties of the SYM theories are recovered in the BLG model. I will discuss this using the example of so-called beta-deformations. Finally, I will present some noncommutative geometries arising in the context of M2-branes ending on M5-branes.
Simón, Joan
Holography: Boltzmann, Shannon & Cardy meet Bekenstein & Hawking
View Abstract Hide Abstract
I will review some of the physical arguments leading to believe that classical gravity is thermodynamical in nature, emphasizing the connections between thermodynamics, gravity and conformal field theory.
Szabo, Richard
Instantons on noncommutative toric varieties
View Abstract Hide Abstract
We construct new noncommutative deformations of toric varieties by combining methods from toric geometry, isospectral deformation theory, and noncommutative geometry in braided monoidal categories. We apply these techniques to the construction of a certain class of noncommutative instantons, and describe the interrelationships between their descriptions in terms of deformed ADHM data, torsion-free modules, and a twistor correspondence.
Teleman, Constantin
Gauged TQFT's in 2 dimensions and the Brauer group of K-theory
View Abstract Hide Abstract
We will describe the gauging by compact Lie groups of the Frobenius categories needed to define 2-dimensional topological quantum field theories. Quantizing the theory requires a compactification of pure gauge theory by a landau-Ginzburg superpotential, which is an element of the Brauer group of cohomology theory or K-theory. We'll also meet some examples from string topology and Mirror Symmetry.

Participants

Name	Institution
Atiyah, Sir Michael	University of Edinburgh
Ben Bassat, Oren	University of Haifa
Braden, Harry	University of Edinburgh
Braun, Volker	Dublin Institute for Advanced Study
Braverman, Alexander	Brown University
Candelas, Philip	University of Oxford
Dalakov, Peter	University of Massachusetts - Amherst
de Medeiros, Paul	University of Edinburgh
Diaconescu, Emanuel	Rutgers University
Donagi, Ron	University of Pennsylvania
Figueroa-O'Farrill, José	University of Edinburgh
Freed, Dan	University of Texas at Austin
Gaitsgory, Dennis	Harvard University
Gasparim, Elizabeth	University of Edinburgh
Gordon, Iain	University of Edinburgh
Grama, Lino	University of Campinas
Hitchin, Nigel	University of Oxford
Jones, John	University of Warwick
Kahle, Alexander	Georg-August University Göttingen
Katzarkov, Ludmil	University of Miami
Köppe, Thomas	University of Edinburgh
Kovacs, Stefano	Dublin Institute for Advanced Studies
Lakuriqi, Enka	University of Utah
Liu, Chiu-Chu	Columbia University
Martinez Garcia, Jesus	University of Edinburgh
Nakajima, Hiraku	Kyoto University
Neitzke, Andrew	University of Texas at Austin
Pantev, Tony	University of Pennsylvania
Ranicki, Andrew	University of Edinburgh
Sämann, Christian	Heriot-Watt University
Simón, Joan	University of Edinburgh
Szabo, Richard	Heriot-Watt University
Teleman, Constantin	UC Berkeley
Valentino, Alessandro	Georg-August University Göttingen
Wendland, Katrin	Universität Freiburg