# Seminars (MTH)

Videos and presentation materials from other INI events are also available.

Search seminar archive

Event When Speaker Title
MTH 6th February 2002
11:30 to 12:30
Non-local string theories
MTH 7th February 2002
14:00 to 15:30
Unknown
MTHW02 11th February 2002
11:00 to 11:30
Thermality in AdS and dS spacetimes and holography
MTHW02 11th February 2002
11:30 to 12:00
M Berkooz Non-local string theories
MTHW02 11th February 2002
12:00 to 12:30
Hyperbolic Lie algebras
MTHW02 11th February 2002
14:30 to 15:00
Supergravity duals of wrapped branes
MTHW02 11th February 2002
15:00 to 15:30
(Non-BPS) Dirichlet branes, orientifolds and K-theory
MTHW02 11th February 2002
16:00 to 16:30
Tachyons, supertubes and supersymmetric braneanti-brane systems
MTHW02 11th February 2002
16:30 to 17:00
B Pioline Exceptional theta series and the quantum BPS membrane
MTHW02 11th February 2002
17:00 to 17:30
MTHW02 12th February 2002
10:00 to 11:00
K-theory and charges
MTHW02 12th February 2002
11:30 to 12:00
Intersecting branes: phenomenology and geometry
MTHW02 12th February 2002
12:00 to 12:30
TBA
MTHW02 12th February 2002
14:30 to 15:00
P West Symmetries of M-Theory
MTHW02 12th February 2002
15:00 to 15:30
Maldacena-Wilson loops
MTHW02 12th February 2002
16:00 to 16:30
Conformal topological Yang-Mills theory and de Sitter holography
MTHW02 12th February 2002
16:30 to 17:00
Fractional branes and N = 1 gauge theories
MTHW02 13th February 2002
10:00 to 11:00
M Douglas D-branes on Calabi-Yau manifolds
MTHW02 13th February 2002
11:30 to 12:00
WZ solitons near the CMS
MTHW02 13th February 2002
12:00 to 12:30
The Topological sector of the deconstructed six-dimensional theories
MTHW02 14th February 2002
10:00 to 11:00
Conifolds in M-Theory
MTHW02 14th February 2002
11:30 to 12:00
The limits of uniqueness
MTHW02 14th February 2002
12:00 to 12:30
Holographic renormalisation
MTHW02 14th February 2002
14:30 to 15:00
I Brunner Orientifolds of curved backgrounds: Geometry and CFT
MTHW02 14th February 2002
15:00 to 15:30
Black holes on cylinders
MTHW02 14th February 2002
16:00 to 16:30
E Kiritsis NS5 brane distributions at weak coupling
MTHW02 14th February 2002
16:30 to 17:00
Moduli spaces of supersymmetric solutions
MTHW02 15th February 2002
10:00 to 11:00
N Berkovits Covariant quantization of the superstring and supermembrane
MTHW02 15th February 2002
11:30 to 12:00
Instanton corrections to circular Wilson loops in N=4 supersymmetric Yang--Mills
MTHW02 15th February 2002
12:00 to 12:30
Observables of string field theory
MTHW02 15th February 2002
14:30 to 15:00
Probing black holes
MTHW02 15th February 2002
15:00 to 15:30
Penrose limits and maximal supersymmetric solutions in string and M-theories
MTHW02 15th February 2002
16:00 to 16:30
A Klemm N = 1 superpotentials and localisation
MTHW02 15th February 2002
16:30 to 17:00
A little wand of deconstruction
MTH 19th February 2002
14:15 to 15:30
Moduli stabilisation from fluxes
MTH 20th February 2002
17:00 to 17:30
Video of "Horizion" programme on M-Theory
MTH 21st February 2002
14:15 to 15:30
Five dimensional supersymmetry and quaternionic structures
MTH 26th February 2002
14:15 to 15:30
F Larsen De Sitter holography and the cosmic microwave background
MTH 28th February 2002
14:15 to 15:30
C Hull De Sitter space, supergravity and M-Theory
MTH 6th March 2002
11:30 to 12:30
A Tseytlin Superstrings in plane wave backgrounds
MTH 7th March 2002
14:15 to 15:30
Monstrous branes
MTH 12th March 2002
14:15 to 15:30
Domain walls in nine dimensions and their ten dimensional origin
MTH 14th March 2002
14:15 to 15:30
M Marino Towards vacuum superstring field theory
MTH 19th March 2002
14:15 to 15:30
The big click: ekpyrosis by remote control in heterotic m-theory
MTH 21st March 2002
14:15 to 15:30
String compactifications with background fluxes
MTHW01 25th March 2002
09:20 to 09:30
Welcome by Deputy Director Dr. Robert Hunt
MTHW01 25th March 2002
09:30 to 11:00
String / M Theory Compactification: An Overview
MTHW01 25th March 2002
11:30 to 13:00
Introduction to derived categories and McKay correspondence (I)
MTHW01 25th March 2002
14:00 to 15:30
Branes, Calibrations and Supergravity
We describe D=11 supergravity and define what is meant by a supersymmetric solution. Manifolds with special holonomy provide examples as do membranes and fivebranes and the connection of the latter solutions with the AdS/CFT (anti-de-Sitter space/conformal field theory) correspondence is mentioned. Switching to the worldvolume description of branes we discuss why branes wrapping calibrated cycles in special holonomy manifolds are supersymmetric and touch on the deformation theory of calibrations. A generalisation of calibrations relevant to D=11 supergravity is described. The last part of the lectures explains how new supersymmetric solutions to D=11 supergravity can be found that describe branes wrapping calibrated cycles. The essential tool is D=7 gauged supergravity and we explain how this arises as the Kaluza-Klein reduction of D=11 supergravity on a four-sphere. The new solutions provide new examples of the AdS/CFT correspondence.
MTHW01 25th March 2002
16:00 to 17:00
V Batyrev Toric Mirror Symmetry
The mirror symmetry attracts interest of mathematicians because it allows to identify mathematical objects of a very different nature: generating functions for Gromov-Witten invariants of rational curves on one Calabi-Yau manifold and power series expansions of special functions on periods of the mirror Calabi-Yau manifold. Many examples of this identification can be computed explicitly for Calabi-Yau hypersurfaces and complete intersections in toric Fano varieties. However, a rigorous mathematical proof of this identification is very nontrivial even in the simplest case of Calabi-Yau quintic 3-folds. We propose a more elementary toric mirror symmetry test using the notion of toric residue and the intersection theory on some simplicial toric varieties which we call Morrison-Plesser moduli spaces.
MTHW01 26th March 2002
09:30 to 11:00
Branes, Calibrations and Supergravity
MTHW01 26th March 2002
11:30 to 13:00
New Metrics with Special Holonomy
MTHW01 26th March 2002
14:00 to 15:30
M Gross Mirror Symmetry
MTHW01 26th March 2002
16:00 to 17:00
Introduction to derived categories and McKay correspondence (II)
MTHW01 27th March 2002
09:30 to 11:00
New Metrics with Special Holonomy
MTHW01 27th March 2002
11:30 to 13:00
Constructing compact manifolds with exceptional holonomy
I introduce the exceptional holonomy groups G2 and Spin(7), and describe various constructions of compact 7-manifolds with holonomy G2 and compact 8-manifolds with holonomy Spin(7). The basic construction involves resolving the singularities of a torus orbifold T^n/G, for G a finite group preserving a flat G2 or Spin(7) structure on T^7 or T^8. But there are also other constructions involving Calabi-Yau 3-folds and 4-orbifolds. Compact G2 manifolds are of interest to String Theorists as candidates for vacua in M-theory.
MTHW01 27th March 2002
14:00 to 14:10
Unknown
MTHW01 27th March 2002
14:10 to 15:30
Branes, Calibrations and Supergravity
MTHW01 27th March 2002
16:00 to 17:00
Introduction to calibrated geometry
This is an introductory talk on minimal submanifolds and calibrated geometry, in particular special Lagrangian submanifolds in Calabi-Yau manifolds, associative and coassociative submanifolds in G2 manifolds, and Cayley submanifolds in Spin(7) manifolds. String Theorists know of these as supersymmetric cycles, classical versions of D-branes. I shall focus on the work of Harvey and Lawson, and McLean, so most of what I have to say was known in 1990, and experts will already be familiar with it.
MTHW01 28th March 2002
09:30 to 11:00
Topological String Theory
MTHW01 28th March 2002
11:30 to 13:00
M Gross Mirror Symmetry
MTHW01 28th March 2002
14:00 to 15:30
Introduction to derived categories and McKay correspondence (III)
MTHW01 28th March 2002
16:00 to 17:00
New Metrics with special Holonomy
MTHW01 1st April 2002
09:30 to 11:00
Exact results in supersymmetric field theory Wolfson Court - Fletcher Molton Room
MTHW01 1st April 2002
11:30 to 13:00
Introduction to D-Branes and boundary CFT - I Wolfson Court - Fletcher Molton Room
These lectures will aim at a pedagogical introduction to Dirichlet branes in string theory, and the associated conformal boundary states. I will cover in particular effective D-brane actions, D-branes in WZW models and other near- horizon geometries, and their holographic interpretation.
MTHW01 1st April 2002
14:00 to 15:30
Exact results in supersymmetric field theory
MTHW01 1st April 2002
16:00 to 17:00
Poster Session Wolfson Court - Law Library
MTHW01 2nd April 2002
09:30 to 11:00
Topological string theory
MTHW01 2nd April 2002
11:30 to 13:00
A Craw The Picard group and the cohomology of G-Hilb
For a finite Abelian subgroup G of SL(3,C), Ito and Nakajima established that the tautological line bundles base the K-theory of G-Hilb, the Hilbert scheme of G-clusters. This talk will focus on the relations between these bundles in Pic(G-Hilb). As a consequence, a basis of the integral cohomology of G-Hilb is constructed, generalising work of Gonzelez-Sprinberg and Verdier for G in SL(2,C). This construction will be illustrated by explicit examples.
MTHW01 2nd April 2002
14:00 to 15:30
Introduction to Homological Mirror Symmetry
A general discussion of homological mirror symmetry illustrated by the exposition of the ideas in the well-understood case of elliptic curves following Kontsevich and Polishchuk-Zaslow
MTHW01 2nd April 2002
16:00 to 17:00
A Craw Stringy Hodge numbers and the McKay correspondence
For a finite subgroup G of SL(n,C), suppose that the quotient C^{n}/G admits a minimal resolution Y. The strong McKay correspondence established by V. Batyrev counts the dimension of the cohomology groups of Y in terms of certain conjugacy classes of G. Even if no such resolution exists, the stringy Hodge numbers of C^{n}/G, which are defined a priori via motivic integration, are also computed in terms of conjugacy classes of G. This talk will review the definition of stringy Hodge numbers, their relation with conjugacy classes of G and the McKay correspondence.
MTHW01 3rd April 2002
09:30 to 11:00
Topological string theory
MTHW01 3rd April 2002
11:30 to 12:30
Singularities of special Lagrangian submanifolds
I describe a programme (work in progress) to study the singularities of special Lagrangian m-submanifolds (SL m-folds), particularly when m=3, and in a suitably generic (almost) Calabi-Yau 3-fold. The first part of this programme is the construction and (to some extent) classification of singular SL m-folds in C^m, so I explain a number of constructions and examples.

The second part will be to use these examples as local models for singularities of SL 3-folds in (almost) Calabi-Yau 3-folds, using analytic methods. I give an outline of how I expect this to work.

MTHW01 3rd April 2002
14:00 to 15:30
Moduli spaces of bundles over Riemann surfaces
The cohomology rings of the moduli spaces M(n,d) of stable holomorphic bundles of coprime rank n and degree d over a fixed compact Riemann surface have been studied for several decades. When n=2 we have a very thorough understanding of the structure of H*(M(n,d)), including an elegant presentation in terms of generators and relations. The aim of this talk is to describe a generalisation (not quite so elegant) of this presentation to n>2.
MTHW01 3rd April 2002
16:00 to 17:15
Special Lagrangian fibrations and the SYZ conjecture
After briefly describing Mirror Symmetry and the SYZ Conjecture, I discuss what kinds of singularities should be expected in special Lagrangian fibrations of generic (almost) Calabi-Yau 3-folds, using the ideas of the previous lecture. I explain some analytical results on the existence and uniqueness of SL 3-folds in C^3 invariant under a certain U(1)-action, and with boundary conditions. Using these one can construct large families of U(1)-invariant SL fibrations of subsets of C^3.

I describe the singular behaviour of these fibrations, and argue that some features of it also hold for generic, non U(1)-invariant SL fibrations. In particular, generic SL fibrations will not be smooth, the singular fibres will be of codimension 1 in the base space, and each singular fibre will have only finitely many singular points.

MTHW01 3rd April 2002
20:00 to 00:00
Conference Dinner - Magdalene College Pre dinner drinks from 19.30 - Benson Hall
MTHW01 4th April 2002
09:30 to 11:00
Derived Equivalences in Homological Mirror Symmetry
The discussion of the symmetries in homological mirror symmetry will be illustrated by examples due to Kontsevich, Seidel-Thomas, Horja and the speaker.
MTHW01 4th April 2002
11:30 to 13:00
Introduction to D-Branes and boundary CFT - II
These lectures will aim at a pedagogical introduction to Dirichlet branes in string theory, and the associated conformal boundary states. I will cover in particular effective D-brane actions, D-branes in WZW models and other near- horizon geometries, and their holographic interpretation.
MTHW01 4th April 2002
14:00 to 15:30
The Yang-Mills stratification revisited
Much information about the topology of these moduli spaces M(n,d) can be obtained from the Morse stratification of the Yang-Mills functional studied by Atiyah and Bott. However for some purposes, and in particular to obtain a complete set of relations for H*(M(n,d)), the Yang-Mills stratification has some unpleasant properties and it is better to use related but different stratifications.
MTHW01 4th April 2002
16:00 to 17:00
Exact results in supersymmetric field theory
MTHW01 5th April 2002
09:30 to 11:00
Exact results in supersymmetric field theory
MTHW01 5th April 2002
11:30 to 13:00
Standard conjectures in Kahler geometry
We will give a survey of what is, on the one hand, known and, on the other hand, unknown but expected to be true, about Kahler-Einstein, constant scalar curvature and extremal Kahler metrics. In the case of Kahler-Einstein metrics on Fano varieties the picture is summed up by conjectures and results of Tian: if a manifold does not admit a Kahler-Einstein metric there should be an associated "obstruction triple". At the formal level, at least, many of the ideas go over the case of constant scalar curvature (i.e. manifolds with arbritrary polarisation). We will give examples of the phenomena that occur and discuss the singularities that need to be allowed in the obstruction triple.
MTHW01 5th April 2002
14:00 to 15:30
Principal bundles on elliptic fibrations
In this talk we discuss the description of the moduli space of regularized principal G-bundles on an elliptic fibration X-->S in terms of cameral covers and their distinguished Prym varieties. The analysis of these moduli spaces is a special case of a general abelianization result which also includes many well-known integrable systems (Hitchin's, Markman's, Sklyanin's, ...) and has a range of other geometric applications.
MTHW01 5th April 2002
16:00 to 17:00
V Batyrev Testing toric mirror symmetry
The mirror symmetry attracts interest of mathematicians because it allows to identify mathematical objects of a very different nature: generating functions for Gromov-Witten invariants of rational curves on one Calabi-Yau manifold and power series expansions of special functions on periods of the mirror Calabi-Yau manifold. Many examples of this identification can be computed explicitly for Calabi-Yau hypersurfaces and complete intersections in toric Fano varieties. However, a rigorous mathematical proof of this identification is very nontrivial even in the simplest case of Calabi-Yau quintic 3-folds. We propose a more elementary toric mirror symmetry test using the notion of toric residue and the intersection theory on some simplicial toric varieties which we call Morrison-Plesser moduli spaces.
MTHW01 8th April 2002
09:30 to 11:00
Heterotic/F-Theory duality
The heterotic string compactified on an (n-1)-dimensional elliptically fibered Calabi-Yau Z-->B is conjectured to be dual to F-theory compactified on an n-dimensional Calabi-Yau X-->B, fibered over the same base with elliptic K3 fibers. In particular, the moduli of the two theories should be isomorphic. The cases most relevant to the physics are n=2, 3, 4, i.e. the compactification is to dimensions d=8, 6 or 4 respectively. Mathematically, the richest picture seems to emerge for n=3, where the moduli space involves an analytically integrable system whose fibers admit rather different descriptions in the two theories. The purpose of this talk is to review some of what is known and what is not yet known about this conjectural isomorphism.
MTHW01 8th April 2002
11:30 to 13:00
M Douglas D-Branes, orbifolds and derived categories
MTHW01 8th April 2002
14:00 to 15:30
B Acharya M theory, G2-holonomy singularities and four dimensional physics
theory on a manifold X of G2-holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and N=1 supersymmetry. The standard features of particle physics, namely non-Abelian gauge symmetries and chiral fermions, emerge from singularities of X. The aim of these lectures is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement and mass gap, receive relatively simple explanations within the context of M theory.

All of the singularities of G2-manifolds we discuss here are are constructed naturally from the familiar ADE-singularities. For instance, codimension seven singular points which support chiral fermions are obtained from a natural modification of the Kronheimer construction of ALE-spaces.

MTHW01 9th April 2002
09:30 to 11:00
B Acharya M theory, G2-holonomy singularities and four dimensional physics
theory on a manifold X of G2-holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and N=1 supersymmetry. The standard features of particle physics, namely non-Abelian gauge symmetries and chiral fermions, emerge from singularities of X. The aim of these lectures is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement and mass gap, receive relatively simple explanations within the context of M theory.

All of the singularities of G2-manifolds we discuss here are are constructed naturally from the familiar ADE-singularities. For instance, codimension seven singular points which support chiral fermions are obtained from a natural modification of the Kronheimer construction of ALE-spaces.

MTHW01 9th April 2002
11:30 to 13:00
Introduction to quantum periods - I
The aim of these lectures is to introduce semi-infinite analogue of variations of Hodge structures associated with families of various non-commutative objects (associative algebras, A-infinity deformations of complex manifolds etc.) and to describe mirror symmetry formulas relating rational Gromov-Witten invariants of n-dimensional Calabi-Yau manifolds with periods of semi-infinite variations of Hodge structures associated with non-commutative deformations of the mirror dual Calabi-Yau manifolds.
MTHW01 9th April 2002
14:00 to 15:30
Mirror symmetry and A-Branes
MTHW01 9th April 2002
16:00 to 17:00
Topological string theory
MTHW01 10th April 2002
09:30 to 11:00
M Douglas D-Branes, orbifolds and derived categories
MTHW01 10th April 2002
11:30 to 13:00
N Hitchin Invariant functionals
Manifolds with special holonomy are traditionally associated with the existence of parallel spinors, but Calabi-Yau threefolds and G2 manifolds also arise naturally in the context of a nonlinear form of Hodge theory: finding critical points of a natural functional defined on the differential p-forms in a fixed cohomology class. The advantage of this point of view is that it gives a natural approach to the moduli spaces of these structures, which appear as open sets in the appropriate cohomology group. (See "The geometry of three-forms in six dimensions", J. Differential Geometry 55 (2000), 547 -- 576.)
MTHW01 10th April 2002
14:00 to 15:30
M Mustata Introduction to motivic integration
MTHW01 10th April 2002
16:00 to 17:00
B Acharya M theory, G2-holonomy singularities and four dimensional physics
M theory on a manifold X of G2-holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and N=1 supersymmetry. The standard features of particle physics, namely non-Abelian gauge symmetries and chiral fermions, emerge from singularities of X. The aim of these lectures is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement and mass gap, receive relatively simple explanations within the context of M theory.

All of the singularities of G2-manifolds we discuss here are are constructed naturally from the familiar ADE-singularities. For instance, codimension seven singular points which support chiral fermions are obtained from a natural modification of the Kronheimer construction of ALE-spaces.

MTHW01 11th April 2002
09:30 to 11:00
B Acharya M theory, G2-holonomy singularities and four dimensional physics
M theory on a manifold X of G2-holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and N=1 supersymmetry. The standard features of particle physics, namely non-Abelian gauge symmetries and chiral fermions, emerge from singularities of X. The aim of these lectures is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement and mass gap, receive relatively simple explanations within the context of M theory.

All of the singularities of G2-manifolds we discuss here are are constructed naturally from the familiar ADE-singularities. For instance, codimension seven singular points which support chiral fermions are obtained from a natural modification of the Kronheimer construction of ALE-spaces.

MTHW01 11th April 2002
11:30 to 13:00
N Hitchin Cohomogeneity one metrics
Manifolds with Killing spinors can also be approached through differential forms via a constrained variational problem, and associated gradient or Hamiltonian flows give effective ways of finding cohomogeneity one metrics with holonomy G2 or Spin(7). (See "Stable forms and special metrics", in Global Differential Geometry: The Mathematical Legacy of Alfred Gray", M. Fernandez and J. A. Wolf (eds.), Contemporary Mathematics 288, American Mathematical Society, Providence (2001).)
MTHW01 11th April 2002
14:00 to 15:30
N Hitchin Generalised Calabi-Yau manifolds
A similar variational problem for forms of mixed degree in 6 dimensions gives a structure whose moduli space is an open set in the even or odd cohomology. We call this structure a "generalized Calabi-Yau manifold". The moduli problem here involves not just the diffeomorphism group, but also the action of the so-called B-field.
MTHW01 11th April 2002
16:00 to 17:00
S Gukov Duality and Fibrations on G$\_$2 Manifolds
MTHW01 12th April 2002
09:30 to 11:00
K-Theory - I
MTHW01 12th April 2002
11:30 to 13:00
S Gukov Fluxes, Superpotential, and Calibrated Geometry
MTHW01 12th April 2002
14:00 to 15:30
M Douglas D-Branes, orbifolds and derived categories
MTHW01 12th April 2002
16:00 to 17:00
Introduction to quantum periods - II
The aim of these lectures is to introduce semi-infinite analogue of variations of Hodge structures associated with families of various non-commutative objects (associative algebras, A-infinity deformations of complex manifolds etc.) and to describe mirror symmetry formulas relating rational Gromov-Witten invariants of n-dimensional Calabi-Yau manifolds with periods of semi-infinite variations of Hodge structures associated with non-commutative deformations of the mirror dual Calabi-Yau manifolds.
MTHW01 15th April 2002
09:30 to 11:00
K-Theory - II
MTHW01 15th April 2002
11:30 to 13:00
A Kovalev From Fano 3-folds to compact G$\_$2-manifolds
G2-manifolds are 7-dimensional Riemannian manifolds whose metrics have holonomy group G2. They are necessarily Ricci-flat and carry parallel spinor fields. In this talk I will explain a systematic way to construct examples of compact G2-manifolds by gluing a pair of asymptotically cylindrical manifolds of holonomy SU(3) at their ends. To obtain the latter SU(3)-manifolds one starts from complex 3-dimensional projective manifolds with $c_1>0$ (Fano 3-folds) endowed with an appropriate choice of the anticanonical K3 divisor. The resulting G2-manifolds are topologically distinct from those previously obtained by Joyce.
MTHW01 15th April 2002
14:00 to 15:30
String/M compactifications and duality
MTHW01 15th April 2002
16:00 to 17:00
Hermitian symmetric domains and Calabi-Yau manifolds
It is well known that the moduli space of lattice polarized K3 surfaces is isomorphic to an arithmetic group quotient of a Hermitian symmetric domain of type IV. There is only a few of examples of moduli spaces of Calabi-Yau higher-dimensional manifolds which are arithmetic quotients of Hermitian symmetric domains. In this talk we shall discuss some of these examples, and will speculate about their possible generalizations.
MTHW01 16th April 2002
09:30 to 11:00
Non supersymmetric orbifolds - I
MTHW01 16th April 2002
11:30 to 13:00
McKay correspondence for symplectic singularities
McKay correspondence predicts the cohomology groups of a crepant resolution of the quotient $X=V/G$ of a vector space $V$ by a finite group $G \subset SL(V)$. We will consider the case when the vector space is symplectic, and the group preserves the symplectic form. We will prove the McKay correspondence conjecture and give some speculations about the multiplicative structure in the cohomology ring.
MTHW01 16th April 2002
14:00 to 15:30
String/M compactification and duality
MTHW01 16th April 2002
16:00 to 17:00
J Sawon Rozaansky-Witten invariants and extended TQFT
MTHW01 17th April 2002
09:30 to 11:00
String / M compactification and duality
MTHW01 17th April 2002
11:30 to 13:00
Representations of the McKay quiver and variation of GIT quotients
Let G be a finite (abelian) subgroup of SL(3, C). We consider the moduli of representations of the McKay quiver of G (satisfying the commutativity condition), or equivalently the moduli of certain G-equivariant coherent sheaves on C^3 which we call G-constellations. This moduli space depends on a GIT-stability parameter $\theta$ and for a particular $\theta$, the moduli space coincides with G-Hilb.
MTHW01 17th April 2002
14:00 to 15:30
Large Complex Structure limits of K3 surfaces
This talk is based on joint work with Mark Gross, published in J. Diff. Geom. 55 (2000), 475 - 546. Motivated by the SYZ picture of mirror symmetry, the authors had made a conjecture concerning the Gromov--Hausdorff limits of Calabi--Yau $n$-folds (with Ricci-flat K\"ahler metric) as one approaches a large complex structure limit point in moduli; a similar conjecture was made independently by Kontsevich, Soibelman and Todorov. Roughly stated, the conjecture says that, if the metrics are normalized to have constant diameter, then this limit is the base of the conjectural special lagrangian torus fibration associated with the large complex structure limit, namely an $n$-sphere, and that the metric on this $S^n$ is induced from a standard (singular) Riemannian metric on the base, the singularities of the metric corresponding to the discriminant locus of the fibration.

This conjecture is trivially true for elliptic curves; in this talk I'll describe its proof for K3 surfaces. Using the standard description of mirror symmetry for K3 surfaces and the hyperk\"ahler rotation trick, we reduce the problem to that of studying K\"ahler degenerations of elliptic K3 surfaces, with the K\"ahler class approaching the wall of the K\"ahler cone corresponding to the fibration and the volume normalized to be one. Here we are able to write down a remarkably accurate approximation to the Ricci-flat metric -- if the elliptic fibres are of area $\epsilon >0$, then the error is $O(e^{-C/\epsilon})$ for some constant $C>0$. This metric is obtained by gluing together a semi-flat metric on the smooth part of the fibration with suitable Ooguri--Vafa metrics near the singular fibres. For small $\epsilon$, this is a sufficiently good approximation that the above conjecture is then an easy consequence.

MTHW01 17th April 2002
16:00 to 17:00
TBA
MTHW01 18th April 2002
09:30 to 11:00
String / M compactification and duality
MTHW01 18th April 2002
11:30 to 13:00
A time dependent background in string theory
MTHW01 18th April 2002
14:00 to 15:30
M Verbitsky Stability of Fourier-Mukai transform
Let $M$ be a K3 surface, $B$ a stable bundle on $M$, and $X$ the coarse moduli of stable deformations of $B$. The Fourier-Mukai transform is a functor $FM:\; D_b(M) \arrow D_b(X)$, where $D_b(M)$, $D_b(X)$ denotes the derived category of coherent sheaves on $M$, $X$.

Consider a stable bundle $B_1$ on $M$, and let $FM(B_1)$ be the corresponding complex of coherent sheaves on $X$. Assume $X$ is compact. It was conjectured that the cohomology of the complex $FM(B_1)$ are polystable sheaves on $X$. This conjecture is known when the bundles $B$, $B_1$ have zero degree. We prove it for arbitrary stable bundles $B$, $B_1$.

The proof uses hyperkaehler geometry. A projectivization of a stable bundle on a K3 surface is hyperholomorphic, that is, holomorphic with respect to any complex structure induced by the hyperkaehler structure. Such bundles are called projectively hyperholomorphic. We prove that a pushforward of a projectively hyperholomorphic bundle has projectively hyperholomorphic cohomology. Projectively hyperholomorphic bundles are stable; therefore, a pushforward of a projectively hyperholomorphic bundle is has stable cohomology.

MTHW01 18th April 2002
16:00 to 17:00
TBA
MTHW01 19th April 2002
09:30 to 11:00
TBA
MTHW01 19th April 2002
11:30 to 13:00
Aspects of mirror symmetry
MTHW01 19th April 2002
14:00 to 15:30
Aspects of mirror symmetry
MTHW01 19th April 2002
16:00 to 17:00
On hyperbolic Kac--Moody algebras of Borcherds type and applications
MTH 23rd April 2002
14:15 to 15:30
D-brane probes and closed string tachyons in flux brane backgrounds
MTH 25th April 2002
14:15 to 15:30
NS5-branes, T-duality and worldsheet instantons
MTH 30th April 2002
14:15 to 15:30
de Sitter space in (stringy) supergravity
MTH 2nd May 2002
11:00 to 12:30
S Kachru New phenomena in string compactifications with flux
MTH 2nd May 2002
14:15 to 15:30
Clean time-dependent string backgrounds from bubble baths
MTH 7th May 2002
14:15 to 15:15
An M-theory unification of the deformed and resolved conifolds
MTH 9th May 2002
14:15 to 15:15
The spectra of PP-wave limits of M/Superstring theory compactified over spheres and holography
MTH 14th May 2002
14:15 to 15:15
D-brane stability and monodromy
MTH 16th May 2002
11:30 to 12:30
Introduction to derived categories for physicists
MTH 16th May 2002
14:15 to 15:15
M Cvetic Standard model and GUT's from orientifolds and $G_2$ holonomy
MTH 21st May 2002
14:15 to 15:15
A Peet S-branes
MTH 23rd May 2002
14:15 to 15:15
Branes and vacua in open string field theory
MTH 28th May 2002
14:15 to 15:15
D Freedman Perturbative gauge theory and string interactions
MTH 30th May 2002
14:15 to 15:15
Tachyon condensation and black hole entropy
MTH 5th June 2002
14:15 to 15:15
K Skenderis Brane in AdS and pp-wave spacetimes
MTH 6th June 2002
14:15 to 15:15
A Hanany Toric duality, Seiberg duality and Picard-Lefshetz transformations
MTH 7th June 2002
15:00 to 16:00
P Di Vecchia W=1 and N=2 refer Yang-Mills theories from wrapped branes
MTH 11th June 2002
14:15 to 15:15
Anti de Sitter branes and holography
MTH 13th June 2002
14:15 to 15:15
Borcherds dualities in supergravities
MTH 18th June 2002
14:15 to 15:15
N Warner N=1 holographic R.G fixed points and their Penrose limits
MTH 20th June 2002
14:15 to 15:15
T Banks de Sitter space and supersymmetry breaking
MTH 25th June 2002
15:30 to 16:30
Worldsheet derivation of a large $N$ duality
MTH 27th June 2002
14:15 to 15:15
Tachyon dynamics
MTH 3rd July 2002
14:15 to 15:15
NA Nekrasov Seiberg-Witten prepotential from instanton counting
MTH 4th July 2002
14:15 to 15:15
Colliding Kaluza-Klein bubbles
MTH 9th July 2002
14:15 to 15:15
Black hole formation at high energies
MTH 10th July 2002
14:15 to 15:15
J Maldacena Introduction to pp-waves
MTH 11th July 2002
16:30 to 17:30
J Maldacena Introduction to pp-waves