Workshop
Geometry of Strings and Fields
Aug 26, 2013  Oct 20, 2013Ever since the birth of string theory, interaction with geometry has been one of the primary driving forces that has led to progress in superstring theory. On one hand, string theory has generated many new geometrical concepts; and on the other hand new ideas from geometry have often found their first applications in string theory. These topics include vertex algebras, conformal field theory, mirror symmetry, topological field theory and string theory, exact solutions of supersymmetric gauge theory and noncommutative field theory. Recent exciting developments include the matrix model approach to N=1 gauge theory, open string mirror symmetry, the derived category approach to Dbranes on CalabiYau manifolds, geometric transitions, proof of the N=2 SeibergWitten solution by instanton methods, wall crossing formulas, the relation between Langlands program and supersymmetric gauge theories, indications of integrable structures in super YangMills theory and AdS string theory. The program will be devoted to geometrical subjects motivated by string theory, and to recent developments in string theory and related physical fields which are of strong mathematical interest. On the mathematical side, the aim is to foster interaction between such areas of mathematics as derived categories, elliptic cohomology, geometric Langlands correspondence, quantum cohomology. On the more physical side, the aim is to foster new progress in the continuing drive towards understanding the foundations of string/Mtheory, and in the wealth of new ideas involving Dbranes, BPS states and various dualities which are of great importance to mathematical subjects such as algebraic geometry. There will be included a training week with introductory lectures to some of these topics.
 Dates of the Conference:
September 8th13th 2013
 Dates of the Training Weeks:
September 1th6th 2013, October 6th12th 2013
Topics
 Quantum field and string theoretical methods and higher geometrical structures
 Generalized complex geometry and supersymmetry
 Topological strings
 Extended topological field theories
 Vertex algebras
 Localization techniques in quantum field theory
Organizers
Francesco Bonechi, I.N.F.N.  Alberto Cattaneo, Zurich University Sergei Gukov, Caltech University
Martin Rocek, Stony Brook University  Domenico Seminara, Universita di Firenze  Maxim Zabzine, Uppsala University
Contact
bonechi@fi.infn.it
Website
http://theory.fi.infn.it/seminara/Geometry_of_Strings_and_Fieds/Main.html
Related events
Geometry of Strings and Fields  Conference (Conference)  Sep 08, 2013
Talks
Date  Speaker  Title  Type  Useful Links  

Aug 27, 2013  11:00  A. Losev  String Einstein equations on schemes  Seminar  
Aug 28, 2013  11:00  S. Shatashvili  Quantization of integrable systems and supersymmetry  Seminar  
Aug 29, 2013  11:00  R. Szabo  Quantization of nongeometric flux backgrounds  Seminar  
Aug 30, 2013  11:00  P. Hekmati  Geometric transforms and differential Ktheory  Seminar  
Sep 02, 2013  11:30  V. Pestun  Localization of supersymmetric quantum field theories on curved background I  Lecture  
Sep 02, 2013  14:30  V. Pestun  Localization of supersymmetric quantum field theories on curved background II  Lecture  
Sep 02, 2013  16:00  N. Rozenblyum  Branes from a derived point of view I  Lecture 
Abstract
Branes from a derived point of view I The goal will be to describe the basics of derived categories of sheaves associated to algebraic varieties with a physically motivated point of view. We will start from the beginning and go on to describe various categorical invariants, such as Hochschild homology, which play an important role in field theory. Time permitting, we will explain integration in the context of derived algebraic geometry and describe its relationship to Feynman integrals. 

Sep 03, 2013  10:00  V. Pestun  Localization of supersymmetric quantum field theories on curved background III  Lecture  
Sep 03, 2013  11:30  V. Pestun  Localization of supersymmetric quantum field theories on curved background IV  Lecture  
Sep 03, 2013  14:30  N. Rozenblyum  Branes from a derived point of view II  Lecture 
Abstract
Branes from a derived point of view II The goal will be to describe the basics of derived categories of sheaves associated to algebraic varieties with a physically motivated point of view. We will start from the beginning and go on to describe various categorical invariants, such as Hochschild homology, which play an important role in field theory. Time permitting, we will explain integration in the context of derived algebraic geometry and describe its relationship to Feynman integrals. 

Sep 04, 2013  10:00  R. Von Unge  The secret life of sigma supermodels I  Lecture 
Abstract
The secret life of sigma supermodels I These lectures will give an introduction to sigma models for mathematicians and physicists. In the first lecture I will introduce sigma models and the various concepts needed to understand them. I will give several simple examples and in particular discuss the intriguing relation between properties of the field theory that defines the sigma model and the geometrical characteristics of its target space. The second lecture will be focussed on supersymmetric sigma models and their target space geometry. I will in particular discuss the relation between Generalized Kähler geometry and (2,2) supersymmetry. The third lecture will give some applications such as quotient constructions (reductions) and Tduality and also discuss the quantum properties of sigma models in more detail. 

Sep 04, 2013  11:30  N. Rozenblyum  Branes from a derived point of view III  Lecture 
Abstract
Branes from a derived point of view III The goal will be to describe the basics of derived categories of sheaves associated to algebraic varieties with a physically motivated point of view. We will start from the beginning and go on to describe various categorical invariants, such as Hochschild homology, which play an important role in field theory. Time permitting, we will explain integration in the context of derived algebraic geometry and describe its relationship to Feynman integrals. 

Sep 05, 2013  10:00  R. Von Unge  The secret life of sigma supermodels II  Lecture 
Abstract
The secret life of sigma supermodels II These lectures will give an introduction to sigma models for mathematicians and physicists. In the first lecture I will introduce sigma models and the various concepts needed to understand them. I will give several simple examples and in particular discuss the intriguing relation between properties of the field theory that defines the sigma model and the geometrical characteristics of its target space. The second lecture will be focussed on supersymmetric sigma models and their target space geometry. I will in particular discuss the relation between Generalized Kähler geometry and (2,2) supersymmetry. The third lecture will give some applications such as quotient constructions (reductions) and Tduality and also discuss the quantum properties of sigma models in more detail. 

Sep 05, 2013  11:30  R. Heluani  (Sheaves of) vertex algebras and stringy manifold invariants I  Lecture 
Abstract
(Sheaves of) vertex algebras and stringy manifold invariants I In these lectures we will introduce and play with the basic notions of vertex algebra theory like Poisson vertex algebras, quasiclassical limits, etc. We will give several examples reproducing the well known examples in the theory like universal enveloping vertex algebras, lattice vertex algebras and Walgebras. We will then explain how to construct a sheaf of vertex algebras attached to any smooth manifold M, known as the chiral de Rham complex of M. Finally, computing the cohomologies of these sheaves we will obtain geometric invariants of M. 

Sep 05, 2013  14:30  D. Calaque  Derived symplectic geometry and topological field theories I  Lecture 
Abstract
Derived symplectic geometry and topological field theories I
Derived geometry provides a way to deal with many problems that arise in geometry: 

Sep 05, 2013  16:00  D. Calaque  Derived symplectic geometry and topological field theories II  Lecture 
Abstract
Derived symplectic geometry and topological field theories II
Derived geometry provides a way to deal with many problems that arise in geometry: 

Sep 06, 2013  10:00  R. Von Unge  The secret life of sigma supermodels II  Lecture 
Abstract
The secret life of sigma supermodels II These lectures will give an introduction to sigma models for mathematicians and physicists. In the first lecture I will introduce sigma models and the various concepts needed to understand them. I will give several simple examples and in particular discuss the intriguing relation between properties of the field theory that defines the sigma model and the geometrical characteristics of its target space. The second lecture will be focussed on supersymmetric sigma models and their target space geometry. I will in particular discuss the relation between Generalized Kähler geometry and (2,2) supersymmetry. The third lecture will give some applications such as quotient constructions (reductions) and Tduality and also discuss the quantum properties of sigma models in more detail. 

Sep 06, 2013  11:30  D. Calaque  Derived symplectic geometry and topological field theories III  Lecture 
Abstract
Derived symplectic geometry and topological field theories III
Derived geometry provides a way to deal with many problems that arise in geometry: 

Sep 06, 2013  14:30  R. Heluani  (Sheaves of) vertex algebras and stringy manifold invariants II  Lecture 
Abstract
(Sheaves of) vertex algebras and stringy manifold invariants II In these lectures we will introduce and play with the basic notions of vertex algebra theory like Poisson vertex algebras, quasiclassical limits, etc. We will give several examples reproducing the well known examples in the theory like universal enveloping vertex algebras, lattice vertex algebras and Walgebras. We will then explain how to construct a sheaf of vertex algebras attached to any smooth manifold M, known as the chiral de Rham complex of M. Finally, computing the cohomologies of these sheaves we will obtain geometric invariants of M. 

Sep 06, 2013  16:00  R. Heluani  (Sheaves of) vertex algebras and stringy manifold invariants III  Lecture 
Abstract
(Sheaves of) vertex algebras and stringy manifold invariants III In these lectures we will introduce and play with the basic notions of vertex algebra theory like Poisson vertex algebras, quasiclassical limits, etc. We will give several examples reproducing the well known examples in the theory like universal enveloping vertex algebras, lattice vertex algebras and Walgebras. We will then explain how to construct a sheaf of vertex algebras attached to any smooth manifold M, known as the chiral de Rham complex of M. Finally, computing the cohomologies of these sheaves we will obtain geometric invariants of M. 

Sep 08, 2013  14:30  Edward Witten  Superstring Perturbation Theory Revisited I  Lecture 
Abstract
Superstring Perturbation Theory Revisited I The main ideas of superstring perturbation theory were wellestablished by the mid1980's, but some details important for understanding the infrared behavior were never fully clarified. To clarify these details, one primarily needs to formulate everything on the moduli space of super Riemann surfaces rather than trying to reduce everything to integration over the moduli space of ordinary Riemann surfaces. 

Sep 16, 2013  14:30  R. Garavuso  Analogues of MathaiQuillen forms in sheaf cohomology and applications to topological field theory  Seminar  
Sep 17, 2013  11:00  M. Billo  Remarks on the εdeformed prepotential of the N=2* theory  Seminar  
Sep 18, 2013  11:00  A. Tanzini  The Stringy Instanton Partition Function  Seminar  
Sep 18, 2013  14:30  G. Bonelli  N=1 Geoemetries via Mtheory  Seminar  
Sep 19, 2013  11:00  N. Nekrasov  BPS/CFT correspondence: vertex operators and Bethe states, part I  Seminar  
Sep 19, 2013  14:30  N. Nekrasov  BPS/CFT correspondence: vertex operators and Bethe states, part II  Seminar  
Sep 20, 2013  11:00  S. Cremonesi  Coulomb branches of 3d N=4 gauge theories: monopole operators and Hilbert series  Seminar  
Sep 23, 2013  11:00  F. Benini  Elliptic general of twodimensional N=2 gauge theories  Seminar  
Sep 24, 2013  11:00  M. Bochicchio  LargeN YangMills as a Topological Field Theory  Seminar  
Sep 25, 2013  11:00  A. Morozov  TBA  Seminar  
Sep 26, 2013  11:00  A. Morozov  TBA  Seminar  
Sep 27, 2013  11:00  D. Waldram  The geometry of N=2 flux backgrounds  Seminar  
Sep 30, 2013  11:00  G. Festuccia  Supersymmetric Theories on curved spaces: part I  Seminar  
Oct 01, 2013  11:00  G. Festuccia  Supersymmetric Theories on curved spaces: part II  Seminar  
Oct 02, 2013  11:00  B. de Wit  Deformations of special geometry: in search of the topological string  Seminar  
Oct 03, 2013  11:00  U Bruzzo  Stacky partial compactifications of moduli spaces of instantons  Seminar  
Oct 04, 2013  11:00  S. Cherkis  Monowall dynamics, melting crystals, and oriented matroids  Seminar  
Oct 07, 2013  14:30  Pavel Mnev  Around moduli spaces of flat connections I  Lecture 
Abstract
Around moduli spaces of flat connections I We will discuss the moduli spaces of flat connections on principal bundles over manifolds and various natural structures supported on them. The cases particularly rich in features are moduli spaces of flat bundles over surfaces and 3manifolds, cases related to ChernSimons topological field theory. We will also discuss supergeometric structures on moduli spaces, their cohomological description and, time permitting, geometric quantization of the moduli spaces of flat connections over a surface. 

Oct 07, 2013  16:00  Gregory Ginot  An introduction to differentiable stacks and moduli space I  Lecture 
Abstract
An introduction to differentiable stacks and moduli space I Available soon 

Oct 08, 2013  10:00  J. Qiu  Localization of 5D super YangMills I  Lecture 
Abstract
Localization of 5D super YangMills I
In these lectures, I plan to go through the rough procedure of computing the perturbative partition of 5D SYM. The content of the lecture will be the following


Oct 08, 2013  11:30  Pavel Mnev  Around moduli spaces of flat connections II  Lecture 
Abstract
Around moduli spaces of flat connections II We will discuss the moduli spaces of flat connections on principal bundles over manifolds and various natural structures supported on them. The cases particularly rich in features are moduli spaces of flat bundles over surfaces and 3manifolds, cases related to ChernSimons topological field theory. We will also discuss supergeometric structures on moduli spaces, their cohomological description and, time permitting, geometric quantization of the moduli spaces of flat connections over a surface. 

Oct 08, 2013  14:30  Edward Witten  Superstring Perturbation Theory Revisited I  Lecture 
Abstract
Superstring Perturbation Theory Revisited I The main ideas of superstring perturbation theory were wellestablished by the mid1980\\\'s, but some details important for understanding the infrared behavior were never fully clarified. To clarify these details, one primarily needs to formulate everything on the moduli space of super Riemann surfaces rather than trying to reduce everything to integration over the moduli space of ordinary Riemann surfaces. 

Oct 08, 2013  16:00  Andrea Cappelli  The Birth of String Theory  Lecture 
Abstract
The Birth of String Theory An historical journey from the first version of the theory (the socalled dual resonance model) in the late sixties, as an attempt to describe the physics of strong interactions outside the framework of quantum field theory, to its reinterpretation around the midseventies as a quantum theory of gravity unified with the other forces, and its successive developments up to the superstring revolution in 1984. 

Oct 09, 2013  10:00  Edward Witten  Superstring Perturbation Theory Revisited II  Lecture 
Abstract
Superstring Perturbation Theory Revisited II The main ideas of superstring perturbation theory were wellestablished by the mid1980\'s, but some details important for understanding the infrared behavior were never fully clarified. To clarify these details, one primarily needs to formulate everything on the moduli space of super Riemann surfaces rather than trying to reduce everything to integration over the moduli space of ordinary Riemann surfaces. 

Oct 09, 2013  11:30  Pavel Mnev  Around moduli spaces of flat connections III  Lecture 
Abstract
Around moduli spaces of flat connections III We will discuss the moduli spaces of flat connections on principal bundles over manifolds and various natural structures supported on them. The cases particularly rich in features are moduli spaces of flat bundles over surfaces and 3manifolds, cases related to ChernSimons topological field theory. We will also discuss supergeometric structures on moduli spaces, their cohomological description and, time permitting, geometric quantization of the moduli spaces of flat connections over a surface. 

Oct 09, 2013  14:30  Marco Aldi  Hamiltonian Quantization of Loop Spaces and Vertex Algebras I  Lecture 
Abstract
Hamiltonian Quantization of Loop Spaces and Vertex Algebras I In these lectures we review some recent results regarding the use of vertex algebras and Poisson vertex algebras in the Hamiltonian quantization of (connected) loop spaces. After recalling the basic constructions, we will explain how the Hamiltonian formalism can be used to study targetspace geometry. Hamiltonian quantization of disconnected loop spaces will be addressed in the last lecture. 

Oct 09, 2013  16:00  Henrique Bursztyn  A gradedgeometric viewpoint to generalized geometry II  Lecture 
Abstract
A gradedgeometric viewpoint to generalized geometry II These lectures will offer a basic introduction to the geometry of graded manifolds. The main goal is discussing how graded symplectic geometry provides a natural approach to \"generalized geometry\", including the study of objects such as Courant algebroids, Dirac structures, generalized complex structures, their symmetries and reduction. 

Oct 10, 2013  10:00  J. Qiu  Localization of 5D super YangMills II  Lecture 
Abstract
Localization of 5D super YangMills II
In these lectures, I plan to go through the rough procedure of computing the perturbative partition of 5D SYM. The content of the lecture will be the following


Oct 10, 2013  11:30  Edward Witten  Superstring Perturbation Theory Revisited III  Lecture 
Abstract
Superstring Perturbation Theory Revisited III The main ideas of superstring perturbation theory were wellestablished by the mid1980s, but some details important for understanding the infrared behavior were never fully clarified. To clarify these details, one primarily needs to formulate everything on the moduli space of super Riemann surfaces rather than trying to reduce everything to integration over the moduli space of ordinary Riemann surfaces. 

Oct 10, 2013  14:30  Marco Aldi  Hamiltonian Quantization of Loop Spaces and Vertex Algebras II  Lecture 
Abstract
Hamiltonian Quantization of Loop Spaces and Vertex Algebras II In these lectures we review some recent results regarding the use of vertex algebras and Poisson vertex algebras in the Hamiltonian quantization of (connected) loop spaces. After recalling the basic constructions, we will explain how the Hamiltonian formalism can be used to study targetspace geometry. Hamiltonian quantization of disconnected loop spaces will be addressed in the last lecture. 

Oct 10, 2013  16:00  Gregory Ginot  An introduction to differentiable stacks and moduli space II  Lecture 
Abstract
An introduction to differentiable stacks and moduli space II Available soon 

Oct 11, 2013  10:00  Gregory Ginot  An introduction to differentiable stacks and moduli space III  Lecture 
Abstract
An introduction to differentiable stacks and moduli space III Available soon 

Oct 11, 2013  11:30  J. Qiu  Localization of 5D super YangMills III  Lecture 
Abstract
Localization of 5D super YangMills III
In these lectures, I plan to go through the rough procedure of computing the perturbative partition of 5D SYM. The content of the lecture will be the following


Oct 11, 2013  14:30  Marco Aldi  Hamiltonian Quantization of Loop Spaces and Vertex Algebras III  Lecture 
Abstract
Hamiltonian Quantization of Loop Spaces and Vertex Algebras III In these lectures we review some recent results regarding the use of vertex algebras and Poisson vertex algebras in the Hamiltonian quantization of (connected) loop spaces. After recalling the basic constructions, we will explain how the Hamiltonian formalism can be used to study targetspace geometry. Hamiltonian quantization of disconnected loop spaces will be addressed in the last lecture. 

Oct 15, 2013  14:30  R. Minasian  Higher derivative corrections, Bfield and N=2 theories  Seminar  
Oct 16, 2013  11:00  J. Minahan  Threepoint functions for short operators  Seminar  
Oct 16, 2013  14:30  A Cattaneo  BV around the corner: A gentle introduction to the BV formalism from scratch to field theories on manifolds with boundary and corners [Part I]  Seminar  
Oct 17, 2013  11:00  A. Cattaneo  BV around the corner: A gentle introduction to the BV formalism from scratch to field theories on manifolds with boundary and corners [Part II]  Seminar 