SCIENTIFIC PROGRAMS AND ACTIVITIES
|July 4, 2015|
Thematic Program on the Geometry of String
|String Theory Thematic Year home page||High Energy Physics Seminars||Audio Links|
|Perimeter Institute String Seminars||Symplectic Geometry Seminars||Guelph-Waterloo Gravity Seminars|
||Atsushi Takahashi, RIMS, Kyoto
Matrix Factorizations and Representations of Quivers
||Jaemo Park, Pohang U
Supertwistor Orbifolds: Gauge Theory Amplitudes and Topological Strings
||Amihay Hanany, MIT
Quivers for Metrics
||Alexei Gorodentsev, ITEP, Moscow
T-stabilities on triangulated categories
||Cobi Sonnenschein, Tel Aviv U
More on the non-critical gauge/gravity duality
||Ofer Aharony, Weitzmann Inst.
Gravitational phase transitions from a field theory perspective
||Matthias Gaberdiel, Zurich, ETH
Topological permutation branes
||Yan Soibelman, Kansas State
Mirror symmetry and non-archimedean analytic geometry
||A M Semikhatov, Lebedev Inst., Moscow
Nonsemisimple Verlinde algebras and quantum groups
||Anirban Basu, Chicago
The M2-M5 Brane System and a Generalized Nahm's Equation
||Juan Cascales, Universidad Autonoma de Madrid-CSIC
Holographic dual of the Standard Model on the throat
||Duco van Straten, U Gutenberg
An Index theorem for Matrix Factorizations
||Piljin Yi, KIAS
Closed Strings and Unstable D-Brane Systems
||Don Marolf, UCSB
Clarifying holographic charges
||Mark Van Raamsdonk, UBC
Phase diagrams for large N gauge theories on compact spaces
|Wed., Sept. 22||Marco Gualtieri, Fields Institute
An introduction to generalized geometry
Abstract: I will provide an introduction to the new field of generalized geometry, initiated by Hitchin (math.DG/0209099) and developed in my thesis (math.DG/0401221). I will concentrate mainly on generalized complex geometry, which is a unification of complex and symplectic geometry. I will make some comments about the implications for mirror symmetry. If time permits I will speak about generalized Riemannian and Kahler geometry.
|Mon., Oct. 4
||Fyodor Malikov, University of Southern
California / Fields Institute
Algebras of chiral differential operators and the Courant bracket
Abstract: This talk is intended to serve a twofold purpose: first, to give an introduction to sheaves of vertex algebras on smooth manifolds and, second, to explain that vertex algebras is a natural framework for the Courant brackets.
|Wed., Oct. 6
||Ke Zhu, Fields Institute
Degeneration of the moduli space of J-holomorphic discs and Legendrian contact homology
Abstract: In this paper, I study the degeneration of the moduli space of $J$-holomorphic discs in the cotangent bundle ending on an exact multicovering Lagrangian submanifold. The main theorem establishes an embedding of the tri-valent gradient flow tree moduli space induced from the exact multicovering Lagrangian submanifold into the above $J$-holomorphic disc moduli space, provided the Lagrangian submanifold is sufficiently close to the zero section and satisfies some generic conditions. As an application, I use the degeneration to show the combinatorial braid invariants defined by Ng is isomorphic to the Legendrian contact homology in the 1-jet space $J^1(T^2)$ for the Legendrian submanifold arising from the braid's monodromy.
||Ionut Ciocan-Fontanine, University
of Minnesota / Fields Institute
A generalisation of the Hori-Vafa Conjecture
Abstract: A few years ago, Hori and Vafa conjectured that the Landau-Ginzburg model mirror to the nonlinear sigma-model on a Grassmannian can be obtained by "symmetrizing" the Landau-Ginzburg model mirror to a product of projective spaces. In particular, this conjecture predicts a precise relation between the J-functions (generating functions for certain genus zero Gromov-Witten invariants) of these varieties. This talk will describe joint work with Aaron Bertram and Bumsig Kim in which we argue that the appropriate general context for the above relationship is that of twisted GW invariants of abelian and nonabelian GIT quotients. As a concrete example, I will present a theorem giving closed formulas for the J-functions of all isotropic partial flag varieties of classical type.
|Mon., Oct. 18
||F. Malikov, University of Southern
California / Fields Institute
Algebras of chiral differential operators and the Courant bracket (part 2)
|Wed., Oct. 20
||Paul Horja, Fields Institute
Toric Deligne-Mumford stacks and mirror symmetry
Abstract: Toric Deligne-Mumford stacks have been studied recently by Borisov, Chen and Smith. As it is the
case with the usual toric varieties, the combinatorial tools provide good testing methods in algebraic geometry.
I will present some results in the context of homological mirror symmetry. This is joint work with Lev Borisov.
|Mon., Oct. 25
University of British Columbia / Fields Institute
On some aspects of the de Rham cohomology of stacks
Abstract: I will start by reviewing the definition of the de Rham cohomology of a stack. By "stack" I mean an Artin stack in the differentiable, holomorphic, or algebraic categories. The standard "Cech - de Rham complex" used to calculate/define the cohomology is rather large, as the de Rham complex does not consist of vector bundles (in the manifold case: the cotangent bundle and its exterior powers) but so called "big sheaves".
We attempt to construct a smaller Cech - de Rham complex for stacks, which is defined in terms of vector bundles over the stack. To do this, we require an extra structure on the stack. We call this structure a "flat connection".
The notion of flat connection on a stack generalizes the notions of flat connection on vector bundles and on gerbes.
|Wed., Oct. 27
||Jean-Yves Welschinger, Ecole Normale
Superieure de Lyon / Fields Institute
Invariants of real symplectic 4-manifolds out of reducible and cuspidal pseudo-holomorphic curves
|Mon., Nov. 1
||Robert Penner, University of Southern
California / Fields Institute
On a cell decomposition of a blow-up of the Deligne-Mumford compactification
|Fri., Nov. 5
||Eric Zaslow, Northwestern University
/ Fields Institute
Affine Manifolds, Torus Fibrations and the Y-Vertex
Abstract: Calabi-Yau threefolds have been conjectured to have a special-Lagrangian torus fibration in an asymptotic sense near the large complex structure limit point of moduli space. "At" the limit, the fibers should become flatter and smaller while the threefold collapses to the base of the fibration, which acquires an affine structure. The locus (in the base) of singular fibers conjecturally becomes a trivalent graph, generically. I will discuss the affine geometry of real threefolds and prove the existence of a Ricci-flat metric on a special-Lagrangian torus fibration in the neighborhood of a trivalent vertex of the singularity locus.
|Mon., Nov. 8
||Wei-Dong Ruan, University of Illinois
at Chicago / Fields Institute
Deformations of integral coisotropic submanifolds in symplectic manifold
|Nov. 10 - 29||No seminars|
|Wed., Dec. 1
||Joint Geometry / String Theory seminar
Vladimir Fock, ITEP
Cluster varieties in everyday life
Wed., Dec. 1
|Jim Bryan, UBC
The local Gromov-Witten theory of curves
Abstract: We study the equivariant Gromov-Witten theory of a rank two vector bundle N over a non-singular curve X of genus g. This theory generalizes the local Calabi-Yau theory of X. We develop a gluing theory for the partition functions by degenerating the base curve. We show that the gluing relations, along with our explicit computations of a few basic partition functions, recursively determine all the invariants. In the case where N is the direct sum of two copies of a square root of the canonical bundle, equipped with the anti-diagonal C^* action, the partition function is a Q-deformation of the classical Hurwitz formula for counting unramified covers. We formulate an equivariant version of the Gromov-Witten/Donaldson-Thomas correspondence and discuss it for the case of N.
|Mon., Dec. 6
|Wed., Dec. 8||Alexei Bondal, Steklov Mathemaical
Institute / Fields Institute
Mirror symmetry via constructible sheaves
Abstract: We will descuss an approach to homological mirror symmetry via constructible sheaves, which allow to prove and to better undestand it for a class of toric varieties.
|Dec. 13-Jan. 5||No seminars|