| Sep 22 (Tue) | ||
| 9:50 - 10:00 | Opening | |
| 10:00 - 11:00 | Masato Taki (RIKEN) | |
| Topological String A-model of Today [pdf] | ||
| In the past years, there has been big progress in topological vertex formalism, and it enables us to compute topological string partition functions (aka Nekrasov partition functions) for a wide range of 5d quantum fields theories, including 5d uplifts of non-Lagrangian 4d theories of class S. In this talk, I will give an overview of these developments. I then discuss our new description of topological string for F-theoretic compactification: 'Tao webs'. The topological vertex for Tao webs leads to BPS partition functions (generating functions of elliptic genera) of 6d SCFTs such as E-strings. | ||
| 11:15 - 12:15 | Andrea Brini (Montpellier) | |
| Chern-Simons theory on spherical 3-manifolds and topological strings | ||
| In a series of papers, Gopakumar, Ooguri and Vafa proposed the existence of a duality between two quantum mechanical models: a topological gauge theory - SU(N) Chern-Simons theory on the three-sphere - on one hand, and a topological string theory - the topological A-model on the so-called "resolved conifold" - on the other. From a physical point of view, the duality provides a concrete instance of the gauge/string correspondence, and one where exact computations can be performed in detail. Mathematically, this connection puts forward a triangle of striking, conjectural relations between quantum invariants (Reshetikhin-Turaev-Witten) of knots and 3-manifolds, curve-counting invariants (Gromov-Witten/Donaldson-Thomas) of some local Calabi-Yau 3-folds, and the Eynard-Orantin topological recursion for a specific class of spectral curves. In this talk I will present a proof of a B-model version of the correspondence for spherical 3-manifolds, and outline its implications. This is joint work with Gaëtan Borot (MPIM Bonn). | ||
| (Break) | ||
| 14:00 - 15:00 | Todor Milanov (IPMU) | |
| Gamma integral structure in quantum cohomology | ||
| I would like to explain a certain conjecture about Iritani's integral structure in the cohomology of a compact Kahler orbifold X whose quantum cohomology is semi-simple. I would like also to discuss several applications of this conjecture, which appear in my joint works with B. Bakalov and Y. Ruan. | ||
| 15:15 - 16:15 | Kazuhiro Sakai (Meijigakuin) | |
| BPS index of E-strings [pdf] | ||
| The E-string theory is a fundamental superconformal field theory (SCFT) in six dimensions. It serves as the glue which holds together all of the other (1,0) SCFTs in six dimensions as well as a mother theory of many rank-one supersymmetric gauge theories in lower dimensions. In this talk I will discuss recent progress in the study of the BPS index of E-strings, which is equivalent to the elliptic genera of E-strings and also to a certain topological string partition function. |