## From integrable structures to topological strings and back |

Time |
Mon |
Tue |
Wed |
Thu |
Fri |

9:30-10:30 | Eynard |
Cavalieri |
Cavalieri |
Cavalieri |
Eynard |

10:30-11:00 | Coffee break | ||||

11:00-12:00 | Cavalieri |
Eynard |
Marshakov |
Eynard |
Wendland |

12:00-13:00 | Katzarkov | Losev |
Losev |
Marshakov |
Losev |

13:00-16:00 | Lunch break / Discussion session |
||||

16:00-16:30 | Coffee break | ||||

16:30-17:30 | Marshakov |
Gasparim | Alim | Braden | Mondello |

17:30-18:30 | Kreuzer | Szendroi | Scheidegger | Roubtsov | Cherkis |

**All talks will take place at the Main Building of SISSA in room D.**

- R. Cavalieri:
*Orbifold Gromov-Witten theory* - B. Eynard:
*Random matrix techniques in enumerative geometry and topological strings*(notes: lecture 1, lecture 2, lecture 3, lecture 4) - A. Losev:
*Topological gauge theories* - A. Marshakov:
*Integrable systems in gauge and string theories*(notes)

Abstract: Recent developments in extending the BCOV holomorphic anomaly equations to the open topologcial string as proposed by Walcher will be presented. Furthermore the polynomial procedure for integrating the holomorphic anomaly found by Yamaguchi and Yau for the quintic is shown to hold for arbitrary target space and is extended to solve Walcher's holomorphic anomaly equations.

Abstract: I will describe recent work on the construction of su(2) monopoles with cyclic symmetry. An ansatz of Sutcliffe for the Nahm equations with this symmetry will be proven necessary and some new results on the reduction of the equations and the attendant spectral curve described.

Abstract: We present a construction of Yang-Mills instantons in curved backgrounds of asymptotically locally flat gravitational instantons. Our construction is formulated in terms of Bow diagrams, which generalize quiver diagrams. We give a string theory motivation of the construction and provide some explicit solutions. We discuss a certain duality acting on bows. Each bow diagram also defines a supersymmetric gauge theory with domain wall impurities. Mirror symmetry action of the gauge theories induces the duality of the corresponding bow diagrams.

Abstract: I summarize the combinatorics of the construction of Calabi-Yau varieties in toric ambient spaces and describe our recent construction of a surprisingly large class of new mirror pairs of Calabi-Yau 3-folds with small Picard numbers by conifold transitions.

Abstract: The Nekrasov conjecture predicts a relation between the partition function for SUSY N=2 Yang-Mills theory and the Seiberg-Witten prepotential. This conjecture was proved for instanton on R^4 by Nekrasov-Okounkov, Nakajima-Yoshioka, and Braverman-Etingof. I will present joint work with Melissa Liu, where we prove the conjecture for instantons on non-compact toric surfaces.

Abstract: Natural cellularizations of the Teichmueller space via ribbon graphs have been invented using decorated hyperbolic surfaces or Jenkins-Strebel differentials. We show that these two constructions are interpolated by the spine construction on infinitely grafted hyperbolic surfaces with boundary. Moreover, we introduce the bordification of arcs of the Teichmueller space, which is gives the finest compactification of the moduli space whose points are separated by lengths of arcs. Finally, we express the Weil-Petersson form in the arc coordinates and we discuss its limit for large boundary components.

Abstract: We construct a quadratic elliptic dynamical RLL algebra with Felder $R-$ elliptic matrix and show that $L$ is a Manin matrix. Then we obtain a quasi-commutative family from minors of $L$ and construct a quantum spectral curve for quantum elliptic $gl_n$ Gaudin model. We revise the Separation of Variables in the case of $gl_2$ model.

Abstract: We review the concept of special geometry with emphasis on N=2 special geometry and its proposed extension to N=1 special geometry. We comment on the relation to open string mirror symmetry, BPS domain wall tensions and counting disk instantons in the context of compact CY 3-folds with D-branes.