From integrable structures to topological strings and back

SCHEDULE

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.

Minicourses

Talks

  • M. Alim: Extended Holomorphic Anomaly and its Polynomial Solution
    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.

  • H. Braden: Cyclic Monopoles, Toda and Spectral Curves
    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.

  • S. Cherkis: Bow diagrams and instantons
    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.

  • L. Katzarkov: Generalized Homological Mirror Symmetry

  • M. Kreuzer: Combinatorics and Mirror Symmetry: Results and Perspectives (notes)
    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.

  • E. Gasparim, Nekrasov conjecture for toric surfaces (slides)
    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.

  • G. Mondello, Riemann surfaces with boundary and natural triangulations of the moduli space (notes)
    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.

  • V. Roubtsov: Manin matrices and Elliptic Gaudin revisited
    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.

  • E. Scheidegger: On N=1 Special Geometry
    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.

  • B. Szendroi, Poincare polynomials of Hilbert schemes of threefolds

  • K. Wendland, On orbifolds and free fermion constructions