From integrable structures to topological strings
|| Coffee break
|| Lunch break /
|| Coffee break
All talks will take place at the Main Building of SISSA in room D.
- R. Cavalieri: Orbifold Gromov-Witten theory
Lecture 1: GW THEORY (notes)
- Lecture 2: ORBIFOLD GW THEORY and G-HODGE INTEGRALS (notes)
Lecture 3: MIRROR SYMMETRY, GIVENTAL'S FORMALISM: A SYSTEMATIC APPROACH TO
GW THEORY OF TORIC STACKS (notes)
- Lecture 4: OPEN GW INVARIANTS OF ORBIFOLDS (notes)
- 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)
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
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
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