Postdoc at the Mathematical Physics sector of SISSA in Italy.
My main research interest is Mathematical Physics and in particular the theory of Integrable Systems.
Poisson Lie groups and Hamiltonian structures for integrable systems. (info).
My preprints can be found here, also here. These are some reviews I wrote for MathSciNet.
We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.
We generalize the Toda lattice hierarchy by considering N+M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are $\epsilon$-series of differential polynomials in the dependent variables, and we use them to provide a Lax pair definition of the extended bigraded Toda hierarchy. Using R-matrix theory we give the bihamiltonian formulation of this hierarchy and we prove the existence of a tau function for its solutions. Finally we study the dispersionless limit and its connection with a class of Frobenius manifolds on the orbit space of the extended affine Weyl groups of the $A$ series.
The Hamiltonian structures of the two-dimensional Toda lattice and R-matrices,We construct the tri-Hamiltonian structure of the two-dimensional Toda hierarchy using the R-matrix theory.
The Extended Toda Hierarchy,We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the $CP^1$ topological sigma model and the extended Toda hierarchy. We also establish an equivalence of the latter with certain extension of the nonlinear Schr\"odinger hierarchy.
Extended Toda Lattice,We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.
Slides of talk (Vrije Universiteit Amsterdam, 15 November 2006) on "Integrable systems, Extended Toda hierarchies and invariants of CP^1".