Mathematics

Research Topics

• Frobenius manifolds and their connections with quantum cohomologies, singularity theory, reflection groups and their generalizations.
• Integrable hierarchies of topological type and Deligne - Mumford moduli spaces.
• Integrable hierarchies and random matrices.
• Geometry of isomonodromy deformations.
• Theta-functions of Riemann surfaces, Painleve' transcendents and other special functions in the theory of nonlinear waves.
• Weakly dispersive nonlinear partial differential equations: oscillatory behavior and critical phenomena.
• Asymptotic methods in the theory of nonlinear waves and Riemann - Hilbert boundary value problems.

Research Group

Visiting Professors

Main External Collaborators

Workshops

(partially funded by MISGAM and ENIGMA)

• Workshop "Geometry and Integrable Systems", Berlin, 3-7 June 2005
• Workshop on "Random Matrices and Other Random Objects", FIM, ETH-Zurich, 17-21 May 2005
• Conference on "Riemann-Hilbert Problems Integrability and Asymptotics", SISSA, Trieste, 20-25 September 2005
• "Affine Hecke algebras, the Langlands Program, Conformal Field Theory and Matrix Models", Centre International de Rencontres Mathématiques (CIRM), Luminy, France, June 19 - July 14 2006
• "Integrable Systems in Applied Mathematics", Colmenarejo (Madrid) 4-8 September 2006. A satellite Conference of the International Congress of Mathematicians (ICM 2006, Madrid 22-30 August 2006)
• Conference "Random Matrices", Centre International de Rencontres Mathématiques (CIRM), Luminy, France, October 30 - November 3 2006
• Workshop on "Higher Structures in Geometry and Physics", IHP, Paris, January 15-19, 2007
• Conference on "Tropical Geometry and Applications", Loughborough University, Leicestershire (UK), April 20-23, 2007
• Summer School on "Aspects of Membrane Dynamics", KTH, Stockholm, June 11-23, 2007
• "ENIGMA Conference on Mathematical Physics", KTH, Stockholm, June 25-28, 2007
• Conference on "Algebraic aspects of integrable systems", Islay, Scotland, July 1-7, 2007
• Conference on "Random and Integrable models in Mathematics and Physics", Solvay Institute, Brussels, 11-15 September 2007
• Frobenius Structures and Singularity Theory, Poznan, 25-29 August 2008
• Conference on Integrable Systems, Geometry, Matrix Models and Applications, Trieste, 14-18 October 2008

COFIN and PRIN

• Geometric methods in the theory of nonlinear waves and their applications - 2006
• Geometric methods in the theory of nonlinear waves and their applications - 2004

European Networks

• Marie Curie RTN "European Network in Geometry, Mathematical Physics and Applications" (ENIGMA 2004-2008) (Project Coordinator G. Falqui)
• ESF Scientific Programme "Methods of Integrable Systems, Geometry, Applied Mathematics" (MISGAM 2004-2009) (Proponents B. Dubrovin and P. Van Moerbeke)
• ERC Advanced Grant FroM-PDE "Frobenius Manifolds and Hamiltonian Partial Differential Equations" (Advanced Investigator Grant Scheme 2009-2013) (Principal investigator B. Dubrovin)