Frobenius manifolds, irregular singularities, and isomonodromy deformations

Events

| Lecture series

February 2021

Giordano Cotti (Group of Mathematical Physics of Lisbon University)

The aim of the course is to give a self-contained introduction to the analytic theory of Frobenius manifolds, ordinary differential equations with rational coefficients in complex domains, and their isomonodromic deformations. Applications to enumerative geometry will also be discussed. In the final part of the mini-course, more recent results in this research area will be presented.

Recommended literature

B. Dubrovin, Geometry of 2D topological field theories, in Integrable Systems and Quantum Groups (Montecatini Terme, 1993), Lecture Notes in Math., Vol. 1620, Springer, Berlin, 1996, 120–348.
B. Dubrovin, Geometry and analytic theory of Frobenius manifolds, Doc. Math. (1998), extra Vol. II, 315–326, arXiv:math.AG/9807034.
C. Hertling, Frobenius manifolds and moduli spaces for singularities, Cambridge Tracts in Mathe- matics, Vol. 151, Cambridge University Press, Cambridge, 2002.
N. Hitchin. Frobenius manifolds. In Gauge theory and symplectic geometry (Montreal, PQ, 1995), volume 488 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pages 69–112. Kluwer Acad. Publ., Dordrecht, 1997.
M. Kontsevich, Yu.I. Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), 525–562.
C. Sabbah, Isomonodromic deformations and Frobenius manifolds, Universitext, Springer & EDP Sciences, 2007, (in French: 2002).