00982nas a2200133   4500008004100000245007000041210006300111260001000174520057500184100002000759700001500779700001800794856003600812       2012                        en  d00aOn the genus two free energies for semisimple Frobenius manifolds0 agenus two free energies for semisimple Frobenius manifolds  bSISSA3 aWe represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.1 aDubrovin, Boris1 aLiu, Si-Qi1 aZhang, Youjin  uhttp://hdl.handle.net/1963/646400741nas a2200097   4500008004100000245005600041210005600097520043400153100002000587856003600607       1998                        en  d00aGeometry and analytic theory of Frobenius manifolds0 aGeometry and analytic theory of Frobenius manifolds3 aMain mathematical applications of Frobenius manifolds are\\r\\nin the theory of Gromov - Witten invariants, in singularity theory, in\\r\\ndifferential geometry of the orbit spaces of reflection groups and of their\\r\\nextensions, in the hamiltonian theory of integrable hierarchies. The theory\\r\\nof Frobenius manifolds establishes remarkable relationships between\\r\\nthese, sometimes rather distant, mathematical theories.1 aDubrovin, Boris  uhttp://hdl.handle.net/1963/648800493nas a2200121   4500008004100000020001800041245004600059210004600105260001000151520015400161100002000315856003600335       1995                        en  d  a3-540-60542-800aGeometry of 2D topological field theories0 aGeometry of 2D topological field theories  bSISSA3 aThese notes are devoted to the theory of “equations of associativity”\\r\\ndescribing geometry of moduli spaces of 2D topological field theories.1 aDubrovin, Boris  uhttp://hdl.handle.net/1963/648301159nas a2200109   4500008004100000245006900041210006800110260001000178520080500188100002000993856003601013       1993                        en  d00aGeometry and integrability of topological-antitopological fusion0 aGeometry and integrability of topologicalantitopological fusion  bSISSA3 aIntegrability of equations of topological-antitopological fusion (being proposed\\r\\nby Cecotti and Vafa) describing the ground state metric on a given 2D topological\\r\\nfield theory (TFT) model, is proved. For massive TFT models these equations\\r\\nare reduced to a universal form (being independent on the given TFT model) by\\r\\ngauge transformations. For massive perturbations of topological conformal field theory\\r\\nmodels the separatrix solutions of the equations bounded at infinity are found\\r\\nby the isomonodromy deformations method. Also it is shown that the ground state\\r\\nmetric together with some part of the underlined TFT structure can be parametrized\\r\\nby pluriharmonic maps of the coupling space to the symmetric space of real positive\\r\\ndefinite quadratic forms.1 aDubrovin, Boris  uhttp://hdl.handle.net/1963/6481