ar X iv : 0 70 5 . 17 92 v 1 [ m at h . A G ] 1 2 M ay 2 00 7 Riemann surfaces , ribbon graphs and combinatorial classes

ar X iv : 0 70 5 . 31 41 v 1 [ as tr o - ph ] 2 2 M ay 2 00 7 The SARG Planet Search

M ar 2 00 3 COMBINATORIAL CLASSES ON M g , n ARE TAUTOLOGICAL

The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces allows to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the tautological classes. We answer affirmatively to this conjecture and find recursively all the polynomials. Moreover we lift the combinatorial classes to the Deligne-Mumfor...

ar X iv : 0 70 5 . 39 48 v 1 [ m at h . R T ] 2 7 M ay 2 00 7 DEGENERATION OF A - INFINITY MODULES

In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasiisomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Z...

ar X iv : 0 90 3 . 53 12 v 2 [ m at h . C O ] 1 1 M ay 2 00 9 GRAPHS , LINKS , AND DUALITY ON SURFACES

We introduce a polynomial invariant of graphs on surfaces, PG , generalizing the classical Tutte polynomial. Poincaré duality on surfaces gives rise to a natural duality result for PG , analogous to the duality for the Tutte polynomial of planar graphs. This property is important from the perspective of statistical mechanics, where Tutte polynomial is known as the partition function of the Pott...

ar X iv : h ep - t h / 92 05 10 6 v 1 2 6 M ay 1 99 2 Matrix Model for Discretized Moduli Space

We study the algebraic geometrical background of the Penner–Kontsevich matrix model with the potential N α tr (− 1 2 ΛXΛX + log(1 − X) + X). We show that this model describes intersection indices of linear bundles on the discretized moduli space right in the same fashion as the Kontsevich model is related to intersection indices (cohomological classes) on the Riemann surfaces of arbitrary gener...