Seminari di Geometria
La Prof.ssa Leonor Godinho e la Dott.ssa Alessia Mandini (Instituto Superior Tecnico, Lisbona) terranno due seminari in sequenza Martedì 12 Febbraio alle ore 11.00 in sala conferenze Tricerri
Dipartimento di Matematica e Informatica U. Dini.
Precisamente:
Prima parte, ore 11-11.45: Hyperpolygons and moduli spaces of parabolic Higgs bundles (Alessia Mandini)
Seconda parte, ore 12-12.45: Polygons in Minkowski 3-space: A quest for a lost family (Leonor Godinho)
PRIMA PARTE, ABSTRACT: In this talk I will prove the existence of an isomorphism between two families of manifolds: hyperpolygon spaces and moduli spaces of stable, rank-2, holomorphically trivial parabolic Higgs bundles over CP^1 with fixed determinant and trace free Higgs field. Using the study of variation of moduli spaces of parabolic Higgs bundles over a curve, I will describe the dependence of hyperpolygon spaces X(a) and their cores on the choice of the parameter a and show that, when a wall is crossed, the hyperpolygon space undergoes an elementary transformation in the sense of Mukai. This is joint work with Leonor Godinho, arXiv:1101.3241.
SECONDA PARTE, ABSTRACT: We consider moduli spaces pf polygons in Minkowski 3-space with a fixed number of sides lying in the future time-like cone and the others in the past (where each side has a fixed Mikowski length) and study their relation with the fixed point set of a natural involution on the space of rank-2 parabolic Higgs bundles over CP^1. This is joint work with I. Biswas, C. Florentino and A. Mandini.