We study links in 3-manifolds which have alternating diagrams onto orientable surfaces of positive genus. When the diagram is sufficiently complicated, we are able to obtain topological and geometrical information about the link exterior. In particular, we can tell if the link is hyperbolic and obtain bounds on volume, know whether the checkerboard surfaces are essential or quasi-fuchsian, and rule out exceptional Dehn fillings. Joint work with Jessica Purcell.
Sala Seminari (Dip. Matematica)
The simplicial volume is a homotopy invariant of compact manifolds introduced in 1982 by Gromov
in his pioneering paper "Volume and Bounded Cohomology". Roughly speaking, the simplicial volume
measures how difficult is to describe a manifold in terms of real singular chains.
In this talk, we will define the ideal simplicial volume, a variation of the ordinary simplicial volume for
compact manifolds with boundary. The main difference between ideal simplicial volume and the ordinary
(Collaborazione con Thang Le) Le algebre skein delle superfici chiuse sono oggetti estremamente ricchi di struttura e studiati. Recentemente, partendo da lavori di Bonahon-Wong e di Muller, Thang Le ha definito una versione delle algebre skein per superfici a bordo. In questo seminario, dopo aver richiamato le definizioni di base, cercherò di spiegare perché questa versione delle algebre skein è particolarmente interessante e cercherò’ di dare un’idea dei risultati (ancora in corso di stesura) di una collaborazione con Thang Le che puntano ad inserire queste algebre in una costruzione di un
Abstract: In the talk we introduce the so-called mean field planning problem: a coupled system of PDEs, a forward continuity equation and a backward Hamilton-Jacobi equation. The problem can be viewed as a modification of the mean field games system as well as a generalization of the classical optimal transportation problem in its dynamic formulation à la Benamou-Brenier. We concentrate on the variational structure of the problem, from which a notion of weak solution can be given.
Abstract: We are interested in proving the triviality of rational points over Atkin-Lehner's quo-
tients of Shimura curves. In fact it is conjectured that, except for nitely many exceptions,
these quotients only have special rational points.
Let p; q be prime numbers. We consider the quotient of the Shimura curve Xpq, of
discriminant pq, by the Atkin-Lehner involution wq. Under certain explicit congruence
conditions, known as the "cas non ramie de Ogg", Parent and Yafaev have found a
On the local-global divisibility and the Tate-Shafarevich group.