SEMINARI DI GEOMETRIA
Given a knot K in S^3, one can consider as invariants the A-polynomial and the coloured Jones polynomial. After illustrating the original AJ conjecture, as formulated by Garoufalidis, I will specify its motivation from quantum SU(2)-Chern-Simons theory, and attempt to make sense of the statement that the two invariants mentioned above are classical and quantum in nature, respectively. This opens the question as of whether one can formulate an analogous conjecture for different Lie groups.
Colleen Robles (Duke University)
Title: Representation theory as a Hodge theoretic tool
Radu Laza (Stony Brook University)
Title: Moduli and periods beyond the classical cases
We show that the mutant 2-component pretzel links P(p,q,-q,-p) and P(p,q,-p,-q) are not concordant for any distinct odd integers p and q greater than 1. As a corollary, we obtain a proof of the slice-ribbon conjecture for 4-stranded 2-component pretzel links. In order to distinguish mutant links up to concordance we consider 3-fold branched covers and use an obstruction based on Donaldson's diagonalization theorem. This is joint work with Min Hoon Kim, JungHwan Park and Arunima Ray.
Si consideri la famiglia dei gruppi finitamente generati che ammettono
una scomposizione k-acilindrica, non-elementare (l'acilindricità è da
intendersi nel senso di Sela). Mostreremo l'esistenza di una funzione
(esplicita) f( - ;k):N--->N, dipendente esclusivamente da k e divergente
all'infinito tale che per ogni gruppo G ed ogni sistema finito di
generatori S di G l'entropia Ent(G,S) di G rispetto ad S sia maggiore o
uguale a f(#(S);k). Spiegheremo come tale disuguaglianza sia la chiave
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.
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