SEMINARI DI GEOMETRIA
Negli anni '70, Thurston introduce il concetto di "degenerazione" di strutture iperboliche su 3-varietà. Questo avrà un ruolo nella dimostrazione del celebre "Teorema dell'orbifold".
Nella sua tesi del 2011, Danciger mostra che spesso in presenza di tale degenerazione c'è anche "transizione" a strutture anti de Sitter (AdS). Per "transizione geometrica", si intende un processo continuo che permette di passare da una geometria a un'altra, come ad esempio la familiare transizione iperbolico-euclideo-sferica all'interno della geometria proiettiva.
We will present a classical conjecture on amenability for groups related
to growth. The original result, which is due to Cohen and,
independently, Grigorchuk, dates back to the 80's: a group Q finitely
presented as F/N, where F is a free group, is amenable if and only if
the exponential growth rates (or _entropies)_ \omega(N) and \omega(F)
of N and F coincide.
In this talk I will describe some invariants for transverse links in
S^3 (endowed with the symmetric contact structure) arising from the
deformations of Khovanov sl_3 homology.
I will start with a brief introduction to the theory of transverse
links in S^3. Afterward, I will recall some known results concerning
transverse invariants in link homologies. In particular, I will focus
on the invariants coming from Khovanov-Rozansky homologies, and those
coming from the deformations of Khovanov homology.
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.