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.
Sala Seminari (Dip. Matematica)
Abstract. Consider the problem of transporting some objects
between N distinct locations. Depending on how we package
together different objects and on how the transport cost (per
unit of distance traveled) depends on the package that we are
moving, we may cook up a minimum-cost transport strategy.
Is it always the best option to let our objects travel independently
of each other, or is it sometimes more cost-efficient to merge/split
packages along the way, following a branched, tree-like, global
Abstract. We show that the classical results about rotating
a line segment in arbitrarily small area, and the existence
of a Besicovitch and a Nikodym set hold if we replace the
line segment by an arbitrary rectifiable set.
This is joint work with Marianna Csörnyei.
Abstract. In the 1930s Sadowsky derived an asymptotic theory for narrow ribbons. We here provide a rigorous derivation of the generalized Sadowsky theory starting from nonlinear three-dimensional elasticity by means of Γ-convergence. On a technical level, this involves capturing a contribution to the asymptotic energy functional generated by a nonlinear constraint which is satisfied only approximately. It also involves the construction of fine-scale ‘corrugations’ capable of reaching a bending energy regime that is strictly below that of the original Sadowsky functional.
Abstract: Our framework here is low dimensional topology, and the main protagonists are Legendrian submanifolds, i.e. those which remains obediently tangent to the contact hyperplane distribution. We will see the subtleties brought by Legendrian knots in comparison with classical smooth knots, and understand the natural cobordism notion coming out, initiated by Arnol'd in the early 80's:
"What is a Legendrian surface between two Legendrian knots?"
There will be infinitely many trivial knots, some bow ties, one swallow tail... and a lot of drawings.
Abstract. We show some recent results on convex sets in Wiener spaces. We characterize the essential and reduced boundary of open convex sets and investigate integration by parts formulae. Of particular interest is the investigation of trace theorems for functions of bouned variation on boundaries of subsets in Wiener spaces.
We study a functional in which perimeter and regularized dipolar repulsion compete under a volume constraint.
In contrast to previously studied similar problems, the nonlocal term contributes to the perimeter term to leading order for small regularization parameters.
In this talk we will consider Schrödinger operators of the form
Hu = - \Delta u + V u
Abstract: Complex projective structures are geometric structures locally modelled on the geometry of the Riemann sphere with its group of Möbius transformations PSL(2,C). As this space appears as a natural boundary at infinity for the hyperbolic space, a typical feature of these structures is the interplay between complex analysis and hyperbolic geometry, which gives rise to a rich deformation theory.