CONFERENCE TALKS xvii
Aspects of free analysis
Motivated by free probability questions, the lecture will deal with duality for the
bialgebra of the free diﬀerence quotient derivation and the highly noncommutative
generalization of the Riemann sphere which appears in this context.
Algebras of p-symbols, noncommutative p-residue, and the Brauer
Importance of the pseudodiﬀerential symbol calculus extends far beyond the
fundamental role it is known to play in Global and Microlocal Analysis. In this
article, we demonstrate that algebras of symbols contribute to subtle phenomena
in characteristic p 0.
Geometric complexity and topological rigidity
In this talk, I will introduce a notion of geometric complexity and discuss its
applications to geometric group theory and rigidity of manifolds. In particular, I
will show how to prove various geometric versions of the Borel conjecture under
certain a ﬁniteness condition on the geometric complexity. This is joint work with
Erik Guentner and Romain Tessera.