Antoine Clais (Uni Lille 1)

IMPAN, Kopernika 18

14 - 16.04.2015 TBA

LI : First I will introduce combinatorial modulus and the CLP in an abstract context. I will give basic properties along with some easy proofs that will help get intuition on these tools. Then I will make a parallel between the CLP and the notion of Loewner spaces and evoke some questions and conjectures.

LII : The aim of this second lecture will be to understand the methods available on boundaries of hyperbolic spaces to control combinatorial modulus and to prove the CLP. Again I will insist on some easy and typical computations and proofs. I will use the remaining time talking about some applications of the combinatorial modulus, in particular a connection with the conformal dimension.