The Poincaré critical exponent
David Hume (University of Birmingham)
Abstract: The Poincaré critical exponent (PCE) assigns to each bounded degree graph X a value p_X ∈ [1,+∞]. PCEs satisfy a strong monotonicity property: whenever there is a Lipschitz, bounded-to-one map X-> Y, it holds p_X ≤ p_Y. In particular, if X and Y are Cayley graphs of finitely generated groups H and G, and H is quasi-isometric to a subgroup of G, then p_X≤ p_Y.
When X is the Cayley graph of a virtually nilpotent group G, p_X is the degree of polynomial growth, and for many hyperbolic groups p_X is the conformal dimension of the boundary of G.
In this talk I will define PCEs, explain some of their properties and highlight many interesting open questions.
algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry
Audience: researchers in the topic
Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/
The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.
| Organizers: | Saul Schleimer*, Robert Kropholler*, Ric Wade |
| *contact for this listing |