Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: On the Cheeger constant of hyperbolic surfaces
Speaker: Nicolas Curien, University of Paris-Saclay
Date: February 13, 2023
Time: 18:30:00 Hours
Venue: via Zoom
Abstract: It is a well-known result due to Bollobas that the maximal Cheeger constant of large d-regular graphs cannot be close to the Cheeger constant of the d-regular tree. We shall prove analogously that the Cheeger constant of closed hyperbolic surfaces of large genus is bounded from above by 2/Ï? â?? 0, 63.... which is strictly less than the Cheeger constant of the hyperbolic plane. The proof uses a random construction based on a Poisson-Voronoi tessellation of the surface with a vanishing intensity and makes an interesting object appear: the pointless Poisson--Voronoi tessellation of the hyperbolic plane. Joint work with Thomas Budzinski and Bram Petri.
Title of Talk: On the Cheeger constant of hyperbolic surfaces
Speaker: Nicolas Curien, University of Paris-Saclay
Date: February 13, 2023
Time: 18:30:00 Hours
Venue: via Zoom
Abstract: It is a well-known result due to Bollobas that the maximal Cheeger constant of large d-regular graphs cannot be close to the Cheeger constant of the d-regular tree. We shall prove analogously that the Cheeger constant of closed hyperbolic surfaces of large genus is bounded from above by 2/Ï? â?? 0, 63.... which is strictly less than the Cheeger constant of the hyperbolic plane. The proof uses a random construction based on a Poisson-Voronoi tessellation of the surface with a vanishing intensity and makes an interesting object appear: the pointless Poisson--Voronoi tessellation of the hyperbolic plane. Joint work with Thomas Budzinski and Bram Petri.