Onsdag 15 mars 2017, Håkan Hedenmalm, KTH
Talare: Håkan Hedenmalm, KTH
Titel: Bloch functions, asymptotic variance, and geometric zero packing
Tid och plats: Onsdag 15 mars 2017, Hopningspunkten, 13.15–14.15
Sammanfattning: In connection with the study of the universal integral means spectrum for quasiconformal mapping, it turns out that the main term for small exponents and small Beltrami coefficients is governed by the asymptotic variance introduced by McMullen for a dynamical situation. This follows from work of Oleg Ivrii. The fact that this universal asymptotic variance is less than 1 is shown here. This then leads to the unexpected result that the quasiconformal universal variance is not of the form assumed so far. To obtain the result, we use duality to turn the problem into a problem of analyzing an improvement in the Cauchy-Schwarz inequality. The resulting dual problem has geometric interpretation in terms of "zero packing". In the planar case this is related with Abrikosov´s analysis of superconductivity for which he obtained the Nobel prize.
Senast uppdaterad: Mon Feb 27 11:06:59 CET 2017