ΣΕΜΙΝΑΡΙΟ ΜΑΘΗΜΑΤΙΚΗΣ ΑΝΑΛΥΣΗΣ
Πέμπτη, 18 Μαΐου 2023, 11.15 – 12.00
Alexander Yu. Solynin, Texas Tech University
“Quadratic differentials in extremal problems”
Περίληψη: We will discuss several extremal problems on capacity and conformal module, where quadratic differentials play a significant role. Among those problems are Teichmuller’s problem on the minimal capacity of rings separating pairs of points, Ahlfors’ problem on separating circles and problems related to Jenkins-Strebel quadratic differentials. We will review known results and present a few new results in the two-dimensional case. Then we will discuss three-dimensional counterparts of the problems mentioned above. In dimension three, only few results are known and most of these problems remain unsolved and notoriously difficult.