Hauptseminar Geometrie

Prof. Dr. Goulnara Arzhantseva , Universität Wien, Österreich

Abstract: An expander is an infinite family of finite graphs, with a growing number of vertices, that are low vertex degree yet highly connected. Expanders are ubiquitous in mathematics and computer science. In this talk, we focus on expanders with girth tending to infinity. First, we briefly indicate their importance for recent results in group theory, metric geometry and operator K-theory. Then we discuss our new explicit construction of finite 4-regular graphs as in the title. For each dimension n≥2, our graphs are suitable Cayley graphs of SLn(Fp) as prime p → ∞. These are the first explicit examples in all dimensions n≥2 (all prior examples were in n=2). Together with Margulis' and Lubotzky-Phillips-Sarnak's classical constructions, these new graphs are the only known explicit logarithmic girth Cayley graph expanders. This is a joint work with Arindam Biswas.

Dienstag, den 25. Oktober 2022 um 13:30 Uhr, in INF 205, SR B Dienstag, den 25. Oktober 2022 at 13:30, in INF 205, SR B

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. A. Wienhard, Prof. P. Albers