October 25th, 2022

Date:
25.10.2022

Speaker:
Goulnara Arzhantseva (University of Vienna)

Title
Logarithmic girth expander Cayley graphs
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 Ktheory. Then we discuss our new explicit construction of finite 4regular graphs as in the title. For each dimension n≥2, our graphs are suitable Cayley graphs of SL_{n}(F_{p}) 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 LubotzkyPhillipsSarnak's classical constructions, these new graphs are the only known explicit logarithmic girth Cayley graph expanders. This is a joint work with Arindam Biswas.
Schedule
10:00  11:30 RTG Lecture 1 (Ana Chavez Caliz)  INF 267, BioQuant, EG, SR 043
11:30  12:00 GetTogether with speaker  INF 267, BioQuant, EG, SR 043
12:00  13:00 Common lunch  reserved at BräuStadel
13:00  13:30 Informal meeting of PhD students  INF 205, Mathematikon, SR B
13:30  14:30 RTG Colloquium: Goulnara Arzhantseva  INF 205, Mathematikon, SR B
14:30  15:15 Common coffee/ tea  INF 205, Mathematikon, Foyer UG
15:15  16:45 RTG Lecture 2 (Wilderich Tuschmann)  INF 267, BioQuant, EG, SR 043

Place:
HD