“Bulletin Board”

 School of Mathematics - December 11, 2006

Mathematical Lecture

Ramanujan conjecture
Jacquet-Langlands correspondence
The construction of Ramanujan graphs and hypergraphs

Alireza Sarveniazi,
University of Bielefeld
Bielefeld, Germany
Jan. 3, 2007

 
 
Ramanujan conjecture
Jacquet-Langlands correspondence
The construction of Ramanujan graphs and hypergraphs


Alireza Sarveniazi,
University of Bielefeld
Bielefeld, Germany



Abstract

In recent years new and important connections have emerged between discrete subgroups of arithmetic groups, automorphic forms and representations on the one side, and questions in discrete mathematics, combinatorics, and graph theory on the other side.
One of the main examples of this interaction is the abstract and explicit construction of Ramanujan graphs and hypergraphs, using the Jacquet-Langlands correspondence and Deligne's theorem (number field case for rank one groups), resp. Lafforgue's theorem (function field case for higher rank groups) on Hecke eigenvalues (Ramanujan conjecture). First I will give a panorama about Langlands functoriality and in particular, I'm going to explain two important problems in arithmetic number theory; namely the Jacquet-Langlands correspondence and the Ramanujan conjecture. I shall devote the rest of my talk to the explicit construction of Ramanujan graphs and hypergraphs. There are great many open problems in these areas, some of which will be addressed in the body of my talk.



Information:


Date:Wednesday, Jan. 3, 2007, 14:00-16:00
Place: Niavaran Bldg., Niavaran Square, Tehran, Iran
 
 
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right