Texas A&M University, Department of
Mathematics, 216 Milner Hall, 14th of April 2004, 3:00-4:00
Groups and Dynamcs Seminar
From Ramanujan
graphs to Ramanujan complexes
Alexander Lubotzky of Hebrew University
of
Jerusalem
Ramanujan graphs are k-regular graphs with optimal bounds on their
eigenvalues. They play a central role in various questions in
combinatorics and computer science. Their construction is based on the
work of Deligne and Drinfeld on the Ramanujan conjecture for GL(2). The
recent work of Lafforge which settles the Ramanujan conjecture for
GL(n) over function fields opens the door to the study of Ramanujan
complexes: these are higher dimensinal analogues which are obtained as
quotients of the Bruhat-Tits building of PGL(n) over local fields.