# Jerusalem Mathematics Colloquium

Thursday, 4th December 2003, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Dr. Mikhail Belolipetsky

(Hebrew University)

"On volumes of arithmetic quotients of SO(1,n)"

** Abstract: **
Extremal hyperbolic manifolds and orbifolds, namely those which have the
smallest possible volume, were a subject of interest for a long time. A
classical example of such an orbifold is the quotient of Klein's quartic
by its group of automorphisms, which can be also obtained as G\SO(1,2)
where G is so-called Hurwitz group (2,3,7). This orbifold and other known
examples of small volume in dimension 3 are all arithmetic by which we
mean that they are uniformized by arithmetic subgroups of SO(1,n).

The goal of my recent research can be formulated as to obtain the higher
dimensional analogues of the Hurwitz group. As a result, for each even
dimension n we prove that there exists a unique minimal arithmetic
hyperbolic n-orbifold and give a formula for its generalized Euler
characteristic. The argument uses G. Prasad's volume formula for
arithmetic quotients of semi-simple groups and Bruhat-Tits theory.

In the talk I will explain main ideas of the proof and also discuss
applications and possible generalizations of the results.

Light refreshments will be served in the faculty lounge at 3:30.

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