Alexander Lubotzky
Hebrew Univeristy, Jerusalem

Visit: April 22, 23, and 26, 2004

Counting Primes, Groups and Manifolds
Thursday, April 22, 4 PM, Math 6627
Friday, April 23, 1-2 PM, Math 6627

Download Lectures:

Colloquium Friday Lecture

ABSTRACT
Let D be a finitely generated group. Let G be a semisimple Lie group, K a maximal compact subgroup and Y=G/K the associated symmetric space. Let x be a positive real number (going to infinity). We will discuss questions of the following type:

• How many primes are there which are smaller than x?
• How many subgroups does D have, of index at most x?
• How many quotient manifolds does Y have, of volume at most x?
  

We will show that these seemingly unrelated questions are actually connected in several different ways.

From Representation Theory to Discrete Mathematics and Geomtry
Monday, April 26, 1-3 PM, Math 6627

Download Lecture:

Monday Lecture

ABSTRACT
Property 'tau' (which is related to Kazhdan Property T in representation theory) has been found to have surprising applications to several areas of mathematics and computer science. We will introduce and review this property and discuss some applications, including:

• Costructions of expanding graphs.
• Producing efficient methods of generating random elements in finite groups.
• Thurston's conjecture on finite covers of hyperbolic manifolds

Background:
Alexander Lubotzky has made fundamental contributions in group theory and its applications to geometry and arithmetic. His wide-ranging interests include topics such as the congruence subgroup problem, lattices in Lie groups and hyperbolic geometry, Kazhdan Property T, subgroup growth, pro-finite groups, generation of finite simple groups. His work with Sarnak and Phillips on the explicit construction of Ramujan graphs via modular forms and the problem of distributing points on the sphere were the subjects of Bourbaki reports and attracted a great deal of attention in computer science and engineering.

Lubotzky has been a Professor of Mathematics at the Hebrew University of Jerusalem since 1985 and has held visiting positions at Columbia, Yale, Stanford, and the University of Chicago. He has published more than 80 papers and is the recipient of the Erdos prize and the Rothschild prize. He twice received the Ferran Sunyer L. Baloger prize for his research monographs "Discrete Groups, Expanding Graphs, and Invariant Measures" and "Subgroup Growth" (written with D. Segal). He was an invited speaker in the Zurich ICM in 1994. He gave the Woodward lectures in Yale in 1998, the Ritt lectures in Columbia in 1999, the Eilenberg lectures in 2000, and the Porter lectures in Rice in 2001.