Algebra

Mark N. Berman, Gabriel Ben Simon, Alexander Goldvard, Shifra Reif
 
The problem of classifying groups of given class is hard. The problem for finite simple groups has been solved, but remains open for many other interesting classes of groups (both finite and infinite). In the class of finitely generated torsion free nilpotent groups, though classification is intractable, it is fruitful to study the growth of subgroups - that is, how the number of subgroups of given index grows with the index. These numbers, encoded in a zeta function, have been studied using tools from a wide variety of other disciplines, such as model theory, representation theory of algebraic groups, combinatorics and arithmetic geometry. Berman is studying this counting problem in special cases as part of a more general project to understand the relationship between the arithmetic of subgroup growth and the structure of the parent group.
Ben Simon deals with Lie groups and geometric group theory. Here we study groups, especially Lie groups  and discrete groups,  via imposing geometrical structures on the groups and study it as a geometrical object. In this approach both sides of the groups are important the algebraic and the geometric one. Strong relations to important fields in mathematics exist.