
Delaram Kahrobaie
University of St. Andrews Scotland, UK


Residual Solvability of Generalized Free Products of Groups
Abstract 1:
In this talk I explore residual solvability of generalized free products of groups; particularly I investigate mostly for two classes of groups: in the first part where the factors are finitely generated nilpotent groups and in the second part I will deal with finitely generated free groups. We show that the generalized free products of finitely generated nilpotent groups are often residually solvable. In the literature residual
finiteness of these kinds of structure has been studied by Gilbert
Baumslag and Joan Landsman Dyer and number of others. In the
second part we I will present some slightly technical theorems on
residual solvability of amalgamated products of finitely generated
free groups. If time allows I will also discuss some interesting
open problems in this area.

Information:
Date: December 29, 2004 at 11:00
Place: Lecture Hall, Niavaran Bldg., Niavaran Square, Tehran, Iran

A Graphic Generalization of Arithmetic
Abstract 2:
In this talk, we extend the classical arithmetic defined over the set of natural
numbers N, to the set of all finite directed connected multigraphs having a pair
of distinguished vertices. Specifically, we introduce a model F on the set of
such graphs, and provide an interpretation of the language of arithmetic L = {0,
1,<,=,+, ×} inside F. The resulting model exhibits the property that the
standard model on N embeds in F as a submodel, with the directed path of length
n playing the role of the standard integer n. We will compare the theory of the
larger structure F with classical arithmetic statements that hold in N. For
example, we explore the extent to which F enjoys properties like the
associativity and commutativity of + and ×, distributivity, cancellation and
order laws, and decomposition into irreducibles. 
Information:
Date: January 1, 2005 at 16:00
Place: Lecture Hall, Niavaran Bldg., Niavaran Square, Tehran, Iran

Some Applications of Polycyclic Groups
Abstract 3:
In this talk I will speak about some algorithmic problems in polycyclic groups
and their applications in theoretical computer science. Part of this work is a
joint work with B. Eick. The talk should be accessible to both Mathematicians
and Computer Scientists.

Information:
Date: January 3, 2005 at 11:00
Place: Lecture Hall, Niavaran Bldg., Niavaran Square, Tehran, Iran

 
