**SMS scnews item created by Stephan Tillmann at Mon 22 Sep 2014 1336**

Type: Seminar

Distribution: World

Expiry: 22 Dec 2014

**Calendar1: 24 Sep 2014 1100-1200**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry-Topology-Analysis Seminar

# The complexity of solutions to equations in free groups

### Murray Elder

GTA Seminar - Wednesday, 24 September, 11:00-12:00 in Carlaw 535A

Please join us for lunch after the talk!

##
The complexity of solutions to equations in free groups

Murray Elder (Newcastle)

This is joint work with Laura Ciobanu (Neuchatel, Switzerland) and Volker
Diekert (Stuttgart, Germany).

An equation in a free group/monoid is an expression like \(aX^2=XY\),
where \(a\) is an element of the group/monoid and \(X,Y\) are variables. A
solution is an assignment of elements to \(X\) and \(Y\) so that the equation is true in
the
group/monoid.

Using some clever new results by Diekert, Jez and Plandowski, we are able to
describe the set of all solutions to an equation in a free group or free
monoid
with involution, as a formal language of reasonably low complexity. In my
talk I
will describe the problem, the relevant formal language classes, and briefly
describe how
the result works.