## Colloquium-Detecting properties from descriptions of groups

**Title:** Detecting properties from descriptions of groups

**Speaker:** Jennifer Chubb, University of San Francisco and GWU

__http://www.cs.usfca.edu/~ jcchubb/__

**D****ate and Time:** Friday, March 23, 1:00-2:00pm**Place:** Rome 204

**Abstract** **:** The complexity of the word, conjugacy, and isomorphism problems of finitely presented groups have long been of interest in combinatorial group theory, logic, and algebra in general. Motivating questions are whether (and ideally, how) the presentation of a group in terms of generators and relators can shed any light on the existence of algorithms that solve these problems, or whether the groups exhibit other properties of interest. These questions are usually formulated as what we'll call detection problems, questions of the form "Does presentation P yield a group which exhibits property P?"

From either perspective we are asking whether, given a simple, finite description of a group in the form of an algorithm, it is possible to effectively determine whether or not the group has some specified property. When there is such an effective procedure, we say the property s

*recursively*

*recognizable*wit

We were originally motivated by a desire to determine from a recursive presentation or atomic diagram whether or not a group is orderable. While we will see results in that vein, we will begin by considering a much broader class of properties, and see precise characterizations of the algorithmic complexity of the detection problems for many of them.

**Bio:**Jennifer Chubb received her PhD from George Washington University in 2009, where she studied mathematical logic and computability theory. Her main interests are in computable structure theory, and the algorithmically accessible content of mathematics in general. In a previous life, she studied physics, applied math, and non-linear dynamics at George Mason University. Jennifer is an Associate Professor at the University of San Francisco's Department of Mathematics in California, and visiting scholar at George Washington University.