Mathematics ColloquiumDate: Time: 4:00 pm–4:50 pm
Affiliation: University of Neuchatel
Local Host: Susan Hermiller
Title: Equations in groups
Additional Public Info:
The Diophantine Problem in group theory can be stated as: is it
algorithmically decidable whether an equation whose coefficients are
elements of a given group has at least one solution in that group?
The talk will be a survey on this topic, with emphasis on what is known
about solving equations in free groups. I will also present some of the
algebraic geometry over groups developed in the last 20 years, and the
connections to logic and geometry. I will conclude with results concerning the
asymptotic behavior of satisfiable homogeneous equations in surface groups.
Refreshments will be served in 348 Avery 3:30-4:00. The talk is free and open to the public.