Mathematics Colloquium

Date: Time: 4:00 pm–4:50 pm
Avery Hall Room: 115
Additional Info: AVH
Contact: Steve Cohn, 402-472-7223, scohn1@math.unl.edu
Speaker: Laura Ciobanu
Affiliation: University of Neuchatel
Local Host: Susan Hermiller
Title: Equations in groups

Additional Public Info:

<b>Abstract</b>:
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.

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