A Survey of Algebraic Geometry and Model Theory for Free and Hyperbolic Groups
Olga Kharlampovich, Hunter College, CUNY
Location: Stevenson 5211
I will survey results of Kharlampovich--Miasnikov and Sela on first-order theories of free and hyperbolic groups. I will show that in the presence of ``negative curvature'' in groups, there exists a robust algebraic geometry and the principal Tarski-type problems are decidable. In particular, there is an algorithm for the elimination of quantifiers (to boolean combinations of AE-formulas). I will also give a description of definable sets in free and hyperbolic groups (joint result with Miasnikov). This solves Malcev's problem from 1965. Tea at 3:30 pm in SC 1425.