Math CS Colloquium, Olga Kharlampovich (Hunter College, CUNY):"Tarski-type questions for group rings"

Thursday, April 28, 2016
4:15 PM - 5:15 PM (ET)
Exley 121
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Han Li

Abstract: We consider some fundamental model-theoretic questions that can be asked about a given algebraic structure (a group, a ring, etc.), or a class of structures, to understand its principal algebraic and logical properties. These Tarski type questions include: elementary classification and decidability of the first-order theory.

We describe  solutions to Tarski's problems in the class of group algebras of free groups. We will show that unlike free groups, two groups algebras of free groups over infinite fields are elementarily equivalent if and only if the groups are isomorphic and the fields are equivalent in the weak second order logic.   We will also show that for any  field, the theory of a  group algebra of a torsion free hyperbolic group is undecidable and for a field of zero characteristic even the diophantine problem is undecidable. (These are joint results with A. Miasnikov)

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