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Papers by Olga Kharlampovich

Research paper thumbnail of What does a group algebra of a free group know about the group?

arXiv (Cornell University), Jul 11, 2016

Research paper thumbnail of 4 Rich groups, weak second-order logic, and applications

De Gruyter eBooks, May 10, 2021

Research paper thumbnail of Equations in Algebras

International Journal of Algebra and Computation, Dec 1, 2018

Research paper thumbnail of Decidability of the Elementary Theory of a Torsion-Free Hyperbolic Group

arXiv (Cornell University), Mar 4, 2013

Research paper thumbnail of Equations in the Q-completion of a torsion-free hyperbolic group

Transactions of the American Mathematical Society, Mar 1, 1999

Research paper thumbnail of On Tarski's Decidability Problem

arXiv (Cornell University), Feb 3, 2014

Research paper thumbnail of On countable elementary free groups

arXiv (Cornell University), Jun 3, 2020

Research paper thumbnail of Equations and Fully Residually Free Groups

Birkhäuser Basel eBooks, 2010

Research paper thumbnail of Algebraic Geometry over Free Groups: Lifting Solutions into Generic Points

arXiv (Cornell University), Jul 7, 2004

Research paper thumbnail of Tarski-type problems for free associative algebras

Journal of Algebra, Apr 1, 2018

Research paper thumbnail of Definable Sets in a Hyperbolic Group

International Journal of Algebra and Computation, Feb 1, 2013

Research paper thumbnail of Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups

Groups, complexity, cryptology, Oct 16, 2019

Research paper thumbnail of Non-$\forall$-homogeneity in free groups

arXiv (Cornell University), Jan 27, 2020

Research paper thumbnail of On Tarski's Decidability Problem: Response to Sela's Report

arXiv (Cornell University), 2014

Research paper thumbnail of Effective JSJ decompositions of maximal -limit quotients

arXiv (Cornell University), Jan 13, 2015

Research paper thumbnail of Quantifier elimination algorithm to boolean combination of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∃</mi><mi mathvariant="normal">∀</mi></mrow><annotation encoding="application/x-tex">\exists\forall</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">∃∀</span></span></span></span>-formulas in the theory of a free group

arXiv (Cornell University), Jul 8, 2012

Research paper thumbnail of Effective JSJ decompositions

Contemporary mathematics, 2005

In this paper we describe an elimination process which is a deterministic rewriting procedure tha... more In this paper we describe an elimination process which is a deterministic rewriting procedure that on each elementary step transforms one system of equations over free groups into a finitely many new ones. Infinite branches of this process correspond to cyclic splittings of the coordinate group of the initial system of equations. This allows us to construct algorithmically Grushko's decompositions of finitely generated fully residually free groups and cyclic [abelian] JSJ decompositions of freely indecomposable finitely generated fully residually free groups. We apply these results to obtain an effective description of the set of homomorphisms from a given finitely presented group into a free group, or, more generally, into an NTQ group.

Research paper thumbnail of Hyperbolic groups and free constructions

Transactions of the American Mathematical Society, 1998

Research paper thumbnail of Undecidability of Equations in Free Lie Algebras

arXiv (Cornell University), Aug 22, 2017

Research paper thumbnail of Undecidability of the first order theories of free non-commutative Lie algebras

arXiv (Cornell University), Apr 25, 2017

Research paper thumbnail of What does a group algebra of a free group know about the group?

arXiv (Cornell University), Jul 11, 2016

Research paper thumbnail of 4 Rich groups, weak second-order logic, and applications

De Gruyter eBooks, May 10, 2021

Research paper thumbnail of Equations in Algebras

International Journal of Algebra and Computation, Dec 1, 2018

Research paper thumbnail of Decidability of the Elementary Theory of a Torsion-Free Hyperbolic Group

arXiv (Cornell University), Mar 4, 2013

Research paper thumbnail of Equations in the Q-completion of a torsion-free hyperbolic group

Transactions of the American Mathematical Society, Mar 1, 1999

Research paper thumbnail of On Tarski's Decidability Problem

arXiv (Cornell University), Feb 3, 2014

Research paper thumbnail of On countable elementary free groups

arXiv (Cornell University), Jun 3, 2020

Research paper thumbnail of Equations and Fully Residually Free Groups

Birkhäuser Basel eBooks, 2010

Research paper thumbnail of Algebraic Geometry over Free Groups: Lifting Solutions into Generic Points

arXiv (Cornell University), Jul 7, 2004

Research paper thumbnail of Tarski-type problems for free associative algebras

Journal of Algebra, Apr 1, 2018

Research paper thumbnail of Definable Sets in a Hyperbolic Group

International Journal of Algebra and Computation, Feb 1, 2013

Research paper thumbnail of Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups

Groups, complexity, cryptology, Oct 16, 2019

Research paper thumbnail of Non-$\forall$-homogeneity in free groups

arXiv (Cornell University), Jan 27, 2020

Research paper thumbnail of On Tarski's Decidability Problem: Response to Sela's Report

arXiv (Cornell University), 2014

Research paper thumbnail of Effective JSJ decompositions of maximal -limit quotients

arXiv (Cornell University), Jan 13, 2015

Research paper thumbnail of Quantifier elimination algorithm to boolean combination of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∃</mi><mi mathvariant="normal">∀</mi></mrow><annotation encoding="application/x-tex">\exists\forall</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">∃∀</span></span></span></span>-formulas in the theory of a free group

arXiv (Cornell University), Jul 8, 2012

Research paper thumbnail of Effective JSJ decompositions

Contemporary mathematics, 2005

In this paper we describe an elimination process which is a deterministic rewriting procedure tha... more In this paper we describe an elimination process which is a deterministic rewriting procedure that on each elementary step transforms one system of equations over free groups into a finitely many new ones. Infinite branches of this process correspond to cyclic splittings of the coordinate group of the initial system of equations. This allows us to construct algorithmically Grushko's decompositions of finitely generated fully residually free groups and cyclic [abelian] JSJ decompositions of freely indecomposable finitely generated fully residually free groups. We apply these results to obtain an effective description of the set of homomorphisms from a given finitely presented group into a free group, or, more generally, into an NTQ group.

Research paper thumbnail of Hyperbolic groups and free constructions

Transactions of the American Mathematical Society, 1998

Research paper thumbnail of Undecidability of Equations in Free Lie Algebras

arXiv (Cornell University), Aug 22, 2017

Research paper thumbnail of Undecidability of the first order theories of free non-commutative Lie algebras

arXiv (Cornell University), Apr 25, 2017

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