# Browse Dissertations and Theses - Mathematics by Contributor "Kapovitch, Ilia"

• (2011-05-25)
A filling subgroup of a finitely generated free group F(X) is a subgroup which does not fix a point in any very small action free action on an R-tree. For the free group of rank two, we construct a combinatorial algorithm ...

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• (2013-05-24)
This dissertation is concerned with geometric and combinatoric problems of curves on surfaces. In Chapter 3, we show that certain families of iso-length spectral hyperbolic surfaces obtained via the Sunada construction are ...

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• (2012-09-18)
For finite group presentations, the word problem is solvable if and only if the Dehn function is computable. Additionally, the bounded word problem is always solvable. For finitely generated decidable group presentations, ...

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• (2011-05-25)
We consider the class non-surjective irreducible endomorphisms of the free group F_n. We show that such an endomorphism \phi is topologically represented by a simplicial immersion f:G \rightarrow G of a marked graph G; ...

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• (2012-05-22)
There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ...

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• (2013-08-22)
This dissertation is concerned with equivalence relations on homotopy classes of curves coming from various spaces of at metrics on a genus g >1 surface. We prove an analog of a result of Randol (building on work of ...

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• (2011-05-25)
In 2006, Bartholdi and Nekrashevych solved a decade-old problem in holomorphic dynamics by creatively applying the theory of self-similar groups. Nekrashevych expanded this work in 2009 to define what we refer to as ...

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• (2010-05-19)
This thesis is a study of the asymptotic behavior of minimal pseudo-Anosov translation lengths on the Teichmuller space. For tori with n marked points, we find an upper bound for the minimal pseudo-Anosov translation ...

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• (2012-05-22)
In this dissertation, we consider an applied problem, namely, pursuit-evasion games. These problems are related to robotics, control theory and computer simulations. We want to find the solution curves of differential ...

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• (2014-05-30)
Culler-Vogtmann Outer Space (denoted $\cv_N$) is the space of all free minimal discrete isometric actions of the free group of rank $N$ ($F_N$) on $\mathbb{R}$-trees, $T$. We say a subset $\Sigma \subseteq F_N$ is ...

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• (2014-05-30)
In this thesis we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed ...

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