FINKELSHTEIN-DISSERTATION-2017.pdf (439.74 kB)
Diophantine properties of groups of toral automorphisms
thesis
posted on 2017-11-01, 00:00 authored by Vladimir FinkelshteinThis dissertation studies a shrinking target problem for the action of an arbitrary subgroup of SL(2,Z) on the 2-torus. This can also be viewed as a non-commutative Diophantine approximation
problem. The methods require construction of spectrally optimal
random walks on groups acting properly cocompactly on Gromov hyperbolic spaces. Additionally, similar estimates for this problem in higher dimension can be obtained by using harmonic analysis.
History
Advisor
Furman, AlexChair
Furman, AlexDepartment
Mathematics, Statistics and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral
Committee Member
Groves, Daniel Whyte, Kevin Hurder, Steve Hartman, YairSubmitted date
August 2017Issue date
2017-06-06Usage metrics
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