Browsing by Thesis Advisor "Iosevich, Alex, 1967"
Now showing items 15 of 5

Erdős distance problem in the hyperbolic halfplane
(University of MissouriColumbia, 2009)The Erd̋os distance problem asks for the minimum number of distinct distances determined by large finite point sets in the plane. The aim of this work is to investigate how the classical techniques employed in the study ... 
Explorations of geometric combinatorics in vector spaces over finite fields
(University of MissouriColumbia, 2008)We study how large a set of points needs to be in a vector space over a finite field in order for the points to determine all of a certain type of geometric structure. In addition we show that there are key differences ... 
Extension theorems in vector spaces over finite fields
(University of MissouriColumbia, 2008)We study the L[superscript p]  L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. ... 
Finite point configurations and projection theorems in vector spaces over finite fields
(University of MissouriColumbia, 2010)We study a variety of combinatorial distance and dot product related problems in vector spaces over finite fields. First, we focus on the generation of the Special Linear Group whose elements belong to a finite field with ... 
Geometric combinatorics in discrete settings
(University of MissouriColumbia, 2011)This thesis is a compilation of work in which the author studies geometric configurations in finite fields and the integers modulo q. The results of this dissertation are threefold. First, we prove a finite field analog ...