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(20170421)This thesis is comprised of two projects in applied computational mathematics. In Chapter 1, we discuss the geometry and combinatorics of geometrically characterized sets. These are finite sets of n+d choose n points in ...
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(20170327)This thesis focuses on using techniques from probability to solve problems from extremal and structural combinatorics. The main problem in Chapter 2 is determining the typical structure of $t$intersecting families in ...
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(20170407)In the first part of this thesis, we will discuss the classical XY model on complete graph in the meanfield (infinitevertex) limit. Using theory of large deviations and Stein's method, in particular, Cramér and Sanovtype ...
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(20170419)The fast developing field of extremal combinatorics provides a diverse spectrum of powerful tools with many applications to economics, computer science, and optimization theory. In this thesis, we focus on counting and ...
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(20170419)In 1996, Masur and Minsky showed that the curve graph is hyperbolic. Recently, Hensel, Przytycki, and Webb proved a stronger result which was the uniform hyperbolicity of the curve graph, and they also gave the first proof ...
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