Dept. of Mathematics
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(2017-04-21)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 ...
(2017-03-27)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 ...
(2017-04-07)In the first part of this thesis, we will discuss the classical XY model on complete graph in the mean-field (infinite-vertex) limit. Using theory of large deviations and Stein's method, in particular, Cramér and Sanov-type ...
(2017-04-19)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 ...
(2017-04-19)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 ...