# Dept. of Mathematics

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• (University of Illinois at Urbana-Champaign, 1953-05-11)

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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 ...

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• (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 ...

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• (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 ...

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• (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 ...

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