Quantum correlations can be viewed as particular abstract states on the tensor product of operator systems which model quantum measurement scenarios. In the paradigm of nonlocal games, this perspective illustrates a ...

The Simplified Wasserstein Barycenter problem, the problem of picking k points each chosen from a distinct set of n points as to minimize the sum of distances to their barycenter, finds applications in various areas of ...

Given a multivariate rational generating function we are interested in computing asymptotic formulas for the sequences encoded by the coefficients. In this thesis we apply the theory of analytic combinatorics in several ...

The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of the graph in the plane. A graph G is k-crossing-critical if its crossing number is at least k and if every proper subgraph H ...

Facial reduction, pioneered by Borwein and Wolkowicz, is a preprocessing method that is commonly used to obtain strict feasibility in the reformulated, reduced constraint system. The importance of strict feasibility is ...

The semi-random graph process is a single-player graph game where the player is initially presented an edgeless graph with n vertices. In each round, the player is offered a vertex u uniformly at random and subsequently ...

While a quantum field theorist has many uses for mathematics of all kinds, the relationship between quantum field theory and mathematics is far too fluid in the world of modern research to be described as the simple provision ...

The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ...

The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$- and $M(K_{k+1})$-minor-free matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use ...

We prove that for every n, there is a graph G with χ(G) ≥ n and ω(G) ≤ 3 such that every induced subgraph H of G with ω(H) ≤ 2 satisfies χ(H) ≤ 4.This disproves a well-known conjecture. Our construction is a digraph with ...