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Browse Dissertations and Theses  Mathematics by Title
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(1990)Given a semisimple linear algebraic group G over an algebraically closed field K, we fix a Borel subgroup B and a maximal torus T. This determines a root system $\Phi$, and a set of simple roots $\Delta$. The subgroups ...
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(1981)This thesis presents a classification up to topological equivalence of those flows on the torus satisfying: (1) all singular points and closed orbits are hyperbolic; and (2) there are no saddle connections. Such flows are ...
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(20150715)Given a $G$toric, foldedsymplectic manifold with coorientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where ...
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(20140916)In the first part of this thesis, we study the application of a clearing mechanism of a financial network to a specific type of financial network, which is established upon an abstract underlying asset. In particular, we ...
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(2009)This work attempts to explain the relationships between natural selection, information theory, and statistical inference. In particular, a geometric formulation of information theory known as information geometry and its ...
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(20100820)In this thesis, we explore a chainlevel construction in smooth Deligne cohomology that produces data for extended topological field theories. For closed oriented manifolds $\Sigma$, this construction takes the form of a ...
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(2006)The second main result identifies GromovHausdorff limits of certain sequences of manifoldswithboundary as Alexandrov spaces of curvature bounded below.
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(20150706)We consider questions regarding the existence of graphs and hypergraphs with certain coloring properties and other structural properties. In Chapter 2 we consider colorcritical graphs that are nearly bipartite and have ...
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(2004)Then, we consider packing problems for ddegenerate graphs. Two graphs G1 and G 2 pack if G1 is a subgraph of the complement G¯2 of G 2. We disprove one of the conjecture of Bollobas and Eldridge and prove an extension ...
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(2004)We also show that lambda(G) = q 2 + q = Delta2  Delta for the incidence graph G of the projective plane PG (2, q). To prove this result, we convert the problem to a problem of packing of bipartite graphs into a complete ...
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(2001)An redgecoloring of Kn is (r, m)splittable if V (Kn) can then be rcolored to avoid totally monochromatic mcliques (introduced by Erdo&huml;s and Gyarfas. We interpret such colorings using a tworound game against an ...
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(20120522)In this thesis we study some extremal problems related to colorings and list colorings of graphs and hypergraphs. One of the main problems that we study is: What is the minimum number of edges in an $r$uniform hypergraph ...
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(1994)Combinatorial methods are used to prove several results in number theory. The chapters may be read independently, and are briefly discussed below.
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(1992)An attempt is made to study the mathematical strength of the weak second order theories of Bounded Arithmetic U$\sbsp{2}{i}$ and V$\sbsp{2}{i}$, i $\geq$ 0, introduced by S. Buss. It is first shown that U$\sbsp{2}{1}$ can ...
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Now showing items 120139 of 1053