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Mathematics Theses and Dissertations: Recent submissions
Now showing items 61-80 of 125
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(University of Oregon, 2018-04-10)The Periodicity theorem of Hopkins and Smith tells us that any finite spectrum supports a $v_n$-map for some $n$. We are interested in finding finite $2$-local spectra that both support a $v_2$-map with a low power of ...
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(University of Oregon, 2017-09-06)The hypertoric variety M_A defined by an arrangement A of affine hyperplanes admits a natural tropicalization, induced by its embedding in a Lawrence toric variety. In this thesis, we explicitly describe the polyhedral ...
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(University of Oregon, 2017-09-06)Let (W, S) be an arbitrary Coxeter system, and let J be the asymptotic Hecke algebra associated to (W, S) via Kazhdan-Lusztig polynomials by Lusztig. We study a subalgebra J_C of J corresponding to the subregular cell C ...
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(University of Oregon, 2017-09-06)This thesis introduces two notions of motive associated to a log scheme. We introduce a category of log motives à la Voevodsky, and prove that the embedding of Voevodsky motives is an equivalence, in particular proving ...
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(University of Oregon, 2017-09-06)This thesis presents two main results on analytic and topological aspects of scalar curvature. The first is a gluing theorem for scalar-flat manifolds with vanishing mean curvature on the boundary. Our methods involve tools ...
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(University of Oregon, 2017-09-06)Working at the prime p = 3, we construct a stably finite spectrum, Z, with a v_2^1 self map f. Further, both Ext_A(H*(Z),Z_3) and Ext_A(H*(Z),H*(Z)) have a vanishing line of slope 1/16 in (t-s,s) coordinates, and the map ...
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(University of Oregon, 2017-09-06)For each finite dimensional Lie algebra $\mathfrak{g}$ and positive integer $k$ there exists a modular tensor category $\mathcal{C}(\mathfrak{g},k)$ consisting of highest weight integrable $\hat{\mathfrak{g}}$-modules of ...
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(University of Oregon, 2017-09-06)We construct a semi-orthogonal decomposition for the equivariant derived category of a hypersurface associated to the sum of two potentials. More specifically, if $f,g$ are two homogeneous poynomials of degree $d$ defining ...
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(University of Oregon, 2017-05-01)Khovanov-Lauda-Rouquier algebras, or KLR algebras, are a family of algebras known to categorify the upper half of the quantized enveloping algebra of a given Lie algebra. In finite type, these algebras come with a family ...
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(University of Oregon, 2016-11-21)We prove that the non-k-equal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit ...
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(University of Oregon, 2016-11-21)This dissertation uses techniques from the theory of categorical actions of Kac-Moody algebras to study the analog of the BGG category O for the queer Lie superalgebra. Chen recently reduced many questions about this ...
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(University of Oregon, 2016-10-27)Let (M,g) be a quasi-Sasaki manifold with Reeb vector field xi. Our goal is to understand the structure of M when g is an Einstein metric. Assuming that the S^1 action induced by xi is locally free or assuming a certain ...
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(University of Oregon, 2016-10-27)In this thesis I show that indecomposable projective and tilting modules in hypertoric category O are obtained by applying a variant of the geometric Jacquet functor of Emerton, Nadler, and Vilonen to certain Gel'fand-Ka ...
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(University of Oregon, 2016-10-27)Let $G$ be a second countable, locally compact group which is either compact or abelian, and let $\rho$ be a unitary representation of $G$ on a separable Hilbert space $\mathcal{H}_\rho$. We examine frames of the form $\{ ...
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(University of Oregon, 2016-10-27)We study representations of Khovanov-Lauda-Rouquier (KLR) algebras of affine Lie type. Associated to every convex preorder on the set of positive roots is a system of cuspidal modules for the KLR algebra. For a balanced ...
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(University of Oregon, 2016-02-23)Hypertoric varieties are a class of conical symplectic resolutions which are very computable. In the current literature, they are only defined constructively, using hyperplane arrangements. We provide an abstract ...
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(University of Oregon, 2015-08-18)This dissertation is concerned with representations of locally compact groups on different classes of Banach spaces. The first part of this work considers representations of compact groups by automorphisms of C*-algebras, ...
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(University of Oregon, 2015-08-18)We construct categories of spectra for two model categories. The first is the category of small categories with the canonical model structure, and the second is the category of directed graphs with the Bisson-Tsemo model ...
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(University of Oregon, 2015-08-18)An abelian arrangement is a finite set of codimension one abelian subvarieties (possibly translated) in a complex abelian variety. We are interested in the topology of the complement of an arrangement. If the arrangement ...
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(University of Oregon, 2015-08-18)This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras $R_\alpha$ of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger ...
Now showing items 61-80 of 125