Now showing items 1-20 of 64

• #### Faithful tropicalization of hypertoric varieties ﻿

(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 ...
• #### On the Subregular J-ring of Coxeter Systems ﻿

(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 ...
• #### Motives of Log Schemes ﻿

(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 ...
• #### Gluing manifolds with boundary and bordisms of positive scalar curvature metrics ﻿

(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 ...
• #### Constructing a v2 Self Map at p=3 ﻿

(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 ...
• #### Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of Unity ﻿

(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 ...
• #### Equivariant Derived Categories Associated to a Sum of Potentials ﻿

(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 ...
• #### Homological Properties of Standard KLR Modules ﻿

(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 ...
• #### Dancing in the Stars: Topology of Non-k-equal Configuration Spaces of Graphs ﻿

(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 ...
• #### Categorical Actions on Supercategory O ﻿

(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 ...
• #### The Geometry of quasi-Sasaki Manifolds ﻿

(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 ...
• #### GKZ Hypergeometric Systems and Projective Modules in Hypertoric Category O ﻿

(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 ...
• #### Frames Generated by Actions of Locally Compact Groups ﻿

(University of Oregon, 2016-10-27)
• #### Linking Forms, Singularities, and Homological Stability for Diffeomorphism Groups of Odd Dimensional Manifolds ﻿

(University of Oregon, 2015-08-18)
Let n > 1. We prove a homological stability theorem for the diffeomorphism groups of (4n+1)-dimensional manifolds, with respect to forming the connected sum with (2n-1)-connected, (4n+1)-dimensional manifolds that are ...