Browsing Mathematics Theses and Dissertations by Title
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Dilts, James (University of Oregon, August 18, 2015)[more][less]Isenberg, James Dilts, James 20150818T23:00:52Z 20150818T23:00:52Z 20150818 http://hdl.handle.net/1794/19237 In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have solutions, global supersolutions which guarantee solutions to the conformal constraint equations for nearconstantmeancurvature (nearCMC) data as well as for farfromCMC data, a proof of the limit equation criterion in the nearCMC case, as well as a model problem on the relationship between the asymptotic constants of solutions and the ADM mass. We also prove a characterization of the Yamabe classes on asymptotically Euclidean manifolds and resolve the (conformally) prescribed scalar curvature problem on asymptotically Euclidean manifolds for the case of nonpositive scalar curvatures. This dissertation includes previously published coauthored material. en_US University of Oregon All Rights Reserved. differential geometry general relativity partial differential equations The Einstein Constraint Equations on Asymptotically Euclidean Manifolds Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Welly, Adam (University of Oregon, October 27, 2016)[more][less]He, Weiyong Welly, Adam 20161027T18:40:22Z 20161027T18:40:22Z 20161027 http://hdl.handle.net/1794/20466 Let (M,g) be a quasiSasaki 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 nonnegativity condition on the transverse curvature, we prove some rigidity results on the structure of (M,g). Naturally associated to a quasiSasaki metric g is a transverse Kahler metric g^T. The transverse KahlerRicci flow of g^T is the normalized Ricci flow of the transverse metric. Exploiting the transverse Kahler geometry of (M,g), we can extend results in KahlerRicci flow to our transverse version. In particular, we show that a deep and beautiful theorem due to Perleman has its counterpart in the quasiSasaki setting. We also consider evolving a Sasaki metric g by Ricci flow. Unfortunately, if g(0) is Sasaki then g(t) is not Sasaki for t>0. However, in some instances g(t) is quasiSasaki. We examine this and give some qualitative results and examples in the special case that the initial metric is etaEinstein. en_US University of Oregon All Rights Reserved. differential geometry Einstein metric Kahler quasiSasaki Ricci flow Sasaki The Geometry of quasiSasaki Manifolds Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Vicinsky, Deborah (University of Oregon, August 18, 2015)[more][less]Sadofsky, Hal Vicinsky, Deborah 20150818T23:06:22Z 20150818T23:06:22Z 20150818 http://hdl.handle.net/1794/19283 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 BissonTsemo model structure. In both cases, the category of spectra is homotopically trivial. This implies that the Goodwillie derivatives of the identity functor in each category, if they exist, are weakly equivalent to the zero spectrum. Finally, we give an infinite family of model structures on the category of small categories. en_US University of Oregon All Rights Reserved. Algebraic topology Goodwillie calculus Homotopy theory Model categories The Homotopy Calculus of Categories and Graphs Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Montgomery, Aaron (University of Oregon, October 3, 2013)[more][less]Levin, David Montgomery, Aaron 20131003T23:37:50Z 20131003T23:37:50Z 20131003 http://hdl.handle.net/1794/13335 We study a family of random walks defined on certain Euclidean lattices that are related to incidence matrices of balanced incomplete block designs. We estimate the return probability of these random walks and use it to determine the asymptotics of the number of balanced incomplete block design matrices. We also consider the problem of collisions of independent simple random walks on graphs. We prove some new results in the collision problem, improve some existing ones, and provide counterexamples to illustrate the complexity of the problem. en_US University of Oregon All Rights Reserved. balanced incomplete block designs collisions of random walks Markov chains Topics in Random Walks Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Sun, Michael (University of Oregon, September 29, 2014)[more][less]Lin, Huaxin Sun, Michael 20140929T17:46:18Z 20140929T17:46:18Z 20140929 http://hdl.handle.net/1794/18368 In this dissertation we explore the question of existence of a property of group actions on C*algebras known as the tracial Rokhlin property. We prove existence of the property in a very general setting as well as specialise the question to specific situations of interest. For every countable discrete elementary amenable group G, we show that there always exists a Gaction ω with the tracial Rokhlin property on any unital simple nuclear tracially approximately divisible C*algebra A. For the ω we construct, we show that if A is unital simple and Zstable with rational tracial rank at most one and G belongs to the class of countable discrete groups generated by finite and abelian groups under increasing unions and subgroups, then the crossed product A ω G is also unital simple and Zstable with rational tracial rank at most one. We also specialise the question to UHF algebras. We show that for any countable discrete maximally almost periodic group G and any UHF algebra A, there exists a strongly outer product type action α of G on A. We also show the existence of countable discrete almost abelian group actions with the "pointwise" Rokhlin property on the universal UHF algebra. Consequently we get many examples of unital separable simple nuclear C*algebras with tracial rank zero and a unique tracial state appearing as crossed products. en_US University of Oregon All Rights Reserved. C*algebras classification crossed product existence group actions tracial Rokhlin property The Tracial Rokhlin Property for Countable Discrete Amenable Group Actions on Nuclear Tracially Approximately Divisible C*Algebras Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Bell, Thomas (University of Oregon, October 3, 2013)[more][less]Lu, Peng Bell, Thomas 20131003T23:31:15Z 20131003T23:31:15Z 20131003 http://hdl.handle.net/1794/13231 In the first chapter we consider the question of uniqueness of conformal Ricci flow. We use an energy functional associated with this flow along closed manifolds with a metric of constant negative scalar curvature. Given initial conditions we use this functional to demonstrate the uniqueness of the solution to both the metric and the pressure function along conformal Ricci flow. In the next chapter we study backward Ricci flow of locally homogeneous geometries of 4manifolds which admit compact quotients. We describe the longterm behavior of each class and show that many of the classes exhibit the same behavior near the singular time. In most cases, these manifolds converge to a subRiemannian geometry after suitable rescaling. en_US University of Oregon All Rights Reserved. Conformal Differential Flow Geometry Homogeneous Ricci Uniqueness of Conformal Ricci Flow and Backward Ricci Flow on Homogeneous 4Manifolds Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon

Arbo, Matthew (University of Oregon, February 23, 2016)[more][less]Proudfoot, Nicholas Arbo, Matthew 20160224T00:17:14Z 20160224T00:17:14Z 20160223 http://hdl.handle.net/1794/19686 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 definition of a hypertoric variety and a new construction using zonotopal tilings and relate the zonotopal construction to the hyperplane construction. en_US University of Oregon All Rights Reserved. Zonotopes and Hypertoric Varieties Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon
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