Browsing Mathematics Theses and Dissertations by Title
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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
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