Browsing Mathematics Theses and Dissertations by Issue Date
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Pearson, Kelly Jeanne, 1970 (2000)[more][less]Pearson, Kelly Jeanne, 1970 20080210T03:23:05Z 20080210T03:23:05Z 2000 0599841095 http://hdl.handle.net/1794/141 vii, 91 p. A print copy of this title is available through the UO Libraries under the call number: MATH QC20.7.H65 P43 2000 The OrlikSolomon algebra of a hyperplane arrangement first appeared from the Brieskorn and OrlikSolomon theorems as the cohomology of the complement of this arrangement (if the ground field is complex). Later, it was discovered that this algebra plays an important role in many other problems. In particular, define the cohomology of an OrlikSolomon algebra as that of the complex formed by its homogeneous components with the differential defined via multiplication by an element of degree one. Cohomology of the OrlikSolomon algebra is mostly studied in dimension one, and very little is known about the higher dimensions. We study this cohomology in higher dimensions. Adviser: Sergey Yuzvinsky. 3856498 bytes 122293 bytes 1483 bytes application/pdf text/plain text/plain en University of Oregon theses, Dept. of Mathematics, Ph. D., 2000 Cohomology operations Homology theory Cohomology of the OrlikSolomon algebras Thesis

Zhang, Tan, 1969 (University of Oregon, 2000)[more][less]Zhang, Tan, 1969 20080210T03:23:11Z 20080210T03:23:11Z 2000 0599845562 http://hdl.handle.net/1794/150 Adviser: Peter B. Gilkey. ix, 128 leaves A print copy of this title is available through the UO Libraries under the call number: MATH QA613 .Z43 2000 Relative to a nondegenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skewsymmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant dimension on the Grassmanian of nondegenerate oriented 2planes. A pseudoRiemannian manifold with a nondegenerate indefinite metric of signature (p, q) is said to be IP if the curvature tensor of the LeviCivita connection is IP at every point; the eigenvalues are permitted to vary with the point. In the Riemannian setting (p, q) = (0, m), the work of Gilkey, Leahy, and Sadofsky and the work of Ivanov and Petrova have classified the IP metrics and IP algebraic curvature tensors if the dimension is at least 4 and if the dimension is not 7. We use techniques from algebraic topology and from differential geometry to extend some of their results to the Lorentzian setting (p, q) = (1, m – 1) and to the setting of metrics of signature (p, q) = (2, m – 2). 5667358 bytes 1473 bytes 177540 bytes application/pdf text/plain text/plain en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2000 Manifolds (Mathematics) Metric spaces Curvature Operator algebras Eigenvalues Manifolds with indefinite metrics whose skewsymmetric curvature operator has constant eigenvalues Thesis

Brandl, MaryKatherine, 1963 (University of Oregon, 2001)[more][less]Brandl, MaryKatherine, 1963 20080210T04:19:31Z 20080210T04:19:31Z 2001 0493364234 http://hdl.handle.net/1794/147 Adviser: Brad Shelton. viii, 49 leaves A print copy of this title is available through the UO Libraries under the call number: MATH LIB. QA251.3 .B716 2001 We examine a family of twists of the complex polynomial ring on n generators by a nonsemisimple automorphism. In particular, we consider the case where the automorphism is represented by a single Jordan block. The multiplication in the twist determines a Poisson structure on affine nspace. We demonstrate that the primitive ideals in the twist are parameterized by the symplectic leaves associated to this Poisson structure. Moreover, the symplectic leaves are determined by the orbits of a regular unipotent subgroup of the complex general linear group. 1894196 bytes 1473 bytes 51748 bytes 53191 bytes application/pdf text/plain text/plain text/plain en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2001 Polynomial rings Poisson algebras Noncommutative rings Primitive and Poisson spectra of nonsemisimple twists of polynomial algebras Thesis

Archey, Dawn Elizabeth, 1979 (University of Oregon, June , 2008)[more][less]Archey, Dawn Elizabeth, 1979 20081220T02:10:58Z 20081220T02:10:58Z 200806 http://hdl.handle.net/1794/8155 viii, 107 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation consists of two related parts. In the first portion we use the tracial Rokhlin property for actions of a finite group G on stably finite simple unital C *algebras containing enough projections. The main results of this part of the dissertation are as follows. Let A be a stably finite simple unital C *algebra and suppose a is an action of a finite group G with the tracial Rokhlin property. Suppose A has real rank zero, stable rank one, and suppose the order on projections over A is determined by traces. Then the crossed product algebra C * ( G, A, Ã Ã Â±) also has these three properties. In the second portion of the dissertation we introduce an analogue of the tracial Rokhlin property for C *algebras which may not have any nontrivial projections called the projection free tracial Rokhlin property . Using this we show that under certain conditions if A is an infinite dimensional simple unital C *algebra with stable rank one and Ã Ã Â± is an action of a finite group G with the projection free tracial Rokhlin property, then C * ( G, A, Ã Ã Â±) also has stable rank one. Adviser: Phillips, N. Christopher en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph.D., 2008; Mathematics Cuntz subequivalence Stable rank one Tracial Rokhlin property Finite group actions Crossed product C*algebras Crossed product C*algebras by finite group actions with a generalized tracial Rokhlin property Thesis

Kronholm, William C., 1980 (University of Oregon, June , 2008)[more][less]Kronholm, William C., 1980 20090113T00:36:10Z 20090113T00:36:10Z 200806 http://hdl.handle.net/1794/8284 x, 72 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. The theory of equivariant homology and cohomology was first created by Bredon in his 1967 paper and has since been developed and generalized by May, Lewis, Costenoble, and a host of others. However, there has been a notable lack of computations done. In this paper, a version of the Serre spectral sequence of a fibration is developed for RO ( G )graded equivariant cohomology of G spaces for finite groups G . This spectral sequence is then used to compute cohomology of projective bundles and certain loop spaces. In addition, the cohomology of Rep( G )complexes, with appropriate coefficients, is shown to always be free. As an application, the cohomology of real projective spaces and some Grassmann manifolds are computed, with an eye towards developing a theory of equivariant characteristic classes. Adviser: Daniel Dugger en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2008; Algebraic topology Equivariant topology Spectral sequence Serre spectral sequence Mathematics The RO(G)graded Serre Spectral Sequence Thesis

Wilson, James B., 1980 (University of Oregon, June , 2008)[more][less]Wilson, James B., 1980 20090115T00:44:03Z 20090115T00:44:03Z 200806 http://hdl.handle.net/1794/8302 viii, 125 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. Finite p groups are studied using bilinear methods which lead to using nonassociative rings. There are three main results, two which apply only to p groups and the third which applies to all groups. First, for finite p groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P : the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of their centers. Unlike for direct product decompositions, Aut P is not always transitive on the set of fully refined central decompositions, and the number of orbits can in fact be any positive integer. The proofs use the standard semisimple and radical structure of Jordan algebras. These algebras also produce useful criteria for a p group to be centrally indecomposable. In the second result, an algorithm is given to find a fully refined central decomposition of a finite p group of class 2. The number of algebraic operations used by the algorithm is bounded by a polynomial in the log of the size of the group. The algorithm uses a Las Vegas probabilistic algorithm to compute the structure of a finite ring and the Las Vegas MeatAxe is also used. However, when p is small, the probabilistic methods can be replaced by deterministic polynomialtime algorithms. The final result is a polynomial time algorithm which, given a group of permutations, matrices, or a polycyclic presentation; returns a Remak decomposition of the group: a fully refined direct decomposition. The method uses group varieties to reduce to the case of p groups of class 2. Bilinear and ring theory methods are employed there to complete the process. Adviser: William M. Kantor en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2008; Computer science Mathematics pgroups Jordan algebras Group decompositions Central products Direct products Algorithms Group decompositions, Jordan algebras, and algorithms for pgroups Thesis

Jordan, Alex, 1979 (University of Oregon, June , 2008)[more][less]Jordan, Alex, 1979 20090113T00:17:10Z 20090113T00:17:10Z 200806 http://hdl.handle.net/1794/8283 vii, 41 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We generalize a theorem of Zhu relating the trace of certain vertex algebra representations and modular invariants to the arena of vertex super algebras. The theorem explains why the space of simple characters for the NeveuSchwarz minimal models NS( p, q ) is modular invariant. It also expresses negative products in terms of positive products, which are easier to compute. As a consequence of the main theorem, the subleading coefficient of the singular vectors of NS( p, q ) is determined for p and q odd. An interesting family of q series identities is established. These consequences established here generalize results of Milas in this field. Adviser: Arkady Vaintrob en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2008; Vertex algebras NeveuSchwarz model Super algebras Zhu's theorem Mathematics A Super Version of Zhu's Theorem Thesis

Vanderpool, Ruth, 1980 (University of Oregon, June , 2009)[more][less]Vanderpool, Ruth, 1980 20100305T01:33:36Z 20100305T01:33:36Z 200906 http://hdl.handle.net/1794/10244 vii, 54 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We investigate the existence of a stable homotopy category (SHC) associated to the category of p complete abelian groups [Special characters omitted]. First we examine [Special characters omitted] and prove [Special characters omitted] satisfies all but one of the axioms of an abelian category. The connections between an SHC and homology functors are then exploited to draw conclusions about possible SHC structures for [Special characters omitted]. In particular, let [Special characters omitted] denote the category whose objects are chain complexes of [Special characters omitted] and morphisms are chain homotopy classes of maps. We show that any homology functor from any subcategory of [Special characters omitted] containing the padic integers and satisfying the axioms of an SHC will not agree with standard homology on free, finitely generated (as modules over the p adic integers) chain complexes. Explicit examples of common functors are included to highlight troubles that arrise when working with [Special characters omitted]. We make some first attempts at classifying small objects in [Special characters omitted]. Committee in charge: Hal Sadofsky, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Daniel Dugger, Member, Mathematics; Sergey Yuzvinsky, Member, Mathematics; Elizabeth Reis, Outside Member, Womens and Gender Studies en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Stable homotopy Pcomplete abelian groups Homology functor Abelian Mathematics Nonexistence of a stable homotopy category for pcomplete abelian groups Thesis

Wade, Jeremy, 1981 (University of Oregon, June , 2009)[more][less]Wade, Jeremy, 1981 20100310T00:12:17Z 20100310T00:12:17Z 200906 http://hdl.handle.net/1794/10245 vii, 99 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We investigate Cesàro summability of the Fourier orthogonal expansion of functions on B d × I m , where B d is the closed unit ball in [Special characters omitted] and I m is the m fold Cartesian product of the interval [1, 1], in terms of orthogonal polynomials with respect to the weight functions (1  z ) α (1 + z ) β (1  x 2 ) λ1/2 , with z ∈ I m and x ∈ B d . In addition, we study a discretized Fourier orthogonal expansion on the cylinder B 2 × [1, 1], which uses a finite number of Radon projections. The Lebesgue constant of this operator is obtained, and the proof utilizes generating functions for associated orthogonal series. Committee in charge: Yuan Xu, Chairperson, Mathematics; Huaxin Lin, Member, Mathematics Jonathan Brundan, Member, Mathematics; Marcin Bownik, Member, Mathematics; Jun Li, Outside Member, Computer & Information Science en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Fourier orthogonal expansions Radon projections Cylindrical functions Cartesian products Mathematics Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving radon projections for functions on the cylinder Thesis

Walsh, Mark, 1976 (University of Oregon, June , 2009)[more][less]Walsh, Mark, 1976 20100312T01:15:37Z 20100312T01:15:37Z 200906 http://hdl.handle.net/1794/10265 x, 164 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We study the topology of the space of metrics of positive scalar curvature on a compact manifold. The main tool we use for constructing such metrics is the surgery technique of Gromov and Lawson. We extend this technique to construct families of positive scalar curvature cobordisms and concordances which are parametrised by Morse functions and later, by generalised Morse functions. We then use these results to study concordances of positive scalar curvature metrics on simply connected manifolds of dimension at least five. In particular, we describe a subspace of the space of positive scalar curvature concordances, parametrised by generalised Morse functions. We call such concordances GromovLawson concordances. One of the main results is that positive scalar curvature metrics which are GromovLawson concordant are in fact isotopic. This work relies heavily on contemporary Riemannian geometry as well as on differential topology, in particular pseudoisotopy theory. We make substantial use of the work of Eliashberg and Mishachev on wrinkled maps and of results by Hatcher and Igusa on the space of generalised Morse functions. Committee in charge: Boris Botvinnik, Chairperson, Mathematics; James Isenberg, Member, Mathematics; Hal Sadofsky, Member, Mathematics; Christopher Phillips, Member, Mathematics; Michael Kellman, Outside Member, Chemistry en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Scalar curvature Morse functions Concordances Wrinkled maps Mathematics Metrics of positive scalar curvature and generalised Morse functions Thesis

Phan, Christopher Lee, 1980 (University of Oregon, June , 2009)[more][less]Phan, Christopher Lee, 1980 20100515T00:13:21Z 20100515T00:13:21Z 200906 http://hdl.handle.net/1794/10367 xi, 95 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We investigate some homological properties of graded algebras. If A is an R algebra, then E (A) := Ext A ( R, R ) is an Ralgebra under the cup product and is called the Yoneda algebra. (In most cases, we assume R is a field.) A wellknown and widelystudied condition on E(A) is the Koszul property. We study a class of deformations of Koszul algebras that arises from the study of equivariant cohomology and algebraic groups and show that under certain circumstances these deformations are PoincaréBirkhoffWitt deformations. Some of our results involve the [Special characters omitted] property, recently introduced by Cassidy and Shelton, which is a generalization of the Koszul property. While a Koszul algebra must be quadratic, a [Special characters omitted] algebra may have its ideal of relations generated in different degrees. We study the structure of the Yoneda algebra corresponding to a monomial [Special characters omitted.] algebra and provide an example of a monomial [Special characters omitted] algebra whose Yoneda algebra is not also [Special characters omitted]. This example illustrates the difficulty of finding a [Special characters omitted] analogue of the classical theory of Koszul duality. It is wellknown that PoincaréBirkhoffWitt algebras are Koszul. We find a [Special characters omitted] analogue of this theory. If V is a finitedimensional vector space with an ordered basis, and A := [Special characters omitted] (V)/I is a connectedgraded algebra, we can place a filtration F on A as well as E (A). We show there is a bigraded algebra embedding Λ: gr F E (A) [Special characters omitted] E (gr F A ). If I has a Gröbner basis meeting certain conditions and gr F A is [Special characters omitted], then Λ can be used to show that A is also [Special characters omitted]. This dissertation contains both previously published and coauthored materials. Committee in charge: Brad Shelton, Chairperson, Mathematics; Victor Ostrik, Member, Mathematics; Christopher Phillips, Member, Mathematics; Sergey Yuzvinsky, Member, Mathematics; Van Kolpin, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Koszul properties Noncommutative graded algebras Yoneda algebra Grobner bases Homological algebra Mathematics Algebra, Homological Algebra, Yoneda Koszul algebras Koszul and generalized Koszul properties for noncommutative graded algebras Thesis

Brown, Jonathan, 1975 (University of Oregon, June , 2009)[more][less]Brown, Jonathan, 1975 20100219T01:28:27Z 20100219T01:28:27Z 200906 http://hdl.handle.net/1794/10201 ix, 114 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. In this work we prove that the finite W algebras associated to nilpotent elements in the symplectic or orthogonal Lie algebras whose Jordan blocks are all the same size are quotients of twisted Yangians. We use this to classify the finite dimensional irreducible representations of these finite W algebras. Committee in charge: Jonathan Brundan, CoChairperson, Mathematics; Victor Ostrik, CoChairperson, Mathematics; Arkady Berenstein, Member, Mathematics; Hal Sadofsky, Member, Mathematics; Christopher Wilson, Outside Member, Computer & Information Science en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Finite Walgebras Nilpotent Symplectic Quantum algebra Mathematics Walgebras Finite Walgebras of classical type Thesis

Collins, John, 1981 (University of Oregon, June , 2009)[more][less]Collins, John, 1981 20100225T23:49:36Z 20100225T23:49:36Z 200906 http://hdl.handle.net/1794/10218 vi, 85 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We define and study a gluing procedure for Bridgeland stability conditions in the situation where a triangulated category has a semiorthogonal decomposition. As one application, we construct an open, contractible subset U in the stability manifold of the derived category [Special characters omitted.] of [Special characters omitted.] equivariant coherent sheaves on a smooth curve X , associated with a degree 2 map X [arrow right] Y , where Y is another curve. In the case where X is an elliptic curve we construct an open, connected subset in the stability manifold using exceptional collections containing the subset U . We also give a new proof of the constructibility of exceptional collections on [Special characters omitted.] . This dissertation contains previously unpublished coauthored material. Committee in charge: Alexander Polishchuk, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Victor Ostrik, Member, Mathematics; Brad Shelton, Member, Mathematics; Michael Kellman, Outside Member, Chemistry en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Stability conditions Equivariant sheaves Derived categories Elliptic curve Mathematics Gluing Bridgeland's stability conditions and Z2equivariant sheaves on curves Thesis

Leeman, Aaron, 1974 (University of Oregon, June , 2009)[more][less]Leeman, Aaron, 1974 20100301T23:23:03Z 20100301T23:23:03Z 200906 http://hdl.handle.net/1794/10227 vii, 34 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We study the Bousfield localization functors known as [Special characters omitted], as described in [MahS]. In particular we would like to understand how they interact with suspension and how they stabilize. We prove that suitably connected [Special characters omitted]acyclic spaces have suspensions which are built out of a particular type n space, which is an unstable analog of the fact that [Special characters omitted]acyclic spectra are built out of a particular type n spectrum. This theorem follows DrorFarjoun's proof in the case n = 1 with suitable alterations. We also show that [Special characters omitted] applied to a space stabilizes in a suitable way to [Special characters omitted] applied to the corresponding suspension spectrum. Committee in charge: Hal Sadofsky, Chairperson, Mathematics; Arkady Berenstein, Member, Mathematics; Daniel Dugger, Member, Mathematics; Dev Sinha, Member, Mathematics; William Rossi, Outside Member, English en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; Chromatic functors Bousfield functors Acyclic spaces Suspension spectrum Algebraic topology Mathematics Stabilization of chromatic functors Thesis

Comes, Jonathan, 1981 (University of Oregon, June , 2010)[more][less]Comes, Jonathan, 1981 20101203T20:42:43Z 20101203T20:42:43Z 201006 http://hdl.handle.net/1794/10867 x, 81 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We give an exposition of Deligne's tensor category Rep(St) where t is not necessarily an integer. Thereafter, we give a complete description of the blocks in Rep(St) for arbitrary t. Finally, we use our result on blocks to decompose tensor products and classify tensor ideals in Rep(St). Committee in charge: Victor Ostrik, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Jonathan Brundan, Member, Mathematics; Alexander Kleshchev, Member, Mathematics; Michael Kellman, Outside Member, Chemistry en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Tensor category Symmetric groups Decomposed blocks Tensor products Tensor ideals Mathematics Theoretical mathematics Blocks in Deligne's category Rep(St) Thesis

Crossed product C*algebras of certain nonsimple C*algebras and the tracial quasiRokhlin propertyBuck, Julian Michael, 1982 (University of Oregon, June , 2010)[more][less]Buck, Julian Michael, 1982 20101130T23:48:55Z 20101130T23:48:55Z 201006 http://hdl.handle.net/1794/10849 viii, 113 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation consists of four principal parts. In the first, we introduce the tracial quasiRokhlin property for an automorphism α of a C *algebra A (which is not assumed to be simple or to contain any projections). We then prove that under suitable assumptions on the algebra A , the associated crossed product C *algebra C *([Special characters omitted.] , A , α) is simple, and the restriction map between the tracial states of C *([Special characters omitted.] , A , α) and the αinvariant tracial states on A is bijective. In the second part, we introduce a comparison property for minimal dynamical systems (the dynamic comparison property) and demonstrate sufficient conditions on the dynamical system which ensure that it holds. The third part ties these concepts together by demonstrating that given a minimal dynamical system ( X, h ) and a suitable simple C *algebra A , a large class of automorphisms β of the algebra C ( X, A ) have the tracial quasiRokhlin property, with the dynamic comparison property playing a key role. Finally, we study the structure of the crossed product C *algebra B = C *([Special characters omitted.] , C ( X , A ), β) by introducing a subalgebra B { y } of B , which is shown to be large in a sense that allows properties B { y } of to pass to B . Several conjectures about the deeper structural properties of B { y } and B are stated and discussed. Committee in charge: Christopher Phillips, Chairperson, Mathematics; Daniel Dugger, Member, Mathematics; Huaxin Lin, Member, Mathematics; Marcin Bownik, Member, Mathematics; Van Kolpin, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Dynamical systems Minimal homeomorphisms Crossed product algebras Tracial property Automorphisms C*algebras QuasiRokhlin property Mathematics Theoretical mathematics Crossed product C*algebras of certain nonsimple C*algebras and the tracial quasiRokhlin property Thesis

Sun, Wei, 1979 (University of Oregon, June , 2010)[more][less]Sun, Wei, 1979 20101222T01:32:21Z 20101222T01:32:21Z 201006 http://hdl.handle.net/1794/10912 vii, 124 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation is a study of the relationship between minimal dynamical systems on the product of the Cantor set ( X ) and torus ([Special characters omitted]) and their corresponding crossed product C *algebras. For the case when the cocyles are rotations, we studied the structure of the crossed product C *algebra A by looking at a large subalgebra A x . It is proved that, as long as the cocyles are rotations, the tracial rank of the crossed product C *algebra is always no more than one, which then indicates that it falls into the category of classifiable C *algebras. In order to determine whether the corresponding crossed product C *algebras of two such minimal dynamical systems are isomorphic or not, we just need to look at the Elliott invariants of these C *algebras. If a certain rigidity condition is satisfied, it is shown that the crossed product C *algebra has tracial rank zero. Under this assumption, it is proved that for two such dynamical systems, if A and B are the corresponding crossed product C *algebras, and we have an isomorphism between K i ( A ) and K i ( B ) which maps K i (C(X ×[Special characters omitted])) to K i (C( X ×[Special characters omitted])), then these two dynamical systems are approximately K conjugate. The proof also indicates that C *strongly flip conjugacy implies approximate K conjugacy in this case. We also studied the case when the cocyles are Furstenberg transformations, and some results on weakly approximate conjugacy and the K theory of corresponding crossed product C *algebras are obtained. Committee in charge: Huaxin Lin, Chairperson, Mathematics Daniel Dugger, Member, Mathematics; Christopher Phillips, Member, Mathematics; Arkady Vaintrob, Member, Mathematics; LiShan Chou, Outside Member, Human Physiology en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Tracial rank Approximate conjugacy C*algebras Minimal dynamical systems Cantor set Torus Mathematics Theoretical mathematics Crossed product C*algebras of minimal dynamical systems on the product of the Cantor set and the torus Thesis

Nash, David A., 1982 (University of Oregon, June , 2010)[more][less]Nash, David A., 1982 20101203T22:54:08Z 20101203T22:54:08Z 201006 http://hdl.handle.net/1794/10871 xii, 76 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. We study the graded representation theory of the IwahoriHecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to calculate the graded decomposition numbers for Hd . The algorithm arrived at is the LascouxLeclercThibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory. We then use the algorithm to compute several examples and to obtain a closed form for the graded decomposition numbers in the case of twocolumn partitions. In this case, we also precisely describe the 'reduction modulo p' process, which relates the graded irreducible representations of Hd over [Special characters omitted.] at a p th root of unity to those of the group algebra of the symmetric group over a field of characteristic p. Committee in charge: Alexander Kleshchev, Chairperson, Mathematics; Jonathan Brundan, Member, Mathematics; Boris Botvinnik, Member, Mathematics; Victor Ostrik, Member, Mathematics; William Harbaugh, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Symmetric groups Specht modules Irreducible representation Graded representation Hecke algebras Mathematics Theoretical mathematics Graded representation theory of Hecke algebras Thesis

Liang, Hutian (University of Oregon, June , 2010)[more][less]Liang, Hutian 20110114T18:44:40Z 20110114T18:44:40Z 201006 http://hdl.handle.net/1794/10938 viii, 133 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. In this dissertation, we will study the crossed product C*algebras obtained from free and minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. We first define stable recursive subhomogeneous algebras (SRSHAs), which differ from recursive subhomogeneous algebras introduced by N. C. Phillips in that the irreducible representations of SRSHAs are infinite dimensional instead of finite dimensional. We show that simple inductive limits of SRSHAs with no dimension growth in which the connecting maps are injective and nonvanishing have topological stable rank one. We then construct C*subalgebras of the crossed product that are analogous to the C*subalgebras in the studies of free minimal [Special characters omitted.] actions on compact metric spaces with finite covering dimension. Finally, we prove that these C*algebras are in fact simple inductive limits of SRSHAs in which the connecting maps are injective and nonvanishing. Thus these C*subalgebras have topological stable rank one. Committee in charge: Christopher Phillips, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Huaxin Lin, Member, Mathematics; Yuan Xu, Member, Mathematics; Dietrich Belitz, Outside Member, Physics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Free minimal action Metric space Subhomogeneous algebras Infinite dimensions Topological stability Mathematics Theoretical mathematics The crossed product of C(X) by a free minimal action of R Thesis

Heuser, Aaron, 1978 (University of Oregon, June , 2010)[more][less]Heuser, Aaron, 1978 20101203T22:34:13Z 20101203T22:34:13Z 201006 http://hdl.handle.net/1794/10870 x, 110 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. This dissertation examines the existence of the selfintersection local time for a superprocess over a stochastic flow in dimensions d ≤ 3, which through constructive methods, gives a Tanaka like representation. The superprocess over a stochastic flow is a superprocess with dependent spatial motion, and thus Dynkin's proof of existence, which requires multiplicity of the logLaplace functional, no longer applies. Skoulakis and Adler's method of calculating moments is extended to higher moments, from which existence follows. Committee in charge: Hao Wang, CoChairperson, Mathematics; David Levin, CoChairperson, Mathematics; Christopher Sinclair, Member, Mathematics; Huaxin Lin, Member, Mathematics; Van Kolpin, Outside Member, Economics en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Selfintersection Tanaka representation Superprocess Stochastic flow Mathematics Theoretical mathematics Generalized selfintersection local time for a superprocess over a stochastic flow Thesis
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