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  1. Minimal Measures for Lagrangian Systems

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    Description: In this thesis we study minimal measures for Lagrangian systems on compact manifolds. This thesis consists of three parts which are closely related. The first part is Chapter 3 and Chapter 4. In Chapter 3 and 4, we consider geodesic flows on compact surfaces with higher genus. We show that...
    Keyword: Minimal Measures
    Subject: Mathematics
    Creator: Fang Wang
    Owner: Scholarly Digital Publishing
    Date Uploaded: 10/02/2018
    Date Modified: 10/02/2018
    Date Created: 2008-08-22
    Rights: In Copyright
    Resource Type: Dissertation
  2. Resurgent analysis of the Witten Laplacian in One Dimension

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    Description: The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Alexander Getmaneko
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/14/2018
    Date Modified: 09/14/2018
    Date Created: 2008-08-11
    Rights: In Copyright
    Resource Type: Dissertation
  3. Index Theorems for Noncommutative Two-Tori and Hochschild Cohomology for Quantum Special Linear Groups

    Work
    Description: This paper covers three main topics. The first is addressing the question of interpolating between disparate index theorems on noncommutative two-tori. The second is to compute Hochschild cohomology for quantum special linear and special unitary groups. The third is producing an orthonormal basis for the vector space of matrix corepresentations...
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Gary Clark Alexander
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/10/2018
    Date Modified: 09/10/2018
    Date Created: 2008-05-09
    Rights: In Copyright
    Resource Type: Dissertation
  4. Topological Splittings of Spectra Related to tmf

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    Description: The homotopy groups of bo^tmf are shown to be isomorphic to the homotopy groups of a wedge of suspensions of spectra related to integral Brown-Gitler spectra. We will then restate Mahowald's proof of the topological splitting of bo^bo and subsequently apply similar techniques to construct a map that realizing the...
    Keyword: integral Brown Gitler spectra, tmf, and Tate spectrum
    Subject: Mathematics
    Creator: Scott MIchael Bailey
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/07/2018
    Date Modified: 09/07/2018
    Date Created: 2008-05-09
    Rights: In Copyright
    Resource Type: Dissertation
  5. Group Actions via Interval Exchange Transformations

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    Description: This dissertation addresses the structure of the group of interval exchange transformations. The two primary topics considered are: a) the classification of interval exchange actions for certain groups; and b) properties of the interval exchange group which are reflected in the dynamics of interval exchange maps. In Chapter 3 a...
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Christopher Novak
    Owner: Scholarly Digital Publishing
    Date Uploaded: 09/06/2018
    Date Modified: 09/06/2018
    Date Created: 2008-05-06
    Rights: In Copyright
    Resource Type: Dissertation
  6. Representing Cohomology Theories in the Triangulated Category of Motives

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    Description: Let X be a quasi-projective complex variety. It follows from the work of Voevodsky that the motivic cohomology of X, denoted as $H^{p,q}(X)$ where q and p are integers with q nonnegative, can be represented in the triangulated category of motives over the field of complex numbers, denoted as $DM^{eff,-}_{Nis}$....
    Keyword: Mathematics
    Subject: Mathematics
    Creator: Chenghao Chu
    Owner: Scholarly Digital Publishing
    Date Uploaded: 08/31/2018
    Date Modified: 08/31/2018
    Date Created: 2008-05-02
    Rights: In Copyright
    Resource Type: Dissertation
  7. Geometric Langlands Duality and Forms of Reductive Groups

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    Description: The Satake category is the category of perverse sheaves on the affine Grassmannian of a complex reductive group G. The global cohomology functor induces a tensor equivalence between the Satake category and the category of finite-dimensional representations of the split form of the Langlands dual group of G. We give...
    Keyword: representation theory, Geometric Langlands program, forms of reductive groups, and Satake isomorphism
    Subject: Mathematics
    Creator: Vivek Dhand
    Owner: Scholarly Digital Publishing
    Date Uploaded: 08/29/2018
    Date Modified: 08/29/2018
    Date Created: 2007-12-07
    Rights: In Copyright
    Resource Type: Dissertation
  8. Homotopy Gerstenhaber Structure on Deformation Complex of a Morphism

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    Description: Homotopy Gerstenhaber structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is extension of a B-infinity algebra by an associative algebra. Actions of B-infinity algebras on associative and B-infinity algebras are analyzed, extensions of B-infinity algebras by associative...
    Keyword: Deformations and associative algebras
    Subject: Mathematics
    Creator: Dennis Borisov
    Owner: Scholarly Digital Publishing
    Date Uploaded: 06/27/2018
    Date Modified: 06/27/2018
    Date Created: 2007-05-07
    Rights: In Copyright
    Resource Type: Dissertation
  9. Results on Polynomial Ergodic Averages

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    Description: We prove the L<SUP>2</SUP>-convergence of polynomial ergodic averages of multiple commuting transformations for totally ergodic systems. We show that for each set of polynomials, each average is controlled by a particular characteristic factor introduced by Host and Kra, which is an inverse limit of nilsystems. We then investigate for which...
    Keyword: ergodic theory and dynamical systems
    Subject: Mathematics
    Creator: Michael Charles Reed Johnson
    Owner: Scholarly Digital Publishing
    Date Uploaded: 06/26/2018
    Date Modified: 06/26/2018
    Date Created: 2007-05-11
    Rights: In Copyright
    Resource Type: Dissertation
  10. A-branes and Mirror Symmetry

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    Description: This thesis is devoted to the study of A-branes on symplectic tori and to the Mirror Symmetry conjecture. Using a method called Seidel's mirror map, we are able to reconstruct the homogeneous coordinate ring of a complex abelian variety using Lagrangian intersection theory on the mirror symplectic torus. Moreover, we...
    Keyword: Mirror Symmertry
    Subject: Mathematics
    Creator: Marco Aldi
    Owner: Scholarly Digital Publishing
    Date Uploaded: 05/30/2018
    Date Modified: 05/30/2018
    Date Created: 2007-05-11
    Rights: In Copyright
    Resource Type: Dissertation