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 Description:
 In this work we explore a connection between some high dimensional asymptotic problems and random matrix theory. In the first part, we establish a link between the Wishart ensemble and random critical points of holomorphic sections over complex projective space and use this to establish asymptotics on the average number...
 Keyword:
 Complex Geometry, Differential Equations, Probability Theory, and High Dimensional
 Subject:
 Mathematics
 Creator:
 Xavier Eduardo Garcia
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 11/19/2019
 Date Modified:
 11/19/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 Description:
 The moduli stack of bundles on a smooth complete curve over a field, is an immensely rich geometric object and is of central importance to the Geometric Langlands program. This thesis represents a contribution towards a motivic, in the sense of Voevodsky and MorelVoevodsky, understanding of this stack. Following the...
 Keyword:
 Geometric Langlands, Ran space, Motives, Space of rational maps, and Motivic homotopy theory
 Subject:
 Mathematics
 Creator:
 Elden Elmanto
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 11/19/2019
 Date Modified:
 11/19/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 Description:
 This thesis is naturally split into two parts. In the first part, we develop the theory of multi linear algebra for Tate objects over exact categories endowed with an exact tensor product. We study all possible choices of tensor product and we give a geometric interpretation of the results. In...
 Keyword:
 Tate objects, determinant, tensor product, and central extension
 Subject:
 Mathematics
 Creator:
 Aron Alexandre Heleodoro
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 04/15/2019
 Date Modified:
 04/15/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 Description:
 In this thesis, we study arithmetic phenomena exhibited by polynomial dynamical systems on the projective line. Specifically, given a number field $K$, we are interested in the arithmetic of orbits of points $\alpha\in K$ under polynomials $\phi\in K[z]$. Given such a polynomial $\phi$ of degree $d\ge2$, we prove a lower...
 Keyword:
 Mathematics
 Subject:
 Mathematics
 Creator:
 Nicole Romain Looper
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 04/09/2019
 Date Modified:
 04/09/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 Description:
 In this paper, we show almostGelfand property of connected symmetric pairs (G, H) over finite fields of large characteristics by showing almostsigmainvariant property of double coset H\G/H where sigma is the associated antiinvolution combining with epsilonversion of Gelfand's trick
 Keyword:
 representation theory, symmetric pair, and Gelfand pair
 Subject:
 Mathematics
 Creator:
 Nan Shi
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 04/01/2019
 Date Modified:
 04/01/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 Description:
 The holomorphic sigmamodel is a field theory that exists in any complex dimension that describes the moduli space of holomorphic maps from one complex manifold to another. We introduce the general notion of a holomorphic field theory, which is one that is sensitive to the underlying complex structure of the...
 Keyword:
 Renormalization, BatalinVilkovisky, Quantum field theory, and Factorization algebras
 Subject:
 Mathematics
 Creator:
 Brian R Williams
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 04/01/2019
 Date Modified:
 04/01/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 Description:
 homotopy theory studies a parametrization of stable homotopy theory in terms of algebraic objects called formal groups. Transchromatic homotopy theory is specifically concerned with the behavior of spaces and cohomology theories as these formal groups change in height. We pursue a central transchromatic object, the K(n − 1) localization of...
 Keyword:
 structured ring spectra, Morava Etheory, Bousfield localization, chromatic homotopy theory, formal groups, and algebraic topology
 Subject:
 Mathematics
 Creator:
 Paul Behrents VanKoughnett
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 04/01/2019
 Date Modified:
 04/01/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 Description:
 We prove a uniform scalar curvature bound for solutions of the conical KahlerRicci flow when the twisted canonical bundle is semiample and the cone divisor is obtained from the associated IitakaKodaira fibration. In the course of the proof we establish uniform bounds for the potential of the metric and its...
 Keyword:
 Conical Kahler Metrics, Geometric Flows, and KahlerRicci Flow
 Subject:
 Mathematics
 Creator:
 Gregory Edwards
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 03/07/2019
 Date Modified:
 03/07/2019
 Date Created:
 20180101
 Resource Type:
 Dissertation

 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:
 20080822
 Resource Type:
 Dissertation

 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 lowlying 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:
 20080811
 Resource Type:
 Dissertation

 Description:
 This paper covers three main topics. The first is addressing the question of interpolating between disparate index theorems on noncommutative twotori. 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:
 20080509
 Resource Type:
 Dissertation

 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 BrownGitler 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:
 tmf, Tate spectrum, and integral Brown Gitler spectra
 Subject:
 Mathematics
 Creator:
 Scott MIchael Bailey
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 09/07/2018
 Date Modified:
 09/07/2018
 Date Created:
 20080509
 Resource Type:
 Dissertation

 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:
 20080506
 Resource Type:
 Dissertation

 Description:
 Let X be a quasiprojective 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:
 20080502
 Resource Type:
 Dissertation

 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 finitedimensional representations of the split form of the Langlands dual group of G. We give...
 Keyword:
 Satake isomorphism, forms of reductive groups, representation theory, and Geometric Langlands program
 Subject:
 Mathematics
 Creator:
 Vivek Dhand
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 08/29/2018
 Date Modified:
 08/29/2018
 Date Created:
 20071207
 Resource Type:
 Dissertation

 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 Binfinity algebra by an associative algebra. Actions of Binfinity algebras on associative and Binfinity algebras are analyzed, extensions of Binfinity algebras by associative...
 Keyword:
 associative algebras and Deformations
 Subject:
 Mathematics
 Creator:
 Dennis Borisov
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 06/27/2018
 Date Modified:
 06/27/2018
 Date Created:
 20070507
 Resource Type:
 Dissertation

 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:
 dynamical systems and ergodic theory
 Subject:
 Mathematics
 Creator:
 Michael Charles Reed Johnson
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 06/26/2018
 Date Modified:
 06/26/2018
 Date Created:
 20070511
 Resource Type:
 Dissertation

 Description:
 This thesis is devoted to the study of Abranes 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:
 20070511
 Resource Type:
 Dissertation

 Description:
 We compute Lawson homology groups and semitopological Ktheory for certain "degenerate" varieties. "Degenerate" varieties are those smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected varieties are examples of such varieties. Our main method of study makes use of a technique of Bloch and...
 Keyword:
 Lawson homology, algebraic cycles, and semitopological Ktheory
 Subject:
 Mathematics
 Creator:
 Mircea Alexandru Voineagu
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 05/25/2018
 Date Modified:
 05/25/2018
 Date Created:
 20070425
 Resource Type:
 Dissertation

 Description:
 In this thesis, we advocate for the use of slice spheres, a common generalization of representation spheres and induced spheres, in parameterized homotopy theory. First, we give an algebraic characterization of the layers of the HillHopkinsRavenel slice filtration. Next, we explore the homology of parameterized symmetric powers from this point...
 Keyword:
 chromatic, homotopy theory, and equivariant
 Subject:
 Mathematics
 Creator:
 Dylan Wilson
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 03/30/2018
 Date Modified:
 03/30/2018
 Date Created:
 20170101
 Resource Type:
 Dissertation

 Description:
 This dissertation contains three results related to modular forms and Galois representations of low weight. In chapter 1, we prove that the Galois pseudorepresentation valued in a Hecke algebra which acts faithfully on a space of weight one Katz modular forms of level prime to p is unramified at p....
 Keyword:
 Crystallinity and Mathematics
 Subject:
 Mathematics
 Creator:
 Joel Specter
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 03/30/2018
 Date Modified:
 03/30/2018
 Date Created:
 20170101
 Resource Type:
 Dissertation

 Description:
 Knot invariants can be defined using Legendrian isotopy invariants of the knot conormal. There are two types of invariants raised in this way: one is the knot contact differential graded algebra together with augmentations associated to this dga, and the other one is the category of simple sheaves microsupported along...
 Keyword:
 contact topology, microlocal sheaf theory, knot invariant, symplectic topology, and knot contact homology
 Subject:
 Mathematics
 Creator:
 Honghao Gao
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 03/29/2018
 Date Modified:
 03/29/2018
 Date Created:
 20170101
 Resource Type:
 Dissertation

 Description:
 This work is concerned with the LaudauGinzburg $A$model, or the FukayaSeidel category, associated with a Laurent polynomial $f: (\C^*)^n \ o \C$. We use constructible sheaves on a real $n$dimensional torus to describe the Lagrangian thimbles associated to $f$. Then we discuss the application to Homological Mirror Symmetry for smooth...
 Keyword:
 Tropical Geometry, Laurent Polynomial, Constructible Sheaf, and Lagrangian Thimble
 Subject:
 Mathematics
 Creator:
 Peng Zhou
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 03/27/2018
 Date Modified:
 03/27/2018
 Date Created:
 20170101
 Resource Type:
 Dissertation

 Description:
 We define multiindexed Deligne extensions and multiindexed logvariations of Hodge structures in the category of (filtered) logarithmic Dmodules, via the idea of Bernstein– Sato polynomials and Kashiwara–Malgrange filtrations, generalizing the Deligne canonical extensions of flat vector bundles. We also obtain many comparison results with perverse sheaves via the logarithmic de...
 Keyword:
 Dmodules, Algebraic Geometry, Birational Geometry, and Hodge theory
 Subject:
 Mathematics
 Creator:
 Lei Wu
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 03/26/2018
 Date Modified:
 03/26/2018
 Date Created:
 20170101
 Resource Type:
 Dissertation

 Description:
 Algebras and their bimodules form a 2category in which 2morphisms are certain zeroth Hochschild cohomology groups. When we derive this structure (i.e., use Hochschild cochains instead of HH^0 for 2morphisms), we find that algebras form a category in dg cocategories. The HochschildKostantRosenberg theorem and noncommutative calculus give a rich algebraic...
 Keyword:
 Mathematics and Algebra
 Subject:
 Mathematics
 Creator:
 Ann Rebecca Wei
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 03/13/2018
 Date Modified:
 03/13/2018
 Date Created:
 20170101
 Resource Type:
 Dissertation

 Description:
 Using EynardOrantin topological recursion, we prove here a result concerning the equivariant GromovWitten invariants for the projective line equipped with the standard action of the 2torus. Our result is that the genus g, n point GromovWitten potential with arbitrary primary insertions may be written as a sum over certain genus...
 Keyword:
 Gromov Witten Theory and Eynard Orantin Recursion
 Subject:
 Mathematics
 Creator:
 Michael John Couch
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 02/13/2018
 Date Modified:
 02/13/2018
 Date Created:
 20160101
 Resource Type:
 Dissertation

 Description:
 We study analytic functions on the open unit padic polydisk centered at the multiplicative identity and prove that such functions only vanish at finitely many ntuples of roots of unity unless they vanish along a translate of the formal multiplicative group. (Note that a root of unity lies on the...
 Keyword:
 ManinMumford and padic
 Subject:
 Mathematics
 Creator:
 Vlad Ioan Serban
 Owner:
 Scholarly Digital Publishing
 Date Uploaded:
 02/13/2018
 Date Modified:
 02/13/2018
 Date Created:
 20160101
 Resource Type:
 Dissertation