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- Description:
- We study analytic functions on the open unit p-adic poly-disk centered at the multiplicative identity and prove that such functions only vanish at finitely many n-tuples 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:
- Manin-Mumford and p-adic
- Subject:
- Mathematics
- Creator:
- Vlad Ioan Serban
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 02/13/2018
- Date Modified:
- 02/13/2018
- Date Created:
- 2016-01-01
- Resource Type:
- Dissertation
-
- Description:
- Using Eynard-Orantin topological recursion, we prove here a result concerning the equivariant Gromov-Witten invariants for the projective line equipped with the standard action of the 2-torus. Our result is that the genus g, n point Gromov-Witten 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:
- 2016-01-01
- Resource Type:
- Dissertation
-
- Description:
- Algebras and their bimodules form a 2-category in which 2-morphisms are certain zero-th Hochschild cohomology groups. When we derive this structure (i.e., use Hochschild cochains instead of HH^0 for 2-morphisms), we find that algebras form a category in dg cocategories. The Hochschild-Kostant-Rosenberg theorem and non-commutative 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:
- 2017-01-01
- Resource Type:
- Dissertation
-
- Description:
- We define multi-indexed Deligne extensions and multi-indexed log-variations of Hodge structures in the category of (filtered) logarithmic D-modules, 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:
- Birational Geometry, Hodge theory, Algebraic Geometry, and D-modules
- Subject:
- Mathematics
- Creator:
- Lei Wu
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 03/26/2018
- Date Modified:
- 03/26/2018
- Date Created:
- 2017-01-01
- Resource Type:
- Dissertation
-
- Description:
- This work is concerned with the Laudau-Ginzburg $A$-model, or the Fukaya-Seidel 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:
- Lagrangian Thimble, Laurent Polynomial, Constructible Sheaf, and Tropical Geometry
- Subject:
- Mathematics
- Creator:
- Peng Zhou
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 03/27/2018
- Date Modified:
- 03/27/2018
- Date Created:
- 2017-01-01
- 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:
- knot invariant, symplectic topology, contact topology, microlocal sheaf theory, 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:
- 2017-01-01
- 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 pseudo-representation 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:
- Mathematics and Crystallinity
- Subject:
- Mathematics
- Creator:
- Joel Specter
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 03/30/2018
- Date Modified:
- 03/30/2018
- Date Created:
- 2017-01-01
- 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 Hill-Hopkins-Ravenel slice filtration. Next, we explore the homology of parameterized symmetric powers from this point...
- Keyword:
- equivariant, chromatic, and homotopy theory
- Subject:
- Mathematics
- Creator:
- Dylan Wilson
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 03/30/2018
- Date Modified:
- 03/30/2018
- Date Created:
- 2017-01-01
- Resource Type:
- Dissertation
-
- Description:
- We compute Lawson homology groups and semi-topological K-theory 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:
- algebraic cycles, semi-topological K-theory, and Lawson homology
- Subject:
- Mathematics
- Creator:
- Mircea Alexandru Voineagu
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 05/25/2018
- Date Modified:
- 05/25/2018
- Date Created:
- 2007-04-25
- Resource Type:
- Dissertation
-
- 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
- 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:
- 2007-05-11
- 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 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:
- 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:
- 2007-05-07
- 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 finite-dimensional representations of the split form of the Langlands dual group of G. We give...
- Keyword:
- Satake isomorphism, Geometric Langlands program, representation theory, and forms of reductive groups
- Subject:
- Mathematics
- Creator:
- Vivek Dhand
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 08/29/2018
- Date Modified:
- 08/29/2018
- Date Created:
- 2007-12-07
- Resource Type:
- Dissertation
-
- 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
- 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:
- 2008-05-06
- 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 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
- Resource Type:
- Dissertation
-
- 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
- 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 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
- 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:
- 2008-08-22
- Resource Type:
- Dissertation
-
- Description:
- In fish, caudally propagating waves of neural activity produce muscle bending moments. These moments, coupled with forces due to the body's elastic properties and forces due to fluid-body interactions, determine the deformation kinematics for swimming. Fully resolved simulations of neurally-activated swimming can be used to decode activation patterns underlying observed...
- Keyword:
- biomechanics, fluid structure interaction, locomotion, neuromechanics, neuromechanical phase lag, and immersed boundary method
- Subject:
- Mathematics
- Creator:
- Namrata Kartik Patel
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 01/09/2019
- Date Modified:
- 01/29/2019
- Date Created:
- 2017-01-01
- Resource Type:
- Dissertation
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