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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
- 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:
- 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:
- 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:
- 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 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:
- 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:
- 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:
- 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:
- 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:
- We prove the Rigidity Conjecture of Goette and Igusa, which states that, after rationalizing, there are no stable exotic smoothings of manifold bundles with closed even dimensional fibers. The key ingredients of the proof are fiberwise Poincaré–Hopf theorems generalizing earlier such results about the Becker–Gottlieb transfer. These theorems show how...
- Keyword:
- Exotic Smooth Structures, K-theory, Torsion, Morse Theory, and Manifolds
- Subject:
- Mathematics and Theoretical mathematics
- Creator:
- Jain, Yajit Kumar
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/28/2021
- Date Created:
- 2021-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:15542 and etdadmin_upload_817174
-
- Description:
- We study plurisubharmonic functions and their applications to K\"ahler geometry. We begin by studying regularity of envelopes of plurisubharmonic functions, particularly when the reference form is degenerate. This is then applied to show regularity of geodesic of K\"ahler metrics on singular varieties, as well as regularity of certain geodesic rays....
- Keyword:
- Kahler Geometry and Plurisubharmonic Functions
- Subject:
- Mathematics
- Creator:
- McCleerey, Nicholas James
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_763826 and http://dissertations.umi.com/northwestern:15252
-
- Description:
- We address the problem of efficient maintenance of the answer to a new type of query: Continuous Maximizing Range-Sum (Co-MaxRS) for moving objects trajectories. The traditional static/spatial MaxRS problem finds a location for placing the centroid of a given (axes-parallel) rectangle $R$ so that the sum of the weights of...
- Keyword:
- Maximizing Range-Sum Query, MaxRS3, Optimal Density Clustering, Bursty Updates, Moving Objects Trajectories, and MaxRS
- Subject:
- Mathematics, Computer engineering, and Computer science
- Creator:
- Mas-ud Hussain, Muhammed
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/12/2020
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:14445 and etdadmin_upload_625938
-
- Description:
- We consider constant scalar curvature K ̈ahler metrics on a smooth minimal model of general type in a neighborhood of the canonical class, which is the perturbation of the canonical class by a fixed K ̈ahler metric. We show that sequences of such metrics converge smoothly on compact subsets away...
- Subject:
- Mathematics
- Creator:
- Liu, Wanxing
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/16/2023
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:16350 and etdadmin_upload_945453
-
- Description:
- In this paper, we study the basic locus in the fiber at $p$ of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus $\widehat{\CM^{ss}}$ is uniformized by a formal scheme $\CN$ which is called Rapoport-Zink space. We show that the irreducible components of the induced...
- Subject:
- Mathematics
- Creator:
- Cho, Sungyoon
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/12/2020
- Date Created:
- 2019-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:14572 and etdadmin_upload_657697
-
- Description:
- We prove the uniqueness of equilibrium states for certain potentials satisfying the Bowen property for two flows related to geodesic flows on surfaces with sufficient hyperbolicity. Our first result is the uniqueness of equilibrium states for Hölder continuous potentials and the geometric potential for products of geodesic flows of rank...
- Keyword:
- conjugate points, hyberbolic dynamics, measure of maximal entropy, geodesic flow, equilibrium state, and thermodynamic formalism
- Subject:
- Mathematics
- Creator:
- McEnroe, Rachel Maxine
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 10/07/2021
- Date Created:
- 2021-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:15743 and etdadmin_upload_844617
-
- Description:
- The Picard group is an important invariant of the $K(n)$-local category. If the prime $p$ is relatively large compared to the height $n$, the Picard group of the $K(n)$-local category is purely algebraic. In \cref{chapter:finitetype}, we describe the necessary and sufficient numerical condition when an element $X$ in the Picard...
- Keyword:
- Chromatic Homotopy Theory and Invertible spectra
- Subject:
- Mathematics
- Creator:
- Li, Guchuan
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/12/2020
- Date Created:
- 2019-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:14617 and etdadmin_upload_661882
-
- Description:
- In this thesis, we discuss classical and recent results around the damped wave equation on compact and noncompact manifolds. We firstly show that on asymptotically cylindrical and conic manifolds, the geometric control condition and the network control condition give exponential and logarithmic decay rates respectively. We then show that a...
- Keyword:
- noncompact manifolds, Carleman estimates, sharp energy decay, and damped waves
- Subject:
- Mathematics
- Creator:
- Wang, Ruoyu P. T.
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 05/31/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_986144 and http://dissertations.umi.com/northwestern:16577
-
- Description:
- We present both semiclassical asymptotics for the wave equation on a stationary Kaluza-Klein spacetime and an index theorem describing the difference of the positive-frequency spectral projectors for two stationary regions in a globally hyperbolic spacetime. The first result involves analyzing the restrictions of the wave trace to isotypic subspaces for...
- Keyword:
- Kaluza-Klein, Spacetime, Quantum, Spectral, Index, and Dirac
- Subject:
- Mathematics
- Creator:
- McCormick, Anthony Ryan
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 05/31/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:16527 and etdadmin_upload_984183
-
- Description:
- The structural aspects of biological systems are tightly paired with their functions. This understanding has been demonstrated over a broad range of length scales, spanning the ultrastructure of a cell to the macroscopic architecture of organs. Connecting structure and function relies on the integration of physical and biological sciences to...
- Keyword:
- Sparse imaging, 3D genome organization, Scanning transmission electron microscopy, Multi-modal chromatin characterization, and Electron tomography
- Subject:
- Mathematics, Applied physics, and Biophysics
- Creator:
- Li, Yue
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/12/2020
- Date Created:
- 2019-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:14813 and etdadmin_upload_685632
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