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-
- 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
-
- Description:
- The BV Laplacian Δ, first introduced by Batalin and Vilkovisky, is a second-order differential operator that appears in the quantum master equation for quantizing gauge theories. The geometric framework for the BV formalism was later recognized by Schwarz as the setting of odd symplectic geometry and Khudaverdian showed that Δ...
- Subject:
- Mathematics and Physics
- Creator:
- Kumar, Nilay
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 10/07/2021
- Date Created:
- 2021-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_845582 and http://dissertations.umi.com/northwestern:15776
-
- Description:
- In this dissertation, we study and prove formulas of Hodge ideals for three types of isolated hypersurface singularities, including quasihomogeneous singularities, Newton non-degenerate singularities and analytically irreducible plane curve singularities. For quasihomogeneous singularities, we provide a formula of Hodge ideals of $D=\alpha Z$ which is a Q-divisor. A direct consequence...
- Keyword:
- isolated singularity, V-filtration, and Hodge ideals
- Subject:
- Mathematics
- Creator:
- Zhang, Mingyi
- 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:15534 and etdadmin_upload_815731
-
- Description:
- In this thesis, we study applications of the theory of perverse sheaves and their enhancements to problems in birational geometry. In the first application, we give positive results towards a conjecture of Batyrev about the nonnegativity of stringy Hodge numbers. In particular, we prove the nonnegativity of $(p,1)$-stringy Hodge numbers...
- Keyword:
- Birational Geomtry, Perverse Sheaves, Hodge Theory, and Hodge Modules
- Subject:
- Mathematics
- Creator:
- Olano, Sebastian
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_763710 and http://dissertations.umi.com/northwestern:15249
-
- Description:
- The variation of entropy in a family of dynamical systems is a natural indication of the bifurcations that the family undergoes. In the context of one-dimensional dynamics, Milnor's monotonicity of entropy conjecture (now a theorem of Bruin and van Strien) asserts that for polynomial interval maps with real critical points...
- Keyword:
- Moduli space of rational maps, Hyperbolic components, Real rational maps, Topological entropy, Quadratic rational maps, and Monotonicity of entropy
- Subject:
- Mathematics
- Creator:
- Filom, Khashayar
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/01/2021
- Date Created:
- 2020-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:15290 and etdadmin_upload_765064
-
- Description:
- This dissertation proves several results for first passage percolation on graphs of polynomial growth.The class of limit shapes for first passage percolation with stationary weights on Cayley graphs of virtually nilpotent groups is characterized. Then strict monotonicity theorems for independent first passage percolation on graphs of polynomial growth and quasi-trees...
- Keyword:
- coarse geometry, first-passage percolation, and Cayley graphs
- Subject:
- Mathematics
- Creator:
- Gorski, Christian Stanley Edward
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 08/23/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:16688 and etdadmin_upload_1009568
-
- Description:
- Even though a number of techniques have been developed for motion generation and perception, few of them focus on the computational efficiency and theoretical guarantees at the same time. Typically, improved guarantees come with increased complexity, making theoretically guaranteed methods challenging use in real-time applications. Thus, existing methods usually have...
- Keyword:
- variational integrator, pose graph optimization, optimization, human pose and shape estimation, and SLAM
- Subject:
- Mathematics and Robotics
- Creator:
- Fan, Taosha
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_879523 and http://dissertations.umi.com/northwestern:15937
-
- Description:
- In this paper we begin the study of the (dual) Steenrod algebra of the motivic Witt cohomology spectrum H_Wℤ by determining the algebra structure of H_Wℤ∗∗H_Wℤ over fields k of characteristic not 2 which are extensions of fields F with K^M_2(F)/2=0. For example, this includes all fields of odd characteristic,...
- Keyword:
- K-Theory, Motivic Homotopy Theory, Witt Theory, Algebraic Topology, and Algebraic Geometry
- Subject:
- Mathematics
- Creator:
- Burghardt, Viktor
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_904176 and http://dissertations.umi.com/northwestern:16112
-
- Description:
- We study Hermitian metrics with constant Chern scalar curvature on a compact complex manifold. In the first part of the thesis, we prove a priori estimates for metrics of constant Chern scalar curvature on a compact complex manifold conditional on an upper bound on the entropy, extending a recent result...
- Keyword:
- complex geometry, differential geometry, partial differential equations, and geometric analysis
- Subject:
- Mathematics
- Creator:
- Shen, Xi Sisi Sisi
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/28/2021
- Date Created:
- 2021-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_818179 and http://dissertations.umi.com/northwestern:15559
-
- Description:
- In this thesis, we study the homological mirror symmetry for the Gross-Siebert program of local mirror symmetry. We construct a pair of mirror objects by lifting a tropical curve in the integral tropical manifold of the Gross-Siebert program. Furthermore, we evaluate the central charges of the mirror objects and show...
- Subject:
- Mathematics
- Creator:
- Wang, Junxiao
- 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:15696 and etdadmin_upload_841422
-
- Description:
- The topic of this dissertation is the coherent-constructible correspondence (CCC). CCC is a version of homological mirror symmetry for toric varieties. It equates the derived category of coherent sheaves on a toric variety and the category of constructible sheaves on a torus whose singular support lies in the specific conical...
- Subject:
- Mathematics
- Creator:
- Suh, Pyongwon
- 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:15571 and etdadmin_upload_819148
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