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-
- 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:
- The action of the automorphisms of a formal group on its deformation space is crucial to understanding periodic families in the homotopy groups of spheres and the unsolved Hecke orbit conjecture for unitary Shimura varieties. This action is called the Lubin-Tate action. We first show sufficient conditions for geometrically modelling...
- Keyword:
- algebraic geometry, homotopy theory, and arithmetic geometry
- Subject:
- Mathematics
- Creator:
- Ray, Catherine
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 08/23/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_1013588 and http://dissertations.umi.com/northwestern:16756
-
- Description:
- The main topic of this thesis is generation in derived categories of coherent sheaves on smooth projective varieties. We develop a new approach that allows us to give a new proof of a recent result by Olander that powers of an ample line bundle generate the bounded derived category of...
- Keyword:
- Derived Categories, Rouquier Dimension, and Algebraic Geometry
- Subject:
- Mathematics and Theoretical mathematics
- Creator:
- Khromenkov, Yaroslav
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 08/23/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_1004198 and http://dissertations.umi.com/northwestern:16672
-
- 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:
- In this thesis, we consider the categories of sheaves with singular support on certain Lagrangians and the categories of microlocal sheaves with support on certain Lagrangians obtained by microlocalization, and study properties of functors between these categories.First, we study one class of the microlocal restriction functor for open inclusions, namely...
- Subject:
- Mathematics
- Creator:
- Li, Wenyuan
- 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:16549 and etdadmin_upload_985220
-
- Description:
- A great deal of work has been done in recent years to construct algebraic invariants ofLegendrian knots, and their higher-dimensional analogues. Here we employ the diagram- matic calculus developed in [3], in order to develop an iterative method for computing the so-called vexillary functions of a class of Legendrian surfaces....
- Keyword:
- Moduli, Legendrian, Knot, Combinatorics, and Microlocal
- Subject:
- Mathematics
- Creator:
- Snadden, John Arthur
- 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:16484 and etdadmin_upload_980155
-
- Description:
- In the first part of the thesis we,given a dg-Lie algebra $\g$, a commutative dg-algebra $A$ and a twisting cochain $\mu$ in $A \otimes \g$, we construct a map from the functor of curved deformations of $\g$ to the functor of curved deformations of the twisted tensor product $A \otimes_\mu...
- Keyword:
- L-infinity algebras, Lie coalgebra, A-infinity algebras, Period map, Quantization, and Deformation theory
- Subject:
- Mathematics
- Creator:
- Papayanov, Grigory
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 05/31/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_985714 and http://dissertations.umi.com/northwestern:16566
-
- Description:
- The purpose of this thesis is to study the empirical measure of the t-distributed stochastic neighbor embedding algorithm (t-SNE) when the input is given by n independent, identically distributed inputs.We show that this sequence of measures converges to an equilibrium measure, which can be described as the solution of a...
- Keyword:
- Probability and Unsupervised Machine Learning
- Subject:
- Mathematics
- Creator:
- Fletcher, Daniel
- 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:16523 and etdadmin_upload_983853
-
- Description:
- In this thesis, we consider the spherical spin glass models at zero temperature. We first determine the structureof the Parisi measure at zero temperature for the spherical p+s spin glass model. We then consider the spherical mixed p-spin model and show that for the spherical spin models with n components,...
- Subject:
- Mathematics
- Creator:
- Zhou, Yuxin
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 05/31/2023
- Date Created:
- 2023-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_985448 and http://dissertations.umi.com/northwestern:16557
-
- 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:
- We introduce empirical measures to study the $L^2$ norms of restrictions of quantum integrable eigenfunctions to the unique rotationally invariant geodesic $H$ on a convex surface of revolution. The weak* limit of these measures describes the dependence of their size on $H$ in terms of the angular momentum. The limit...
- Keyword:
- convex surface of revolution, asymptotics, eigenfunctions, empirical measure, and spectrum
- Subject:
- Mathematics
- Creator:
- Geis, Michael Leamy
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 09/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:16276 and etdadmin_upload_929536
-
- Description:
- The purpose of this thesis is to derive three results in probability theory. The first is a proof that small powers of the normalized absolute characteristic polynomial of a random matrix sampled from either the Gaussian Orthogonal or Symplectic Ensemble converges in law to a Gaussian multiplicative chaos measure. The...
- Keyword:
- Probability and Random Matrices
- Subject:
- Mathematics
- Creator:
- Kivimae, Pax
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 09/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_923657 and http://dissertations.umi.com/northwestern:16191
-
- 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:
- In this dissertation, we study the birational geometry of log pairs over the field of complex numbers, with an emphasis on the positivity properties of log pairs and their applications. First, we study the nonvanishing conjecture in the minimal model program. We prove the nonvanishing conjecture for uniruled log canonical...
- Keyword:
- Birational Geometry, Positivity Properties, and Log Pairs
- Subject:
- Mathematics
- Creator:
- Meng, Fanjun
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:15958 and etdadmin_upload_883432
-
- Description:
- This dissertation provides an introduction to the diffraction and scattering theory for the Aharonov--Bohm Hamiltonian with one or multiple poles on $\mathbf{R}^2$. It shows the propagation of diffractive singularities of the wave equation with the magnetic Hamiltonians with singular vector potential, which is related to the so-called Aharonov--Bohm effect. Based...
- Keyword:
- Scattering, Wave Trace, Resonance, Diffraction, Aharonov-Bohm, and Resolvent
- Subject:
- Mathematics
- Creator:
- Yang, Mengxuan
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:16059 and etdadmin_upload_901993
-
- Description:
- This thesis is composed of two major parts. The first major part includes the first two chapters. In Chapter 1, we go over the history and background of spin glass theory and introduce the Sherrington-Kirkpatrick (SK) model and the Ghatak-Sherrington (GS) model. In Chapter 2, we introduce the Thouless-Anderson-Palmer (TAP)...
- Keyword:
- Probability and Spin Glass
- Subject:
- Mathematics
- Creator:
- Chen, Xi
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:16090 and etdadmin_upload_903175
-
- Description:
- We study the complexification of Laplace Eigenfunctions on the Grauert tube of a compact real analytic manifold. Our main results concern scaling asymptotics of Fourier coefficients of the Szego kernel on the Grauert tube boundary in a Heisenberg frequency scaled neighborhood of the geodesic flow. We show that in the...
- Subject:
- Mathematics and Theoretical mathematics
- Creator:
- Rabinowitz, Abraham
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 06/22/2022
- Date Created:
- 2022-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- etdadmin_upload_903279 and http://dissertations.umi.com/northwestern:16093
-
- Description:
- Parshin's conjecture expects that the higher algebraic $K$-groups of smooth projective varieties over a finite field are torsion. In this thesis we prove that with the assumption of finite generation of higher \'etale algebraic $K$-theory of smooth projective varieties over a finite field, one can reduce Parshin's conjecture to the...
- Keyword:
- Lefschetz, Grothendieck, and Algebraic K-theory
- Subject:
- Mathematics
- Creator:
- Yousefzadehfard, Aydin
- Owner:
- Scholarly Digital Publishing
- Language:
- en
- Date Uploaded:
- 02/02/2022
- Date Created:
- 2021-01-01
- Resource Type:
- Dissertation
- Alternate Identifier:
- http://dissertations.umi.com/northwestern:15827 and etdadmin_upload_856824
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