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-
- Description:
- Let X,Y be algebraic varieties defined over the reals. Assume Y is smooth and X is Gorenstein. Suppose f:X -> Y is a flat R-morphism such that all the fibers have rational singularities. We show that the pushforward of any smooth, compactly supported measure on X has a continuous density...
- Keyword:
- Measures and Rational singularities
- Subject:
- Mathematics
- Creator:
- Andrew Reiser
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/24/2019
- Date Modified:
- 11/24/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- We compare two different methods to compute the mod 2 homology of an infinite loop space. One method is to approximate the infinite loop functor using functor calculus. The other is to approximate the spectrum using an Adams resolution. We show that these two ways lead to isomorphic spectral sequences....
- Keyword:
- spectral sequences, Goodwillie calculus, Adams resolution, and power operations
- Subject:
- Mathematics
- Creator:
- Johan W T Konter
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/24/2019
- Date Modified:
- 11/24/2019
- Date Created:
- 2018-01-01
- 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 Morel-Voevodsky, understanding of this stack. Following the...
- Keyword:
- Space of rational maps, Ran space, Motivic homotopy theory, Motives, and Geometric Langlands
- Subject:
- Mathematics
- Creator:
- Elden Elmanto
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/19/2019
- Date Modified:
- 11/19/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- 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:
- High Dimensional, Complex Geometry, Differential Equations, and Probability Theory
- Subject:
- Mathematics
- Creator:
- Xavier Eduardo Garcia
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 11/19/2019
- Date Modified:
- 11/19/2019
- Date Created:
- 2018-01-01
- 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, tensor product, central extension, and determinant
- Subject:
- Mathematics
- Creator:
- Aron Alexandre Heleodoro
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/15/2019
- Date Modified:
- 04/15/2019
- Date Created:
- 2018-01-01
- 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:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- In this paper, we show almost-Gelfand property of connected symmetric pairs (G, H) over finite fields of large characteristics by showing almost-sigma-invariant property of double coset H\G/H where sigma is the associated anti-involution combining with epsilon-version of Gelfand's trick
- Keyword:
- symmetric pair, representation theory, and Gelfand pair
- Subject:
- Mathematics
- Creator:
- Nan Shi
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/01/2019
- Date Modified:
- 04/01/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- The holomorphic sigma-model 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:
- Factorization algebras, Renormalization, Batalin-Vilkovisky, and Quantum field theory
- Subject:
- Mathematics
- Creator:
- Brian R Williams
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/01/2019
- Date Modified:
- 04/01/2019
- Date Created:
- 2018-01-01
- 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:
- chromatic homotopy theory, formal groups, Morava E-theory, Bousfield localization, algebraic topology, and structured ring spectra
- Subject:
- Mathematics
- Creator:
- Paul Behrents VanKoughnett
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 04/01/2019
- Date Modified:
- 04/01/2019
- Date Created:
- 2018-01-01
- Resource Type:
- Dissertation
-
- Description:
- We prove a uniform scalar curvature bound for solutions of the conical Kahler-Ricci flow when the twisted canonical bundle is semiample and the cone divisor is obtained from the associated Iitaka-Kodaira fibration. In the course of the proof we establish uniform bounds for the potential of the metric and its...
- Keyword:
- Geometric Flows, Kahler-Ricci Flow, and Conical Kahler Metrics
- Subject:
- Mathematics
- Creator:
- Gregory Edwards
- Owner:
- Scholarly Digital Publishing
- Date Uploaded:
- 03/07/2019
- Date Modified:
- 03/07/2019
- Date Created:
- 2018-01-01
- 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
-
- 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:
- 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:
- 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 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 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:
- 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:
- 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:
- 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:
- 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:
- 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
-
- 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