Browsing Mathematics by Issue Date
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Local cohomology at generic singularities of Schubert varieties in cominuscule flag varieties
(20120913)We study the local cohomology of a Schubert variety in a cominuscule flag variety at a generic singularity. Let $G$ be a reductive complex algebraic group with a Borel subgroup $B$, let $W$ be the Weyl group of $G$ with ... 
A TensorTriangulated Approach to Derived Categories of NonNoetherian Rings
(20120913)We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending previous work done under a Noetherian hypothesis. Maps between rings R → S induce adjoint functors between ... 
Isolated Curves for Hyperelliptic Curve Cryptography
(20130225)We introduce the notion of isolated genus two curves. There is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap. Thus there is no known way of transporting ... 
Smoothness of Loewner Slits
(20130225)In this dissertation, we show that the chordal Loewner differential equation with C^{beta} driving function generates a C^{beta + 1/2} slit for 1/2 < beta <= 2, except when beta = 3/2 the slit is only proved to be weakly C^{1,1}. 
An Inverse Source Problem in Radiative Transfer
(20130225)We consider the inverse source problem for the radiative transfer equation, under various assumptions on the scattering and absorption parameters, as well as on the accessible data. In such a setup, we measure the outgoing ... 
The OrnsteinUhlenbeck Process In Neural DecisionMaking: Mathematical Foundations And Simulations Suggesting The Adaptiveness Of Robustly Integrating Stochastic Neural Evidence
(20130225)This master's thesis reviews the concepts behind a stochastic process known as the OrnsteinUhlenbeck Process, and then uses that process as a way to investigate neural decision making. In particular, MATLAB simulations ... 
FiniteDifference Methods for the Wave Equation with Reduced Dispersion Errors
(20130417)A new methodology was proposed in Finkelstein and Kastner (2007,2008) to derive finitedifference (FD) schemes in the joint timespace domain to reduce dispersion error. The key idea is that the true dispersion relation ... 
A Geometric Perspective on FirstPassage Competition
(20130417)We study the macroscopic geometry of firstpassage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ... 
Polynomials in Multiview Geometry
(20130417)We study multiview geometry and some of its applications through the use of polynomials. A threedimensional world point gives rise to n ≥ 2 twodimensional projections in n given cameras. The object of focus in this ... 
Deformations of Categories of Coherent Sheaves and FourierMukai Transforms
(20130725)In modern algebraic geometry, an algebraic variety is often studied by way of its category of coherent sheaves or derived category. Recent work by Toda has shown that infinitesimal deformations of the category of coherent ... 
The Radiative Transfer Equation in Photoacoustic Imaging
(20130725)Photoacoustic tomography is a rapidly developing medical imaging technique that combines optical and ultrasound imaging to exploit the high contrast and high resolution of the respective individual modalities. Mathematically, ... 
Markov chain mixting time, card shuffling and spin systems dynamics
(20130725)The mixing time of a Markov chain describes how fast the Markov chain converges to its stationary distribution. In this thesis, we survey some of the knowledge and main tools available in this field by looking at examples. ... 
Estimating Norms of Matrix Functions using Numerical Ranges
(20131114)We study Crouzeix's conjecture: for any polynomial p and any square matrix A, the spectral norm of the matrix p(A) is at most double of the supremum norm of the polynomial p on the numerical range of the matrix A. 
Mathematical Aspects of Gerrymandering
(20131114)Every 10 years the United States performs a census, and this census determines how many members of congress will represent each state. Then begins an unfortunate battle, as cartographers manipulate the boundaries for ... 
Eigenvalue Fluctuations of Random Matrices beyond the Gaussian Universality Class
(20131114)The goal of this thesis is to develop one of the threads of what is known in random matrix theory as universality, which essentially is that a large class of matrices generalizing the Gaussian matrices (certain Wigner ... 
Thermoacoustic Tomography in Elastic Media
(20131114)We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, nonhomogeneous elastic wave equation, given measurements of u on [0, T ] × boundary of Omega, where Omega in R3 ... 
Hybrid Inverse Problems Arising from AcoustoElectric Coupling
(20131114)We study hybrid imaging techniques that aim to overcome the illposedness of the Electric Impedance Tomography using the acoustoelectric coupling. For the isotropic case, we consider the problem of reconstructing the ... 
Hopf algebras of finite GelfandKirillov dimension
(20131114)We study Hopf algebras of finite GelfandKirillov dimension. By analyzing the free pointed Hopf algebra F(t), we show the existence of certain Hopf subalgebras of pointed Hopf domains H whose GKdimension are finite and ... 
Hybrid inverse problems
(20131114)Inverse problems arise in different disciplines including exploration geophysics, medical imaging and nondestructive evaluation. In some settings, a single modality displays either high contrast or high resolution but not ... 
Four Problems in Probability and Optimization
(20140224)This thesis studies bootstrap percolation, a problem in probability, as well as several topics in the application of sums of squares to combinatorial optimization. In the chapter on percolation, we bound the critical ...