Browsing Department of Mathematics by Title
Now showing items 302321 of 829

Geometric and algebraic properties of polyomino tilings
(Massachusetts Institute of Technology, 2004)In this thesis we study tilings of regions on the square grid by polyominoes. A polyomino is any connected shape formed from a union of grid cells, and a tiling of a region is a collection of polyominoes lying in the region ... 
Geometric approaches to computing Kostka numbers and LittlewoodRichardson coefficients
(Massachusetts Institute of Technology, 2004)Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers and LittlewoodRichardson coefficients (the type A weight multiplicities and ClebschGordan coefficients). ... 
Geometric Langlands in prime characteristic
(Massachusetts Institute of Technology, 2012)Let C be a smooth projective curve over an algebraically closed field k of sufficiently large characteristic. Let G be a semisimple algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the ... 
Geometric manipulation of light : from nonlinear optics to invisibility cloaks
(Massachusetts Institute of Technology, 2012)In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study ... 
Geometric quantization and dynamical constructions on the space of Kähler metrics
(Massachusetts Institute of Technology, 2008)This Thesis is concerned with the study of the geometry and structure of the space of Kihler metrics representing a fixed cohomology class on a compact Kähler manifold. The first part of the Thesis is concerned with a ... 
A geometric theory of outliers and perturbation
(Massachusetts Institute of Technology, 2002)We develop a new understanding of outliers and the behavior of linear programs under perturbation. Outliers are ubiquitous in scientific theory and practice. We analyze a simple algorithm for removal of outliers from a ... 
The geometry and dynamics of twisted quadratic differentials
(Massachusetts Institute of Technology, 2019)This thesis examines twisted quadratic differentials, also known as dilation surfaces. These are variants of translation surfaces, their more wellstudied counterpart. In this work, we study questions about the realizability ... 
The geometry and topology of quotient varieties
(Massachusetts Institute of Technology, 1991) 
Geometry of conebeam reconstruction
(Massachusetts Institute of Technology, 2002)Geometry is the synthetic tool we use to unify all existing analytical conebeam reconstruction methods. These reconstructions are based on formulae derived by Tuy [Tuy, 1983], Smith [Smith, 1985] and Grangeat [Grangeat, ... 
Geometry of Ricciflat Kähler manifolds and some counterexamples
(Massachusetts Institute of Technology, 2004)In this work, we study geometry of Ricciflat Kähler manifolds, and also provide some counterexample constructions. We study asymptotic behavior of complete Ricciflat metrics at infinity and consider a construction of ... 
Geometry of river networks
(Massachusetts Institute of Technology, 2000) 
The geometry of the generic line complex
(Massachusetts Institute of Technology, 1995) 
Germ expansion, endoscopic transfer, and unitary periods
(Massachusetts Institute of Technology, 2019)In this thesis, we study the germ expansions in the JacquetRallis transfer. We prove an identity that relates certain nilpotent orbital integrals for any smooth matching in this transfer. We give two applications of this ... 
Getting a handle on contact manifolds
(Massachusetts Institute of Technology, 2019)In this thesis, we develop the details of a surgery theory for contact manifolds of arbitrary dimension via convex structures, extending the 3dimensional theory developed by Giroux. The theory is analogous to that of ... 
Goodwillie calculus and algebras over a spectral operad
(Massachusetts Institute of Technology, 2013)The overall goal of this thesis is to apply the theory of Goodwillie calculus to the category Algo of algebras over a spectral operad. Its first part generalizes many of the original results of Goodwillie in [14] so that ... 
The Gowers norm in the testing of Boolean functions
(Massachusetts Institute of Technology, 2009)A property tester is a fast, randomized algorithm that reads only a few entries of the input, and based on the values of these entries, it distinguishes whether the input has a certain property or is "different" from any ... 
Graded rings, modules and algebras.
(Massachusetts Institute of Technology, 1970) 
Grammar for vision.
(Massachusetts Institute of Technology, 1975) 
Graph polynomials and statistical physics
(Massachusetts Institute of Technology, 2007)We present several graph polynomials, of which the most important one is the Tutte polynomial. These various polynomials have important applications in combinatorics and statistical physics. We generalize the Tutte polynomial ... 
Graphs, matrices, and populations : linear algebraic techniques in theoretical computer science and population genetics
(Massachusetts Institute of Technology, 2013)In this thesis, we present several algorithmic results for problems in spectral graph theory and computational biology. The first part concerns the problem of spectral sparsification. It is known that every dense graph can ...