Browsing Department of Mathematics by Title
Now showing items 120 of 827

The 1dimensional [lambda]self shrinkers in R² and the nodal sets of biharmonic Steklov problems
(Massachusetts Institute of Technology, 2016)This thesis contains two of my projects. Chapter 1 and 2 describe the behavior of 1dimensional [lambda]self shrinkers, which are also known as [lambda]curves in other literature. Chapter 3 and 4 focus on the estimation ... 
2loop perturbative invariants of lens spaces and a test of ChernSimons quantum field theory
(Massachusetts Institute of Technology, 1996) 
A 24dimensional spin manifold.
(Massachusetts Institute of Technology, 1969) 
The 3D instability of a strained vortex and its relation to turbulence
(Massachusetts Institute of Technology, 1989) 
An a priori inequality for the signature operator.
(Massachusetts Institute of Technology, 1978) 
Ainfinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks
(Massachusetts Institute of Technology, 2015)For a Lagrangian submanifold, we define a moduli space of trees of holomorphic disk maps with Morse flow lines as edges, and construct an ambient space around it which we call the quotient space of disk trees. We show that ... 
Abelian algebras and adjoint orbits
(Massachusetts Institute of Technology, 1981) 
Accelerated clustering through localitysensitive hashing
(Massachusetts Institute of Technology, 2012)We obtain improved running times for two algorithms for clustering data: the expectationmaximization (EM) algorithm and Lloyd's algorithm. The EM algorithm is a heuristic for finding a mixture of k normal distributions ... 
Active flows and networks
(Massachusetts Institute of Technology, 2018)Coherent, large scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by smallscale local energy input. In the first part of this thesis, we introduce and explore two ... 
Adnilpotent ideals of complex and real reductive groups
(Massachusetts Institute of Technology, 2007)In this thesis, we study adnilpotent ideals and its relations with nilpotent orbits, affine Weyl groups, sign types and hyperplane arrangements. This thesis is divided into three parts. The first and second parts deal ... 
Adaptive protocols for the quantum depolarizing channel
(Massachusetts Institute of Technology, 2007)In the first part, we present a family of entanglement purification protocols that generalize four previous methods, namely the recurrence method, the modified recurrence method, and the two methods proposed by ManevaSmolin ... 
Adelic FourierWhittaker coefficients and the CasselmanShalika formula
(Massachusetts Institute of Technology, 2009)In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are nontrivial covering groups of usual algebraic ... 
Adiabatic limit and SzegÅ‘ projections
(Massachusetts Institute of Technology, 2003) 
Admissible nilpotent coadjoint orbits of padic reductive Lie groups
(Massachusetts Institute of Technology, 1998) 
Admissible ordinals and recursion theory,
(Massachusetts Institute of Technology, 1971) 
Affine quantum algebras, Weyl groups and constructible functions
(Massachusetts Institute of Technology, 2002)This thesis consists of two parts. In the first part we study the affine quantum group of type A, giving a geometric description of its natural inner product, and studying the theory of cells attached to the canonical ... 
The affine Yangian of gl₁, and the infinitesimal Cherednik algebras
(Massachusetts Institute of Technology, 2014)In the first part of this thesis, we obtain some new results about infinitesimal Cherednik algebras. They have been introduced by EtingofGanGinzburg in [EGG] as appropriate analogues of the classical Cherednik algebras, ... 
An algebra for theoretical genetics
(Massachusetts Institute of Technology, 1940) 
Algebraic and combinatorial properties of minimal border strip tableaux
(Massachusetts Institute of Technology, 2003)Motivated by results and conjectures of Stanley concerning minimal border strip tableaux of partitions, we present three results. First we generalize the rank of a partition [lambda] to the rank of a shifted partition ... 
An algebraic approach to the operator product expansion
(Massachusetts Institute of Technology, 2000)