Browsing Department of Mathematics by Title
Now showing items 612631 of 829

Recognition of topological invariants by iterative arrays.
(Massachusetts Institute of Technology, 1969) 
Recursion on inadmissible ordinals
(Massachusetts Institute of Technology, 1976) 
Reducibilities in recursive function theory.
(Massachusetts Institute of Technology, 1966) 
Regularity and boundary variations for the Neumann problem
(Massachusetts Institute of Technology, 1997) 
Regularity and removal lemmas and their applications
(Massachusetts Institute of Technology, 2017)In this thesis, we analyze the regularity method pioneered by Szemerédi, and also discuss one of its prevalent applications, the removal lemma. First, we prove a new lower bound on the number of parts required in a version ... 
Regularity aspects of the theory of infinite dimensional representations of Lie groups.
(Massachusetts Institute of Technology, 1970) 
Regularity of Neumann solutions to an elliptic free boundary problem
(Massachusetts Institute of Technology, 2003)We examine the regularity properties of solutions to an elliptic free boundary problem, near a Neumann fixed boundary. Consider a nonnegative function u which minimizes the functional ... on a bounded, convex domain ... ... 
Relations in the homotopy of simplicial abelian Hopf algebras
(Massachusetts Institute of Technology, 1994) 
Relative Hilbert scheme methods in pseudoholomorphic geometry
(Massachusetts Institute of Technology, 2004)This thesis takes up a program initiated by S. Donaldson and I. Smith aimed at using symplectic Lefschetz fibration techniques to obtain information about pseudoholomorphic curves in symplectic 4manifolds. Donaldson and ... 
Relativization of the theory of computational complexity.
(Massachusetts Institute of Technology, 1972) 
Reliable validation : new perspectives on adaptive data analysis and crossvalidation
(Massachusetts Institute of Technology, 2018)Validation refers to the challenge of assessing how well a learning algorithm performs after it has been trained on a given data set. It forms an important step in machine learning, as such assessments are then used to ... 
Representation of quantum algebras arising from noncompact quantum groups : quantum orbit method and supertensor products
(Massachusetts Institute of Technology, 1996) 
Representation theory of the global Cherednik algebra
(Massachusetts Institute of Technology, 2017)This thesis studies the representation theory of Cherednik algebras associated to a complex algebraic varieties which carries the action of a finite group. First, we prove that the KnizhnikZamolodchikov functor from the ... 
Representations of Cherednik algebras in positive characteristic
(Massachusetts Institute of Technology, 2004)In this thesis, we first classify the irreducible representations of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the "quantum" case, where "Planck's constant" is nonzero ... 
Representations of semisimple Lie groups and an enveloping algebra decomposition.
(Massachusetts Institute of Technology, 1970) 
Representations of vertex operator algebras and superalgebras
(Massachusetts Institute of Technology, 1995) 
Residue functionals on the algebra of adiabatic pseudodifferential operators
(Massachusetts Institute of Technology, 1999) 
Resonance in dispersive wave systems
(Massachusetts Institute of Technology, 1999)The focus of this thesis is to investigate the differences that arise in weakly nonlinear wave interactions under the assumption of a discrete or continuous spectrum. In particular the latter is investigated in detail for ... 
Response to Steele Prize Award
(American Mathematical Society, 1988) 
A restriction estimate in R³
(Massachusetts Institute of Technology, 2019)In this thesis, I proved a restriction estimate for paraboloid in R³ based on the polynomial partitioning method introduced by Larry Guth and the "two ends argument" introduced by Wolff and Tao.