Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (p. 59). / by James M. Turner. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Title as it appeared in Massachusetts Institute of Technology Graduate List, February, 1987 : Secondary instability in Ekman flow. / Bibliography: leaves [120]-[121]. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 51). / An origami manifold is a manifold equipped with a closed 2-form which is symplectic everywhere except on a hypersurface, where it is a folded form whose kernel defines a circle fibration. In this thesis I explain how an origami manifold can be unfolded into a collection of symplectic pieces and conversely, how a collection of symplectic pieces can be folded (modulo compatibility conditions) into an origami manifold. Using equivariant versions of these operations, I show how classic symplectic results of convexity and classification of toric manifolds translate to the origami world. Several examples are presented, including a complete classification of toric origami surfaces. Furthermore, I extend the results above to the case of nonorientable origami manifolds. / by Ana Rita Pissarra Pires. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996. / Includes bibliographical references (p. 85-86). / by Charles W. Rezk. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. / Includes bibliographical references (p. 121-122). / In this thesis, we improve the loop linearization process from the classical article of Atiyah and Bott on Bott periodicity. The linearization process is made explicit in terms of formulae for smooth loops. Using this improvement allows us to extend K-theory (including periodicity) to a class of locally convex algebras vastly larger then the one of Banach algebras. We find various ways to represent periodicity by explicit formulae. For finite Laurent loops formulae yielding finite matrices to represent the associated Ko classes are obtained. The methods used also allow us to reinterpret some recent results of Melrose on smooth classifying spaces for K-theory. The relationship between the universal even and odd Chern characters and periodicity is investigated, giving correspondences between the various representatives in the form of family index theorems for loop groups. In the discussion Ko and the even Chern character are primarily formulated in the language of involutions. The paper also demonstrates the universality of the involution terminology with respect to vector bundles. / by Gyula Lakos. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 83-84). / In this thesis we develop a version of classical scissors congruence theory from the perspective of algebraic K-theory. Classically, two polytopes in a manifold X are defined to be scissors congruent if they can be decomposed into finite sets of pairwise-congruent polytopes. We generalize this notion to an abstract problem: given a set of objects and decomposition and congruence relations between them, when are two objects in the set scissors congruent? By packaging the scissors congruence information in a Waldhausen category we construct a spectrum whose homotopy groups include information about the scissors congruence problem. We then turn our attention to generalizing constructions from the classical case to these Waldhausen categories, and find constructions for cofibers, suspensions, and products of scissors congruence problems. / by Inna Zakharevich. / Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 129-132). / This thesis consists of three parts. In the first part, we study the eleven dimensional supergravity equations on B 7 x S 4 considered as an edge manifold. We compute the indicial roots of the linearized system using the Hodge decomposition, and using the edge calculus and scattering theory we prove that the moduli space of solutions, near the Freund-Rubin states, is parameterized by three pairs of data on the bounding 6-sphere. In the second part, we consider the family of constant curvature fiber metrics for a Lefschetz fibration with regular fibers of genus greater than one. A result of Obitsu and Wolpert is refined by showing that on an appropriate resolution of the total space, constructed by iterated blow-up, this family is log-smooth, i.e. polyhomogeneous with integral powers but possible multiplicities, at the preimage of the singular fibers in terms of parameters of size comparable to the length of the shrinking geodesic. This is joint work with Richard Melrose. In the third part, the resolution of a compact group action in the sense described by Albin and Melrose is applied to the conjugation action by the unitary group on self-adjoint matrices. It is shown that the eigenvalues are smooth on the resolved space and that the trivial tautological bundle smoothly decomposes into the direct sum of global one-dimensional eigenspaces. / by Xuwen Zhu. / Ph. D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1968. / Bibliography: leaf [14]. / by Steven Gero. / M.S.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999. / Includes bibliographical references (p. 77-78). / by Sergiu Moroianu. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. / Includes bibliographical references (p. 81-83). / We introduce new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is the powerful Chekanov-Eliashberg differential graded algebra, which we reformulate and generalize. We give applications to Legendrian knots and links in three-space and in the solid torus. A related question, the calculation of the maximal Thurston-Bennequin number for a link, is answered for some large classes of links. / by Lenhard Lee Ng. / Ph.D.