Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 55). / The Heegaard Floer hat invariant is defined on closed 3-manifolds, with a related invariant for 4-dimensional cobordisms, forming a 3+1 topological quantum field theory. Bordered Heegaard Floer homology generalizes this invariant to parametrized Riemann surfaces and to cobordisms between them, yielding a 2+1 TQFT. We discuss an approach to synthesizing these two theories to form a 2+1+1 TQFT, by defining Heegaard Floer invariants for Lefschetz fibrations with corners. / by Tova Helen Fell Brown. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 83). / Let g be a complex, reductive Lie algebra. We prove a theorem parametrizing the set of nilpotent orbits in g in terms of even nilpotent orbits of subalgebras of g and show how to determine these subalgebras and how to explicitly compute this correspondence. We prove a theorem parametrizing nilpotent orbits for strong involutions of G in terms of even nilpotent orbits of complex subalgebras of g and show how to explicitly compute this correspondence. / by Peter Speh. / Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999. / Includes bibliographical references (p. 61-63). / by Chak-On Chow. / S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 121-124). / This doctoral dissertation is on the theory of Minimal Surfaces and of singularities in Mean Curvature Flow, for smooth submanifolds Y" in an ambient Riemannian (n+ 1)-manifold Nn+1, including: (1) New asymptotically conical self-shrinkers with a symmetry, in R"+1. (1') Classification of complete embedded self-shrinkers with a symmetry, in IR"+1, and of asymptotically conical ends with a symmetry. (2) Construction of complete, embedded self-shrinkers E2 C R3 of genus g, with asymptotically conical infinite ends, via minimal surface gluing. (3) Construction of closed embedded self-shrinkers y2 C R3 with genus g, via minimal surface gluing. In the work there are two central geometric and analytic themes that cut across (1)-(3): The notion of asymptotically conical infinite ends in (1)-(1') and (2), and in (2) and (3) the gluing methods for minimal surfaces which were developed by Nikolaos Kapouleas. For the completion of (2) it was necessary to initiate the development of a stability theory in a setting with unbounded geometry, the manifolds in question having essentially singular (worse than cusp-like) infinities. This was via a Schauder theory in weighted Hölder spaces for the stability operator, which is a Schrodinger operator of Ornstein-Uhlenbeck type, on the self-shrinkers viewed as minimal surfaces. This material is, for the special case of graphs over the plane, included as part of the thesis. The results in (1)-(1') are published as the joint work [KMø 1] with Stephen Kleene, and the result in (2) was proven in collaboration with Kleene-Kapouleas, and appeared in [KKMø 0]. The results in (3) are contained in the preprint [Mø1]. / by Niels Martin Moøller. / Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 47-50). / Because many invariants and properties of elliptic curves are difficult to understand directly, the study of arithmetic statistics instead looks at what happens "on average", using heights to make this notion rigorous. Previous work has primarily used the naive height, which can be calculated easily but is not defined intrinsically. We give an asymptotic formula for the number of elliptic curves over Q with bounded Faltings height. Silverman [34] has shown that the Faltings height for elliptic curves over number fields can be expressed in terms of the minimal discriminant and period of the elliptic curve. We use this to recast the problem as one of counting lattice points in an unbounded region in R2 defined by transcendental equations, and understand this region well enough to give a formula for the number of these lattice points. / by Ruthi Hortsch. / Ph. D.

Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1965. Ph.D. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1968. / Vita. / Bibliography: leaves 178-179. / by Lenore C. Blum. / Ph.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995. / Includes bibliographical references (leaves 19-21). / by C.E. Jesurum. / M.S.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1961. / Includes bibliographical references (leaves [36]-[37]). / by Ramesh Gangolli. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (p. 85-87). / by Eduardo de Sequeira Esteves. / Ph.D.