Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1966. Ph.D. / Bibliography: leaves 41-42. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. / Includes bibliographical references (p. 191-193). / The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types. / by Jacob Lurie. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (p. 41-42). / by Laura Anderson. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1973. / Vita. / Bibliography: leaves 64-67. / by Ridgway Scott. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997. / Includes bibliographical references (p. 78-82). / by Thoams Colthurst. / Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 157-159). / Chromatic localization can be seen as a way to calculate a particular infinite piece of the homotopy of a spectrum. For example, the (finite) chromatic localization of a p-local sphere is its rationalization, and the corresponding chromatic localization of its Adams E2 page recovers just the zero-stem. We study a different localization of Adams E2 pages for spectra, which recovers more information than the chromatic localization. This approach can be seen as the analogue of chromatic localization in a category related to the derived category of comodules over the dual Steenrod algebra, a setting in which Palmieri has developed an analogue of chromatic homotopy theory. We work at p = 3 and compute the E2 page and first nontrivial differential of a spectral sequence converging to ... (where P is the Steenrod reduced powers), and give a complete calculation of other localized Ext groups, including ... / by Eva Kinoshita Belmont. / Ph. D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (leaf 17). / by Ana M.L.G. Canas da Silva. / M.S.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. / Includes bibliographical references (p. 53-55). / This work has three purposes. The first one is to prove unobstructedness of deformation of pseudoholomorphic curves with cusps and tacnodes. We show that if the first Chern class of a 4-dimensional symplectic manifold is sufficiently positive then the deformation is unobstructed. We prove this result when the curves have cusps and nodes, not in a prescribed position. We also prove a similar result when the curves have cusps and tacnodes in a prescribed position with a prescribed tangency and in addition nodes, not in a prescribed position. The second part of this work deals with the local symplectic isotopy problem for cuspidal curves. Let B be the unit ball in R4 with the standard symplectic form wst. Let J0 be a wst-tame almost complex structure. Let Co c B be a connected J-holomorphic curve in B with a isolated singularity at 0 E B and without multiple components. Assume in addition that the boundary OCo is smoothly embedded. We prove that any two connected, reduced pseudoholomorphic curves in B, with the same number of irreducible components, the same number of nodal points and at most one ordinary cusp point, both sufficiently close to Co, are symplectic isotopic to each other. The third part of this work deals with the global symplectic isotopy problem. As an application of unobstructedness of deformation, we show that any irreducible rational pseudo-holomorphic curve in CP2 of degree d, with only nodes and m ordinary cusps as its singularities, is symplectic isotopic to a holomorphic curve as long as d > m. / by Sandra Francisco. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996. / Includes bibliographical references (p. 49-50). / by Olga Kravchenko. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002. / Includes bibliographical references (p. 91-94). / 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 high-dimensional data set and show the algorithm to be asymptotically good. We extend this result to distributions that we can access only by sampling, and also to the optimization version of the problem. Our results cover both the discrete and continuous cases. This is joint work with Santosh Vempala. The complexity of solving linear programs has interested researchers for half a century now. We show that an arbitrary linear program subject to a small random relative perturbation has good condition number with high probability, and hence is easy to solve. This is joint work with Avrim Blum, Daniel Spielman, and Shang-Hua Teng. This result forms part of the smoothed analysis project initiated by Spielman and Teng to better explain mathematically the observed performance of algorithms. / by John D. Dunagan. / Ph.D.