Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1966. Ph.D. / Bibliography: leaves 102-103. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (leaves 63-64). / by Jianke Yang. / Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 153-155). / Consider an instance h of the Gaussian free field on a simply connected domain ... We study several properties of the level lines: continuity, monotonicity, reversibility and target-independence ... In the second part, we study Liouville quantum gravity(LQG). / by Menglu Wang. / Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994. / Includes bibliographical references (leaves 139-141). / by Gábor Hetyei. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996. / Includes bibliographical references (p. 133-135). / by Dimitri Vaynblat. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. / In title on title page, "N" of GLN appears as subscript of upper case letter N. Cataloged from PDF version of thesis. / Includes bibliographical references (p. 73). / Let C be a smooth connected projective curve of genus > 1 over an algebraically closed field k of characteristic p > 0, and c [epsilon] k \ Fp. Let BunN be the stack of rank N vector bundles on C and Ldet the line bundle on BunN given by determinant of derived global sections. In this thesis, we construct an equivalence of derived categories of modules for certain localizations of the twisted crystalline differential operator algebras DBunNet and DBunN, L-1/cdet The first step of the argument is the same as that of [BB] for the non-quantum case: based on the Azumaya property of crystalline differential operators, the equivalence is constructed as a twisted version of Fourier-Mukai transform on the Hitchin fibration. However, there are some new ingredients. Along the way we introduce a generalization of p-curvature for line bundles with non-flat connections, and construct a Liouville vector field on the space of de Rham local systems on C. / by Roman Travkin. / Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 99-101). / We study optimal and nearly-optimal quantum strategies for non-local XOR games. First, we prove the following general result: for every non-local XOR game, there exists a set of relations with the properties: (1) a quantum strategy is optimal for the game if and only if it satisfies the relations, and (2) a quantum strategy is nearly optimal for the game if and only if it approximately satisfies the relations. Next, we focus attention on a specific infinite family of XOR games: the CHSH(n) games. This family generalizes the well-known CHSH game. We describe the general form of CHSH(n) optimal strategies. Then, we adapt the concept of intertwining operator from representation theory and use that to characterize nearly-optimal CHSH(n) strategies / by Dimiter Ostrev. / Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 69-70). / The purpose of this work is give some field notes on exploring the idea that a generalized Tate construction tk reduces chromatic level in stable homotopy theory. The first parts introduce the construction and discuss chromatic reduction. The next section makes a computation and gives the duals of L(n) = L(n)1. The last part looks ahead, mentioning how this computation could be extended to finding the duals of Steinberg summands in corresponding Thom spectra of negative representations, L(n)-q, and presents an equivariant loopspace machine. Finally, observations made are pulled together and brought back to compute the base case of the generalized Tate construction, evaluated on a sphere. Results parallel work of A. Cathcart, B. Guillou and P. May, and N. Stapleton, among others. / by Olga Stroilova. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987. / Bibliography: p. [163-168]. / by Günter M. Ziegler. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 171-175). / The Colemani integral is a p-adice line integral that can be used to encapsulate several quantities relevant, to a study of the arithmetic of varieties. In this thesis, I describe algorithms for computing Coleman integrals on hyperelliptic curves and discuss some immediate applications. I give algorithms to compute single and iterated integrals on odd models of hyperelliptic curves, as well as the necessary modifications to iplemieit these algorithms for even models. Furthermore, I show how these algorithinis can be used in various situations. The first application is the method of Chabatv to find rational points on curves of genus greater than 1. The second is Mlihyong Kim's recent nonabelian analogue of the Chabauty method for elliptic curves. The last two applications concern p-adic heights on Jacobians of hyperelliptic curves. necessary to formulate a p-adic analogue of the Birch and Swinnerton-Dyer conjecture. I conclude by stating the analogue of the Mazur-Tate-Teitelbaum conjecture iii our setting and presenting supporting data. / by Jennifer Sayaka Balakrishnan. / Ph.D.