Browsing Mathematics - Ph.D. / Sc.D. by Title
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Browsing Mathematics - Ph.D. / Sc.D. by Title
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(Massachusetts Institute of Technology, 2001)
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(Massachusetts Institute of Technology, 1997)
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(Massachusetts Institute of Technology, 1996)
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(Massachusetts Institute of Technology, 2011)Recently, unexpected connections have been discovered between characters of representations and lattice models in statistical mechanics. The bridge was first formed from Kuperberg's solution to the alternating sign matrix ...
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(Massachusetts Institute of Technology, 2006)In this thesis, we study degenerate Monge-Ampere equations over projective manifolds. The main degeneration is on the cohomology class which is Kähler in classic cases. Our main results concern the case when this class is ...
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(Massachusetts Institute of Technology, 2004)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. ...
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(Massachusetts Institute of Technology, 2008)We develop a theory of less commutative algebraic geometry where the role of commutative rings is assumed by En-rings, that is, rings with multiplication parametrized by configuration spaces of points in Rn. As n increases, ...
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(Massachusetts Institute of Technology, 2010)This work focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into ...
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(Massachusetts Institute of Technology, 2003)In the field of genomics, this thesis presents algorithms for identifying non-coding RNA (ncRNA) genes. It describes a rapid and highly reliable comparative statistical method for identification of functionally significant ...
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(Massachusetts Institute of Technology, 1989)
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(Massachusetts Institute of Technology, 1987)
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(Massachusetts Institute of Technology, 1993)
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(Massachusetts Institute of Technology, 1972)
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(Massachusetts Institute of Technology, 1995)
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(Massachusetts Institute of Technology, 1989)
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(Massachusetts Institute of Technology, 2007)This thesis consists of two parts. In the first part of the thesis, we prove an index theorem for Dirac operators of conic singularities with codimension 2. One immediate corollary is the generalized Rohklin congruence ...
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(Massachusetts Institute of Technology, 2007)How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic ...
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(Massachusetts Institute of Technology, 1986)
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(Massachusetts Institute of Technology, 1980)
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(Massachusetts Institute of Technology, 2005)In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical subalgebra eH(t, 1)e of the Double Affine Hecke algebra H(t, ...
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