Browsing Mathematics  Ph.D. / Sc.D. by Title
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A qanalogue of spanning trees : nilpotent transformations over finite fields
(Massachusetts Institute of Technology, 2009)The main result of this work is a qanalogue relationship between nilpotent transformations and spanning trees. For example, nilpotent endomorphisms on an ndimensional vector space over Fq is a qanalogue of rooted spanning ... 
Quantifier rank spectrum of Linfinityomega
(Massachusetts Institute of Technology, 2006)In Part A we will study the quantifier rank spectrum of sentences of L!1,!. We will show that there are scattered sentences with models of arbitrarily high but bounded quantifier rank. We will also consider the case of ... 
Quantitative invertibility of random matrices : a combinatorial perspective
(Massachusetts Institute of Technology, 2020)In this thesis, we develop a novel framework for investigating the lower tail behavior of the least singular value of random matrices  a subject which has been intensely studied in the past two decades. Our focus is on ... 
Quantization of nilpotent coadjoint orbits
(Massachusetts Institute of Technology, 1996) 
Quantized multiplicative quiver varieties and actions of higher genus braid groups
(Massachusetts Institute of Technology, 2011)In this thesis, a new class of algebras called quantized multiplicative quiver varieties A (Q), is constructed, depending upon a quiver Q, its dimension vector d, and a certain "moment map" parameter . The algebras Ad(Q) ... 
Quantum and Floer cohomology have the same ring structure
(Massachusetts Institute of Technology, 1996) 
Quantum geometric Langlands correspondence in positive characteristic: the GLN case
(Massachusetts Institute of Technology, 2012)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 ... 
Quantum intertwiners and integrable systems
(Massachusetts Institute of Technology, 2016)We present a collection of results on the relationship between intertwining operators for quantum groups and eigenfunctions for quantum integrable systems. First, we study the EtingofKirillov Jr. expression of Macdonald ... 
The quantum Johnson homomorphism and symplectomorphism of 3folds
(Massachusetts Institute of Technology, 2016)introduce a subset K2,A of the symplectic mapping class group, and an invariant ... that associates a characteristic class in Hochschild cohomology to every symplectomorphism ... K2,A. These are analogues to the familiar ... 
Quantum proof systems and entanglement theory
(Massachusetts Institute of Technology, 2009)Quantum complexity theory is important from the point of view of not only theory of computation but also quantum information theory. In particular, quantum multiprover interactive proof systems are defined based on ... 
Quillen cohomology of pialgebras and application to their realization by Martin Frankland.
(Massachusetts Institute of Technology, 2010)We use the obstruction theory of BlancDwyerGoerss to study the realization space of certain  algebras with 2 nontrivial groups. The main technical tool is a result on the Quillen cohomology of truncated algebras, which ... 
Quotientsingularities in characteristic p
(Massachusetts Institute of Technology, 1980) 
Radiation field for Einstein vacuum equations
(Massachusetts Institute of Technology, 2010)The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions ... 
Random partitions and the quantum BenjaminOno hierarchy
(Massachusetts Institute of Technology, 2016)Stanley's Cauchy identity for Jack symmetric functions defines a Jack measure, a model random partitions for every analytic real function v(w) on the unit circle and parameters E2 < 0 < E1. Jacks are eigenfunctions of the ... 
Random planar matching and bin packing
(Massachusetts Institute of Technology, 1985) 
Random tilings : gap probabilities, local and global asymptotics
(Massachusetts Institute of Technology, 2017)In the thesis we explore and develop two different approaches to the study of random tiling models. First, we consider tilings of a hexagon by rombi, viewed as 3D random stepped surfaces with a measure proportional to ... 
Randomness versus nondeterminism in distributed computing
(Massachusetts Institute of Technology, 1995) 
Rational families of vector bundles on curves
(Massachusetts Institute of Technology, 2002)We find and describe the irreducible components of the space of rational curves on moduli spaces M of rank 2 stable vector bundles with odd determinant on curves C of genus g [greater than or equal to] 2. We prove that the ... 
Rational matrix differential operators and integrable systems of PDEs
(Massachusetts Institute of Technology, 2017)A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite ... 
Real, complex and quaternionic toric spaces
(Massachusetts Institute of Technology, 1993)