Browsing Department of Mathematics by Title
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Topologies of group algebras and a theorem of Littlewood
(American Mathematical Society, 1957)An important problem in Fourier analysis is that of investigating the relationship between the "size" of a function and the "size" of its Fourier transform. The present paper can be regarded as a contribution to this problem. 
Topology and combinatorics of ordered sets
(Massachusetts Institute of Technology, 1981) 
The topology of Baues complexes and flip graphs
(Massachusetts Institute of Technology, 2017)This thesis contains several results on the connectedness of Baues complexes and flip graphs, which are topological spaces modeling certain sets coming from geometric combinatorics. These sets include the triangulations ... 
Topology of combinatorial differential manifolds
(Massachusetts Institute of Technology, 1994) 
The topology of GKM spaces and GKM fibrations
(Massachusetts Institute of Technology, 2009)This thesis primarily consists of results which can be used to simplify the computation of the equivariant cohomology of a GKM space. In particular we investigate the role that equivariant maps play in the computation of ... 
The topology of Hecke correspondences
(Massachusetts Institute of Technology, 1994) 
Topology of KacMoody groups
(Massachusetts Institute of Technology, 1998) 
Topology of the nodal and critical point sets for eigenfunctions of elliptic operators,
(Massachusetts Institute of Technology, 1971) 
Total positivity and real flag varieties
(Massachusetts Institute of Technology, 1998) 
Totaltopeak ratios of high purity germanium gamma ray detector
(Massachusetts Institute of Technology, 2004)This study is concerned with the percentage of [gamma]rays of a certain energy having their energy correctly measured by a high purity Germanium [gamma]ray detector. The ratio between the total counts and the counts ... 
Totally positive spaces : topology and applications
(Massachusetts Institute of Technology, 2019)This thesis studies topological spaces arising in total positivity. Examples include the totally nonnegative Grassmannian Gr[subscripts >_0](k, n), Lusztig's totally nonnegative part (G/P)[subscripts >_0] of a partial flag ... 
Towards a functor between affine and finite Hecke categories in type A
(Massachusetts Institute of Technology, 2018)In this thesis we construct a functor from the perfect subcategory of the coherent version of the affine Hecke category in type A to the finite constructible Hecke category, partly categorifying a certain natural homomorphism ... 
Towards an integrated understanding of neural networks
(Massachusetts Institute of Technology, 2018)Neural networks underpin both biological intelligence and modern Al systems, yet there is relatively little theory for how the observed behavior of these networks arises. Even the connectivity of neurons within the brain ... 
Towards characterizing morphims between high dimensional hypersurfaces
(Massachusetts Institute of Technology, 2003)This thesis is organized into two papers. All results are proven over an algebraically closed field of characteristic zero. Paper 1 concerns morphisms between hypersurfaces in Pn, n =/> 4. We show that if the two hypersurfaces ... 
Traffic allocation methods for use in impact fee assessment
(Massachusetts Institute of Technology, 1987) 
A trajectory equation for walking droplets : hydrodynamic pilotwave theory
(Massachusetts Institute of Technology, 2014)Yves Couder and coworkers have demonstrated that millimetric droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm, including singleparticle ... 
Transfer for compact lie groups, induced representations, and braid relations
(Massachusetts Institute of Technology, 1988) 
Transport methods and universality for [beta]ensembles
(Massachusetts Institute of Technology, 2018)In this thesis, we investigate the local and global properties of the eigenvalues of [beta]ensembles. A lot of attention has been drawn recently on the universal properties of [beta]ensembles, and how their local statistics ... 
Transportlimited aggregation and dense granular flow
(Massachusetts Institute of Technology, 2005)In this thesis, transport of interacting particles is studied in two different physical systems. In the first part, a model for interfacial growth driven by general transport processes is proposed to generalize Laplacian ... 
Traveling salesman path problems
(Massachusetts Institute of Technology, 2005)In the Traveling Salesman Path Problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination ...