Browsing Mathematics  Ph.D. / Sc.D. by Title
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Ktheoretic Hall algebras for quivers with potential
(Massachusetts Institute of Technology, 2020)Given a quiver with potential (Q, W), KontsevichSoibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q, W). As shown by DavisonMeinhardt, this algebra comes with a filtration whose ... 
Ktheory and index theory on manifolds with boundary
(Massachusetts Institute of Technology, 1991) 
Kac's random walk and coupon collector's process on posets
(Massachusetts Institute of Technology, 2008)In the first part of this work, we study a long standing open problem on the mixing time of Kac's random walk on SO(n, R) by random rotations. We obtain an upper bound mix = O (n2.5 log n) for the weak convergence which ... 
KazhdanLusztig polynomials and cells for affine Weyl groups and unequal parameters
(Massachusetts Institute of Technology, 1996) 
Kähler structures on cotangent bundles of real analytic Riemannian manifolds
(Massachusetts Institute of Technology, 1990) 
L2(q) and the rank two lie groups : their construction, geometry, and character formulas
(Massachusetts Institute of Technology, 1994) 
The Laplacian for spaces with conelike singularities
(Massachusetts Institute of Technology, 1990) 
Large, noisy, and incomplete : mathematics for modern biology
(Massachusetts Institute of Technology, 2009)In recent years there has been a great deal of new activity at the interface of biology and computation. This has largely been driven by the massive in flux of data from new experimental technologies, particularly ... 
Largescale optimization Methods for datascience applications
(Massachusetts Institute of Technology, 2019)In this thesis, we present several contributions of large scale optimization methods with the applications in data science and machine learning. In the first part, we present new computational methods and associated ... 
The lebesgue density theorem in abstract measure spaces
(Massachusetts Institute of Technology, 1947) 
Lie algebra cohomology and the representations of semisimple Lie groups
(Massachusetts Institute of Technology, 1976) 
Limit linear series in positive characteristic and Frobeniusunstable vector bundles on curves
(Massachusetts Institute of Technology, 2004)(cont.) yield a new proof of a result of Mochizuki yield a new proof of a result of Mochizuki Frobeniusunstable bundles for C general, and hence obtaining a selfcontained proof of the resulting formula for the degree of V₂. 
Limiting behavior of Ricci flows
(Massachusetts Institute of Technology, 2004)Consider the unnormalized Ricci flow ...Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times ... then the solution can be extended beyond T. In the thesis we prove that ... 
Lines on Fano hypersurfaces
(Massachusetts Institute of Technology, 2003)In this thesis, the Hilbert scheme of lines on smooth hypersurfaces is studied. The main result is that the Hilbert scheme of lines on any smooth Fano hypersurface of degree d =/< 6 in ... has the expected dimension 2n  ... 
Link complements and imaginary quadratic number fields
(Massachusetts Institute of Technology, 1981) 
Local complex singularity exponents for isolated singularities
(Massachusetts Institute of Technology, 2004)In this thesis, I studied the stability of local complex'singularity exponents (lcse) for holomorphic functions whose zero sets have only isolated singularities. For a given holomorphic function f defined on a neighborhood ... 
Localrules based topological modeling of tetrahedral ceramic network structures
(Massachusetts Institute of Technology, 1998) 
LocaltoGlobal extensions for wildly ramified covers of curves
(Massachusetts Institute of Technology, 2018)Given a Galois cover of curves X > Y with Galois group G which is totally ramified at a point x and unramified elsewhere, restriction to the punctured formal neighborhood of x induces a Galois extension of Laurent series ... 
Localization at b₁₀ in the stable category of comodules over the Steenrod reduced powers
(Massachusetts Institute of Technology, 2018)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 plocal sphere is its rationalization, and the ... 
Localization genus of classifying spaces
(Massachusetts Institute of Technology, 2002)We show that for a large class of torsionfree classifying spaces, Ktheory filtered ring is an invariant of the genus. We apply this result in two ways. First, we use it to show that the powerseries ring on n indeterminates ...