Browsing Department of Mathematics by Title
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Coherent sheaves on varieties arising in Springer theory, and category 0
(Massachusetts Institute of Technology, 2015)In this thesis, we will study three topics related to Springer theory (specifically, the geometry of the exotic nilpotent cone, and twoblock Springer fibers), and stability conditions for category 0. In the first chapter, ... 
A cohomological interpretation of the scalar product on the elliptic class functions
(Massachusetts Institute of Technology, 1994) 
The cohomology of weight varities
(Massachusetts Institute of Technology, 1999) 
Coleman integration for hyperelliptic curves : algorithms and applications
(Massachusetts Institute of Technology, 2011)The Colemani integral is a padice 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 ... 
Color image quantization for frame buffer display
(Massachusetts Institute of Technology, 1980) 
Coloring with defects
(Massachusetts Institute of Technology, 1995) 
Combinatorial aspects of polytope slices
(Massachusetts Institute of Technology, 2013)We studies two examples of polytope slices, hypersimplices as slices of hypercubes and edge polytopes. For hypersimplices, the main result is a proof of a conjecture by R. Stanley which gives an interpretation of the Ehrhart ... 
Combinatorial aspects of the theory of canonical forms
(Massachusetts Institute of Technology, 1996) 
Combinatorial aspects of total positivity
(Massachusetts Institute of Technology, 2005)In this thesis I study combinatorial aspects of an emerging field known as total positivity. The classical theory of total positivity concerns matrices in which all minors are nonnegative. While this theory was pioneered ... 
Combinatorial decompositions of characters of SL(n,C)
(Massachusetts Institute of Technology, 1985) 
Combinatorial enumeration of weighted Catalan numbers
(Massachusetts Institute of Technology, 2010)This thesis is devoted to the divisibility property of weighted Catalan and Motzkin numbers and its applications. In Chapter 1, the definitions and properties of weighted Catalan and Motzkin numbers are introduced. Chapter ... 
A combinatorial flag space
(Massachusetts Institute of Technology, 1994) 
Combinatorial incremental problems
(Massachusetts Institute of Technology, 2018)We study the class of Incremental Combinatorial optimization problems, where solutions are evaluated as they are built, as opposed to only measuring the performance of the final solution. Even though many of these problems ... 
Combinatorial methods in multilinear algebra
(Massachusetts Institute of Technology, 1993) 
Combinatorial properties of shifted complexes
(Massachusetts Institute of Technology, 2003)In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face ... 
Combinatorics in Schubert varieties and Specht modules
(Massachusetts Institute of Technology, 2011)This thesis consists of two parts. Both parts are devoted to finding links between geometric/algebraic objects and combinatorial objects. In the first part of the thesis, we link Schubert varieties in the full flag variety ... 
Combinatorics of acyclic orientations of graphs : algebra, geometry and probability
(Massachusetts Institute of Technology, 2015)This thesis studies aspects of the set of acyclic orientations of a simple undirected graph. Acyclic orientations of a graph may be readily obtained from bijective labellings of its vertexset with a totally ordered set, ... 
The combinatorics of adinkras
(Massachusetts Institute of Technology, 2013)Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory ... 
Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields
(Massachusetts Institute of Technology, 2012)In the first part of this thesis we study factorizations of the permutation (1; 2,..., n) into k factors of given cycle type. Using representation theory, Jackson obtained for each k an elegant formula for counting these ... 
Combinatorics of determinantal identities
(Massachusetts Institute of Technology, 2008)In this thesis, we apply combinatorial means for proving and generalizing classical determinantal identities. In Chapter 1, we present some historical background and discuss the algebraic framework we employ throughout the ...