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#### Closed quasigeodesics, escaping from polygons, and conflict-free graph coloring

(Massachusetts Institute of Technology, 2018)

Closed quasigeodesics. A closed quasigeodesic on the surface of a polyhedron is a loop which can everywhere locally be unfolded to a straight line: thus, it's straight on faces, uniquely determined on edges, and has as ...

#### Quillen cohomology of pi-algebras and application to their realization by Martin Frankland.

(Massachusetts Institute of Technology, 2010)

We use the obstruction theory of Blanc-Dwyer-Goerss to study the realization space of certain - algebras with 2 non-trivial groups. The main technical tool is a result on the Quillen cohomology of truncated -algebras, which ...

#### 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 ...

#### Diagrams of affine permutations and their labellings

(Massachusetts Institute of Technology, 2013)

We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by Fomin- Greene-Reiner-Shimozono, and we extend this notion to ...

#### Geometric Langlands in prime characteristic

(Massachusetts Institute of Technology, 2012)

Let C be a smooth projective curve over an algebraically closed field k of sufficiently large characteristic. Let G be a semisimple algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the ...

#### Geometric algorithms for reconfigurable structures

(Massachusetts Institute of Technology, 2011)

In this thesis, we study three problems related to geometric algorithms of reconfigurable structures. In the first problem, strip folding, we present two universal hinge patterns for a strip of material that enable the ...

#### Algorithms for genomics and genetics : compression-accelerated search and admixture analysis

(Massachusetts Institute of Technology, 2013)

Rapid advances in next-generation sequencing technologies are revolutionizing genomics, with data sets at the scale of thousands of human genomes fast becoming the norm. These technological leaps promise to enable corresponding ...

#### Monomization of power Ideals and parking functions

(Massachusetts Institute of Technology, 2010)

A zonotopal algebra is the quotient of a polynomial ring by an ideal generated by powers of linear forms which are derived from a zonotope, or dually it's hyperplane arrangement. In the case that the hyperplane arrangement ...

#### Matrix probing, skeleton decompositions, and sparse Fourier transform

(Massachusetts Institute of Technology, 2013)

In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...

#### On affine embeddings of reductive groups

(Massachusetts Institute of Technology, 2011)

In this thesis, we study the properties and the classification of embeddings of homogeneous spaces, especially the case of affine normal embeddings of reductive groups. We might guess that as in the case of toric varieties, ...