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Now showing items 1-10 of 29

#### Probabilistic methods in combinatorial and stochastic optimization

(Massachusetts Institute of Technology, 2005)

(cont.) Packing/Covering problems, we prove upper and lower bounds on the adaptivity gap depending on the dimension. We also design polynomial-time algorithms achieving near-optimal approximation guarantees with respect ...

#### New examples of four dimensional AS-regular algebras

(Massachusetts Institute of Technology, 2005)

This thesis deals with AS-regular algebras, first defined by Michael Artin and William Schelter in Graded Algebras of Global Dimension 3. All such algebras of dimension three have been classified, but the corresponding ...

#### Partition identity bijections related to sign-balance and rank

(Massachusetts Institute of Technology, 2005)

In this thesis, we present bijections proving partitions identities. In the first part, we generalize Dyson's definition of rank to partitions with successive Durfee squares. We then present two symmetries for this new ...

#### The tautological classes of the moduli spaces of stable maps to flag varieties

(Massachusetts Institute of Technology, 2005)

We study the tautological classes of the Kontsevich-Manin moduli spaces of genus 0 stable maps to SL flag varieties. We prove that the rational cohomology and rational Chow rings of these spaces are isomorphic and that ...

#### Double affine Hecke algebras and noncommutative geometry

(Massachusetts Institute of Technology, 2005)

In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical subalgebra eH(t, 1)e of the Double Affine Hecke algebra H(t, ...

#### Transport-limited 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 ...

#### The Severi problem for rational curves on del Pezzo surfaces

(Massachusetts Institute of Technology, 2005)

Let X be a smooth projective surface and choose a curve C on X. Let VC be the set of all irreducible divisors on X linearly equivalent to C whose normalization is a rational curve. The Severi problem for rational curves ...

#### The p-adic local langlands conjecture

(Massachusetts Institute of Technology, 2005)

Let k be a p-adic field. Split reductive groups over k can be described up to k- isomorphism by a based root datum alone, but other groups, called rational forms of the split group, involve an action of the Galois group ...

#### 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 ...

#### The bidimensionality theory and its algorithmic applications

(Massachusetts Institute of Technology, 2005)

Our newly developing theory of bidimensional graph problems provides general techniques for designing efficient fixed-parameter algorithms and approximation algorithms for NP- hard graph problems in broad classes of graphs. ...