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#### Limit linear series in positive characteristic and Frobenius-unstable 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 Frobenius-unstable bundles for C general, and hence obtaining a self-contained proof of the resulting formula for the degree of V₂.

#### Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients

(Massachusetts Institute of Technology, 2004)

Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers and Littlewood-Richardson coefficients (the type A weight multiplicities and Clebsch-Gordan coefficients). ...

#### Facility location and the analysis of algorithms through factor-revealing programs

(Massachusetts Institute of Technology, 2004)

In the metric uncapacitated facility location problem (UFLP), we are given a set of clients, a set of facilities, an opening cost for each facility, and a connection cost between each client and each facility satisfying ...

#### Relative Hilbert scheme methods in pseudoholomorphic geometry

(Massachusetts Institute of Technology, 2004)

This thesis takes up a program initiated by S. Donaldson and I. Smith aimed at using symplectic Lefschetz fibration techniques to obtain information about pseudoholomorphic curves in symplectic 4-manifolds. Donaldson and ...

#### Frobenius transfers and p-local finite groups

(Massachusetts Institute of Technology, 2004)

In this thesis we explore the possibility of defining the p-local finite groups of Broto, Levi and Oliver in terms of their classifying spaces. More precisely, we consider the question posed by Haynes Miller, whether an ...

#### Geometric and algebraic properties of polyomino tilings

(Massachusetts Institute of Technology, 2004)

In this thesis we study tilings of regions on the square grid by polyominoes. A polyomino is any connected shape formed from a union of grid cells, and a tiling of a region is a collection of polyominoes lying in the region ...

#### A compact moduli space for Cohen-Macaulay curves in projective space

(Massachusetts Institute of Technology, 2004)

We define a moduli functor parametrizing finite maps from a projective (locally) Cohen-Macaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most ...

#### Chain and antichain enumeration in posets, and b-ary partitions

(Massachusetts Institute of Technology, 2004)

The Greene-Kleitman theorem says that the lengths of chains and antichains in any poset are intimately related via an integer partition, but very little is known about the partition [lambda](P) for most posets P. Our first ...

#### Analytic aspects of periodic instantons

(Massachusetts Institute of Technology, 2004)

The main result is a computation of the Nahm transform of a SU(2)-instanton over R x T³, called spatially-periodic instanton. It is a singular monopole over T³, a solution to the Bogomolny equation, whose rank is computed ...

#### Derived algebraic geometry

(Massachusetts Institute of Technology, 2004)

The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. ...