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Now showing items 1-10 of 16

#### Orbital varieties and unipotent representations of classical semisimple Lie group

(Massachusetts Institute of Technology, 2001)

Let G be a complex semi-simple and classical Lie group. The notion of a Lagrangian covering can be used to extend the method of polarizing a nilpotent coadjoint orbit to obtain a unitary representation of G. W. Graham and ...

#### Decidable prime models

(Massachusetts Institute of Technology, 2001)

A set S of types over a theory T is strongly free if for all subsets X [strict subset] S, there is a countable model of T which realizes X and omits S\X. Throughout, all theories are assumed complete and consistent unless ...

#### Invariants of Legendrian links

(Massachusetts Institute of Technology, 2001)

We introduce new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is ...

#### The eta invariant for manifolds with boundary and holomorphic maps into the the restricted Grassmannian

(Massachusetts Institute of Technology, 2001)

#### A homotopy theory for stacks

(Massachusetts Institute of Technology, 2001)

We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal ...

#### Character sheaves on symmetric spaces

(Massachusetts Institute of Technology, 2001)

Inspired by the work of Lusztig, we apply the theory of character sheaves on a symmetric space (h la Ginzburg and Grojnowski) to the problem of determining the spherical functions (averages of the irreducible characters) ...

#### Calibrations and minimal Lagrangian submanifolds

(Massachusetts Institute of Technology, 2001)

This thesis will be concerned with the geometry of minimal submanifolds in certain Riemannian manifolds which possess some special geometric structure. Those Riemannian manifolds will fall into one of the following categories: ...

#### Noncommutative symmetric functions of type B

(Massachusetts Institute of Technology, 2001)

The noncommutative symmetric functions Sym of Gelfand et al. give not only a lifting of the well-developed commutative theory of symmetric functions to the non-commutative level, but also relate the descent algebras of ...

#### Probability theory on Galton-Watson trees

(Massachusetts Institute of Technology, 2001)

By a Galton-Watson tree T we mean an infinite rooted tree that starts with one node and where each node has a random number of children independently of the rest of the tree. In the first chapter of this thesis, we prove ...

#### Mathematical methods for protein structural motif recognition

(Massachusetts Institute of Technology, 2001)

In this thesis, two algorithms for protein structural motif recognition are presented. A program is described which successfully recognizes the occurrence of the right-handed parallel 8-helix fold from protein sequence ...