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Now showing items 1-10 of 191

#### Tight contact structures on small Seifert spaces

(Massachusetts Institute of Technology, 2004)

In this thesis, we discuss the relation between the Euler number of a tight contact small Seifert space and the contact framing of Legendrian vertical circles in it, and apply this relation to classify up to isotopy tight ...

#### Nonparametric modeling of dependencies for spatial interpolation

(Massachusetts Institute of Technology, 2000)

Crucial in spatial interpolation of stochastic processes is the determination of the underlying dependency of the data. The dependency can be represented by an underlying covariogram, variogram, or generalized covariogram. ...

#### [rho]-compact groups as framed manifolds

(Massachusetts Institute of Technology, 2002)

We describe a natural way to associate to any [rho]-compact group an element of the [rho]-local stable stems, which, applied to the [rho]-completion of a compact Lie group G, coincides with the element represented by the ...

#### Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions

(Massachusetts Institute of Technology, 2002)

Enumerative geometry of algebraic varieties is a fascinating field of mathematics that dates back to the nineteenth century. We introduce new computational tools into this field that are motivated by recent progress in ...

#### Localization genus of classifying spaces

(Massachusetts Institute of Technology, 2002)

We show that for a large class of torsionfree classifying spaces, K-theory filtered ring is an invariant of the genus. We apply this result in two ways. First, we use it to show that the powerseries ring on n indeterminates ...

#### Affine quantum algebras, Weyl groups and constructible functions

(Massachusetts Institute of Technology, 2002)

This thesis consists of two parts. In the first part we study the affine quantum group of type A, giving a geometric description of its natural inner product, and studying the theory of cells attached to the canonical ...

#### The involution principle and h-positive symmetric functions

(Massachusetts Institute of Technology, 2001)

The criterion of h-positivity corresponds to the criterion that a polynomial representation of the general linear group of V is a sum of tensor products of symmetric powers of V. Expanding the iterated exponential function ...

#### Modeling and prediction of sunspot cycles

(Massachusetts Institute of Technology, 2001)

Solar activity, as indexed by sunspots, has a cycle of length varying from about 9 to 13 years. Statisticians have fitted several models to predict sunspot numbers one year ahead. We instead focus on predicting the magnitudes ...

#### Noncommutative ring spectra

(Massachusetts Institute of Technology, 2006)

Let A be an Ax ring spectrum. We give an explicit construction of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another family of polyhedra called cyclohedra. Using this construction ...

#### Topological Hochschild homology of twisted group algebras

(Massachusetts Institute of Technology, 2006)

Let G be a group and A be a ring. There is a stable equivalence of orthogonal spectra ... between the topological Hochschild homology of the group algebra A[G] and the smash product of the topological Hochschild homology ...