This doctoral dissertation is on the theory of Minimal Surfaces and of singularities in Mean Curvature Flow, for smooth submanifolds Y" in an ambient Riemannian (n+ 1)-manifold Nn+1, including: (1) New asymptotically conical ...

We present new techniques for generation of unstructured meshes for geometries specified by implicit functions. An initial mesh is iteratively improved by solving for a force equilibrium in the element edges, and the ...

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 ...

The Scott rank of a countable structure A, denoted sr(A), was observed by Nadel to be at most wA + 1, where wA4 is the least ordinal not recursive in A. Let T be weakly scattered and L(a,T) be E2-admissible. We give a ...

There are two algebras associated to a reductive Lie algebra g: the De Concini- Kac quantum algebra and the Kac-Moody Lie algebra. Recent results show that the principle block of De Concini -Kac quantum algebra at an odd ...

Fix integers n and b with n =/> 3 and 1 =/< b < n - 1. Let k be an algebraically closed field. Consider the moduli space X of hypersurfaces in P" of fixed degree I whose singular locus is at least b-dimensional. We prove ...

In this thesis we give a probabilistic proof of the Morse inequalities in the nondegenerate and degenerate case. For the nondegenerate case the kernel associated with the Witten Laplacian has an expression via the Malliavin ...