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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 ...
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 ...
Testing and learning Boolean functions
(Massachusetts Institute of Technology, 2009)
Given a function f on n inputs, we consider the problem of testing whether f belongs to a concept class C, or is far from every member of C. An algorithm that achieves this goal for a particular C is called a property ...
Towards characterizing morphims between high dimensional hypersurfaces
(Massachusetts Institute of Technology, 2003)
This thesis is organized into two papers. All results are proven over an algebraically closed field of characteristic zero. Paper 1 concerns morphisms between hypersurfaces in Pn, n =/> 4. We show that if the two hypersurfaces ...
Smooth K-theory and locally convex algebras
(Massachusetts Institute of Technology, 2003)
In this thesis, we improve the loop linearization process from the classical article of Atiyah and Bott on Bott periodicity. The linearization process is made explicit in terms of formulae for smooth loops. Using this ...
The instability of time-dependent jets
(Massachusetts Institute of Technology, 2002)
The central focus of my thesis is to study the instability jets of various complexity by analyzing the linear and nonlinear dynamics. We applied this methodology to four different situations in order to learn the following. ...
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). ...
Symplectic isotopy for cuspidal curves
(Massachusetts Institute of Technology, 2005)
This work has three purposes. The first one is to prove unobstructedness of deformation of pseudoholomorphic curves with cusps and tacnodes. We show that if the first Chern class of a 4-dimensional symplectic manifold is ...
Some subvarieties of the De Concini-Procesi compactification
(Massachusetts Institute of Technology, 2005)
This thesis is concerned with the intrinsic structure of the De Concini-Procesi compactification of semi-simple adjoint algebraic groups and some relations with other topics of algebraic groups. In chapter 1, we study the ...
Expressions for the generating function of the Donaldson invariants for CP²
(Massachusetts Institute of Technology, 2007)
The Donaldson invariants for CP2 were obtained as the u-plane integral from a N = 2 supersymmetric topological U(1)-gauge theory by Moore and Witten. We derive the generating function for the Donaldson invariants of CP2 ...