Browsing Department of Mathematics by Title
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Conformal loop ensembles and the Gaussian free field
(Massachusetts Institute of Technology, 2015)The study of twodimensional statistical physics models leads naturally to the analysis of various conformally invariant mathematical objects, such as the Gaussian free field, the SchrammLoewner evolution, and the conformal ... 
Connections on conformal blocks
(Massachusetts Institute of Technology, 2011)For an algebraic group G and a projective curve X, we study the category of Dmodules on the moduli space Bung of principal Gbundles on X using ideas from conformal field theory. We describe this category in terms of the ... 
Constraining the QSO luminosity function using gravitational lensing statistics
(Massachusetts Institute of Technology, 2004)In this thesis we use gravitational lensing statistics to constrain the QSO luminosity function at a variety of redshifts. We present a theoretical discussion of gravitational lensing statistics and illustrate how high ... 
Constructibility in impredicative set theory.
(Massachusetts Institute of Technology, 1965) 
Continuousspin Ising ferromagnets.
(Massachusetts Institute of Technology, 1976) 
Contributions on secretary problems, independent sets of rectangles and related problems
(Massachusetts Institute of Technology, 2011)We study three problems arising from different areas of combinatorial optimization. We first study the matroid secretary problem, which is a generalization proposed by Babaioff, Immorlica and Kleinberg of the classical ... 
Contributions to higher recursion theory
(Massachusetts Institute of Technology, 1993) 
Contributions to recursion theory on higher types (or, a proof of Harrington's conjecture),
(Massachusetts Institute of Technology, 1973) 
Contributions to the theory of Ehrhart polynomials
(Massachusetts Institute of Technology, 2006)In this thesis, we study the Ehrhart polynomials of different polytopes. In the 1960's Eugene Ehrhart discovered that for any rational dpolytope P, the number of lattice points, i(P,m), in the mth dilated polytope mP is ... 
Contributions to the variational theory of convection
(Massachusetts Institute of Technology, 1996) 
Convergence of empirical probability measures
(Massachusetts Institute of Technology, 1982) 
Convergence of the homology spectral sequence of a cosimplical space
(Massachusetts Institute of Technology, 1995) 
Convexity and duality in optimization theory
(Massachusetts Institute of Technology, 1977) 
Convexity theorems for diametral families of sets
(Massachusetts Institute of Technology, 1992) 
A counterexample to a conjecture of Serre
(Massachusetts Institute of Technology, 1980) 
Counting elliptic curves of bounded Faltings height
(Massachusetts Institute of Technology, 2016)Because many invariants and properties of elliptic curves are difficult to understand directly, the study of arithmetic statistics instead looks at what happens "on average", using heights to make this notion rigorous. ... 
Coxeter systems, multiplicity free representations, and twisted KazhdanLusztig Theory
(Massachusetts Institute of Technology, 2013)This thesis considers three topics related to the representations of Coxeter systems, their Hecke algebras, and related groups. The first topic concerns the construction of generalized involution models, as defined by Bump ... 
Critical phenomena in evolutionary dynamics
(Massachusetts Institute of Technology, 2010)This thesis consists of five essays on evolutionary dynamics. In Chapters 1 and 2, we study the evolution of trust from the perspective of game theory. In the trust game, two players have a chance to win a sum of money. ... 
Cut structures and randomized algorithms in edgeconnectivity problems
(Massachusetts Institute of Technology, 1997) 
Cycle types of permutations with restricted positions and a characterization of a new class of interval orders
(Massachusetts Institute of Technology, 1996)