Browsing Mathematics  Ph.D. / Sc.D. by Title
Now showing items 486505 of 746

The padic local langlands conjecture
(Massachusetts Institute of Technology, 2005)Let k be a padic field. Split reductive groups over k can be described up to k isomorphism by a based root datum alone, but other groups, called rational forms of the split group, involve an action of the Galois group ... 
padic modular forms over Shimura curves over Q
(Massachusetts Institute of Technology, 1999) 
Parabolic equations without a minimum principle
(Massachusetts Institute of Technology, 2007)In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a twopoint boundary value problem for a one dimensional diffusion equation. We show the uniqueness and ... 
Parabolic Springer resolution
(Massachusetts Institute of Technology, 2016)Let G be a reductive group over a field k = k. Let P be a parabolic subgroup. We construct a functor Groupoid ... is a connected space, which induces an action of generalizing a classical result. It is also a part of a ... 
A parallel processing model of musical structures.
(Massachusetts Institute of Technology, 1971) 
Parallel repetition of multiparty and quantum games via anchoring and fortification
(Massachusetts Institute of Technology, 2017)Parallel repetition is a fundamental operation for amplifying the hardness inherent in multiplayer games. Through the efforts of many researchers in the past two decades (e.g. Feige, Kilian, Raz, Holentstein, Rao, Braverman, ... 
Parallelism on psurfaces in Riemannian manifolds.
(Massachusetts Institute of Technology, 1965) 
Parametrized higher category theory
(Massachusetts Institute of Technology, 2017)We develop foundations for the category theory of [infinity]categories parametrized by a base occategory. Our main contribution is a theory of parametrized homotopy limits and colimits, which recovers and extends the ... 
Partition identity bijections related to signbalance and rank
(Massachusetts Institute of Technology, 2005)In this thesis, we present bijections proving partitions identities. In the first part, we generalize Dyson's definition of rank to partitions with successive Durfee squares. We then present two symmetries for this new ... 
Path integrals on ultrametric spaces
(Massachusetts Institute of Technology, 1994) 
Pattern avoidance for alternating permutations and reading words of tableaux
(Massachusetts Institute of Technology, 2012)We consider a variety of questions related to pattern avoidance in alternating permutations and generalizations thereof. We give bijective enumerations of alternating permutations avoiding patterns of length 3 and 4, of ... 
Patternavoidance in binary fillings of grid shapes
(Massachusetts Institute of Technology, 2009)A grid shape is a set of boxes chosen from a square grid; any Young diagram is an example. We consider a notion of patternavoidance for 01 fillings of grid shapes, which generalizes permutation patternavoidance. A filling ... 
Permutations statistics of indexed and poset permutations
(Massachusetts Institute of Technology, 1992) 
Permutations with forbidden subsequences, and, stacksortable permutations
(Massachusetts Institute of Technology, 1990) 
The perturbation theory of some Volterra operators
(Massachusetts Institute of Technology, 1963) 
The Picard scheme of a curve and its compactification
(Massachusetts Institute of Technology, 1981) 
The pilotwave dynamics of walking droplets in confinement
(Massachusetts Institute of Technology, 2015)A decade ago, Yves Couder and coworkers discovered that millimetric droplets can walk on a vibrated fluid bath, and that these walking droplets or "walkers" display several features reminiscent of quantum particles. We ... 
Point processes of representation theoretic origin
(Massachusetts Institute of Technology, 2019)There are two parts to this thesis. In the first part we compute the correlation functions of the 4parameter family of BC type Zmeasures. The result is given explicitly in terms of Gauss's hypergeometric function. The ... 
Polynomial maps with applications to combinatorics and probability theory
(Massachusetts Institute of Technology, 1994) 
Polynomial partitioning and incidence problems in higher dimensions
(Massachusetts Institute of Technology, 2017)Incidence geometry is the study of the intersection patterns of simple geometric objects. One of the breakthroughs in this field is the polynomial partitioning technique introduced by Guth and Katz. In this thesis, I will ...