Malon, Christopher D(Massachusetts Institute of Technology, 2005)
Let k be a p-adic 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 ...
Pang, Huadong(Massachusetts Institute of Technology, 2007)
In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and ...
Boger, D. (Dorin)(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 ...
Bavarian, Mohammad(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, ...
Shah, Jay (Jay Hungfai Gautam)(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 ...
Boulet, Cilanne Emily(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 ...
Lewis, Joel Brewster(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 ...
Spiridonov, Alexey(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 pattern-avoidance for 0-1 fillings of grid shapes, which generalizes permutation pattern-avoidance. A filling ...
This article introduces, informally, the substance and the spirit of
Grothendieck's theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger ...