Let R be an o-minimal field and V a proper convex subring of R with residue field k. Let kind be the expansion of the residue field by the standard parts of definable relations on R. We investigate the definable sets in ...

We utilize Floer theory and an index relation relating the Maslov index, Morse index and Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function to state and prove some nonexistence results ...

In this thesis, we examine a conjecture of N. Boston which says that given an odd irreducible mod p Galois representation, there exist lifts which behave according to prescribed behavior when restricted to inertia subgroups ...

Let C be a class of finite groups closed under the operations of taking subgroups, quotients, and extensions. Let H and K be pro-C-groups and let $G=H*K$ be their free pro-C-product. An open question in the theory of ...

In this thesis we give a generalization of a theorem of C. Fefferman and E. M. Stein on maximal operators on the Hardy classes of tempered distributions H('p)((//R)('n)) for 0 < p (LESSTHEQ) 1. Fix p, 0 < p (LESSTHEQ) ...