Some consequences of Schanuel's conjecture

We study the algebraic independence of two inductively defined sets. Under the hypothesis of Schanuel's conjecture we prove that the exponential power tower E and its related logarithmic tower L are linearly disjoint.     

Phase Retrievable Projective Representation Frames for Finite Abelian Groups

Journal of Fourier Analysis and Applications - We consider the problem of characterizing projective representations that admit frame vectors with the maximal span property, a property that allows...     

Multiplicity one of regular Serre weights

We consider a potentially Barsotti-Tate deformation problem of a modular Galois representation. By constructing a Diamond-Taylor-Wiles system, we prove an R = T theorem and a multiplicity one result in characteristic 0. Applying this result, we then prove a multiplicity one result in characteristic p, which provides certain evidence for a conjecture of Breuil.