BACKGROUND
Percutaneous aortic valve replacement represents an endovascular alternative to conventional open heart surgery without the need for sternotomy, aortotomy, or cardiopulmonary bypass.
… (More)

OBJECTIVES
Transcatheter aortic valve replacement (AVR) is a promising approach to aortic valve disease. The implications of this new therapy are not entirely known. We describe the potential for the… (More)

Suppose that f (resp. g) is a modular form of integral (resp. half-integral) weight with coefficients in the ring of integers OK of a number field K. For any ideal m ⊂ OK , we bound the first prime p… (More)

Let E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on Γ0(N) associated to it by modularity. Building on an idea of S. Zhang, the article [DRS] describes the construction of… (More)

1.1. Shimura varieties are like a brightly colored toy. The motivation for their study comes from considering moduli spaces of Hodge structures. LetX be a smooth, complex, projective variety of… (More)

Recall that our ultimate goal is to prove a modularity lifting theorem (stated in Andrew’s talk “Overview of the Taylor-Wiles method”), which we have reduced to showing an R = T theorem. That is, we… (More)

Transcatheter aortic valve implantation has evolved rapidly since the first successful procedure over 5 years ago. The femoral arterial and the left ventricular apical approaches are currently… (More)

v det([1− ρ(Frobv)q v ]|W Iv )−1, W Iv = subspace of W fixed by inertia at v. Grothendieck gave a related description of ζ∗ X using continuous p-adic representations GF → GL(H ét,c(XF ,Qp)) =: GL(W… (More)