If ρ: Gal(Qac/Q) → GL2(C) is a continuous odd irreducible representation with nonsolvable image, then under certain local hypotheses we prove that is the representation associated to a weight 1 modular form and hence ...

This paper presents the first examples of K3 surface automorphisms \(f : X \rightarrow X\) with Siegel disks (domains on which f acts by an irrational rotation). The set of such examples is countable, and the surface \(X\) ...

We prove that the L-function of any regular (distinct Hodge numbers), irreducible, rank two motive over the rational numbers has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.

We prove the compatibility of local and global Langlands correspondences for \(GL_n\), which was proved up to semisimplification in M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, ...

We show that the times separating the birth of benign, invasive, and metastatic tumor cells can be determined by analysis of the mutations they have in common. When combined with prior clinical observations, these analyses ...

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all ...

Let \(M\) be a closed, connected, orientable 3-manifold. The purpose of this paper is to study the Seiberg-Witten Floer homology of \(M\) given that \(S^1 \times M\) admits a symplectic form.