A skew brane is a codimension 2 submanifold in affine space such that the tangent spaces at any two distinct points are not parallel. We show that if an oriented closed manifold has a non-zero Euler characteristic χ then it is not a skew brane; generically, the number of oppositely oriented pairs of parallel tangent spaces is not less than χ/4. We give a version of this result for immersed surf...

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

We survey the techniques used in our recent resolution of the Kadison– Singer problem and proof of existence of Ramanujan Graphs of every degree: mixed characteristic polynomials and the method of interlacing families of polynomials. To demonstrate the method of interlacing families of polynomials, we give a simple proof of Bourgain and Tzafriri’s restricted invertibility principle in the isotr...

The amount of information produced in the last decades has grown notably. Much of this information only exists in the form of electronic documents and it has often to be stored for long periods. Therefore, digital archives are increasingly needed. However, for the documents to remain trustworthy while they are archived, they need to be protected by the archivists. Important protection goals tha...

In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. In contrast with the principal–agent models that are extended within, here the presence of ties in the agents’ best–response correspondences yields discontinuous payoff function...

We consider two-dimensional water waves of infinite depth, periodic in the horizontal direction. It has been proven by Wu (in the slightly different nonperiodic setting) that solutions to this initial value problem exist in the absence of surface tension. Recently Ambrose has proven that solutions exist when surface tension is taken into account. In this paper, we provide a shorter, more elemen...

The semantics of name-passing calculi is often defined employing coalgebraic models over presheaf categories. This elegant theory lacks finiteness properties, hence it is not apt to implementation. Coalgebras over named sets, called history-dependent automata, are better suited for the purpose due to locality of names. A theory of behavioural functors for named sets is still lacking: the semant...

We study the stability/instability of the subsonic travelling waves of the Nonlinear Schrödinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the GrillakisShatah-Strauss theory, proof of existence of an unstable eigenvalue via an Evans function) or stability. For the later, we show how to construct in a systematic way a Liapounov functional fo...