Related papers: Grothendieck's Double Limit Theorem and Model Theo…

This is the first in a series of papers on type I Howe duality for finite fields, concerning the restriction of an oscillator representation of the symplectic group to a product of a symplectic and an orthogonal group. The goal of the…

We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many…

This paper attempts to relate some ideas of Grothendieck in his Esquisse d'un programme and some of the recent results on 2-dimensional topology and geometry. Especially, we shall discuss the Teichm\"uller theory, the mapping class groups,…

In this paper, we study the problem, initiated by Grothendieck, of the transfer of the properties of two preadic noetherian algebras over a field to their completed tensor product.

This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It…

One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…

The quasi-two-dimensional modeling of the small adiabatic perturbation on the background of the stationary configuration of the selfgravitating gas with the weak transverse nonhomogeneity approximation is presented. The space periodic…

This technical report yields detailed calculations of the paper [1] (B. Bid\'egaray-Fesquet, "Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations", Technical report, LMC-IMAG, 2005) which have been however automated…

We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…

It has long been accepted that the foundations of Grothendieck duality are complicated. This has changed recently. By "Grothendieck duality" we mean what, in the old literature, used to go by the name "coherent duality". This isn't to be…

The generalization to N colors of a recently proposed non unitary two color model for the gravitational interaction in non relativistic quantum mechanics is considered. The N->Infinity limit is proven to be equivalent to the…

In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to compare and contrast the different results by proposing a…

We exhibit proofs of two ergodic-theoretic results in the study of multiple recurrence using an analog of the density-increment argument of Roth and Gowers: Furstenberg's Multiple Recurrence Theorem (which implies Szemer\'edi's Theorem),…

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…

This is the first part of a two-part monograph about the Grothendieck inequality and its extensions.

Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are described and critiqued. Each proof provides valuable insights which should be useful for constructing future, more complete proofs. Rather than merely summarizing…

In this paper, we study the Skorokhod problem with two constraints, where the constraints are in a nonlinear fashion. We prove the existence and uniqueness of the solution and also provide the explicit construction for the solution. In…

We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…

Theory of $n$-complements with applications is presented.

We show analytically and numerically the existence of double vortex solutions in two-Higgs systems. These solutions are generalizations of the \no vortices and exist for all values of the parameters in the Lagrangians considered. We derive…