This paper provides a complete solution to the existence of equilibria in games with any number of players that may be finite, infinite, or even uncountable; arbitrary strategy spaces that may be discrete, continuum, non-compact or non-convex; payoffs (resp. preferences) that may be discontinuous or do not have any form of quasi-concavity (resp. nontotal, nontransitive, discontinuous, nonconvex...

We use descent theoretic methods to solve the homotopy limit problem for Hermitian $K$-theory over quasi-compact and quasi-separated base schemes. As another application of these methods, we compute cellular Picard group 2-complete $\mathop{Spec}(\mathbb{C})$, showing that only invertible spectra are suspensions tensor unit.

A quantum version of Bochner’s theorem characterising Fourier transforms of probability measures on locally compact Abelian groups gives a characterisation of the Fourier transforms of Wigner quasi-joint distributions of position and momentum. An analogous quantum Bochner theorem characterises quasi-joint distributions of components of spin. In both cases quantum states in which a true distribu...

This paper considers the existence of Nash equilibria in games with any number of players that may be finite, infinite, or even uncountable; arbitrary strategy spaces that may be discrete, continuum, non-compact or non-convex; payoffs (resp. preferences) that may be discontinuous or do not have any form of quasi-concavity (resp. nontotal, nontransitive, discontinuous, nonconvex, or nonmonotonic...

Abstract We construct explicitly a finite cover of the moduli stack compact Riemann surfaces with given group symmetries by smooth quasi-projective variety.

We give a compact non-technical presentation of two basic principles for reducing the description of nonequilibrium systems based on the quasi-equilibrium approximation. These two principles are: construction of invariant manifolds for the dissipative microscopic dynamics, and coarse-graining for the entropy-conserving microscopic dynamics. Two new results are presented: first, an application o...

We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for the variety of characters of normalcrossing quasi-projective orbifold groups. Finally, we extend Sakuma’s formula for the first Betti number of abelian cove...

We show that T (F)= = E can be completely axiomatized when = E is a quasi-free theory. Quasi-free theories are a wider class of theories than permutative theories of Mal71] for which Mal'cev gave decision results. As an example of application, we show that the rst order theory of T (F)= = E is decidable when E is a set of ground equations. Besides, we prove that the 1-fragment of the theory of ...

We provide a proof of Nagata’s compactification theorem: any separated map of finite type between quasi-compact and quasi-separated schemes (e.g., noetherian schemes) factors as an open immersion followed by a proper morphism. This is a detailed exposition of private notes of Deligne that translate Nagata’s method into modern terms, and includes some applications of general interest in the theo...

The concept of quasi-continuity and the new concept of almost compactness for a function are the basis for the extension of the contraction principle in large devi­ ations presented here. Important equivalences for quasi-continuity are proved in the case of metric spaces. The relation between the exponential tightness of a sequence of stochastic processes and the exponential tightness of its tr...