Related papers: Topological reducibilities for discontinuous funct…

We present a coalgebraic framework for studying generalisations of dynamic modal logics such as PDL and game logic in which both the propositions and the semantic structures can take values in an algebra $\mathbf{A}$ of truth-degrees. More…

We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the second one extends Wadge reducibility from sets (i.e.,…

Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. We bound the number of rational points of bounded height that approximate this set very well. Our result is formulated and proved in the…

Based on the work of Guillarmou, Kupiainen, and Rhodes, we construct compactified imaginary Toda theory on closed Riemann surfaces, extending the rank-one construction to the higher-rank setting. This theory is expected to describe critical…

This paper studies topological duals of Banach function spaces (BFS). We assume a finite measure but our arguments extend to general locally convex function spaces whose topology is generated by seminorms that satisfy the usual BFS axioms.…

We generalize some classical results about quasicontinuous and separately continuous functions with values in metrizable spaces to functions with values in certain generalized metric spaces, called Maslyuchenko spaces. We establish…

It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically…

Let $\mathbbm{P}^{1,an}$ be the Berkovich projective line over a complete, algebraically closed, non-Archimedean field. Let $\phi$ be a degree $\geq 2$ rational map with potential good reduction, acting on $\mathbbm{P}^{1,an}$. In this…

We formulate a strengthening of the Zariski dense orbit conjecture for birational maps of dynamical degree one. So, given a quasiprojective variety $X$ defined over an algebraically closed field $K$ of characteristic $0$, endowed with a…

We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear function in the size of its support, therefore showing that…

The Riemann hierarchy is the simplest example of rank one, ($1$+$1$)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the Korteweg-de Vries hierarchy. In the language of formal…

We identify a canonical structure J associated to any first-order theory, the {\it space of definability patterns}. It generalizes the imaginary algebraic closure in a stable theory, and the hyperimaginary bounded closure in simple…

Consider all the level sets of a real function. We can group these level sets according to their Hausdorff dimensions. We show that the Hausdorff dimension of the collection of all level sets of a given Hausdorff dimension can be…

We study several distinguished function algebras on a Polish group $G$, under the assumption that $G$ is Roelcke precompact. We do this by means of the model-theoretic translation initiated by Ben Yaacov and Tsankov: we investigate the…

We discuss variants of construction of measurable subgradients for multivariate convex functions and the problem of characterization of the $\Delta_2$-condition in terms of their directional derivatives. Furthermore we study related basic…

We give a notion of Scott rank for separable metric structures based on the definability of the (metric closures of) automorphism orbits in continuous infinitary logic. This is a continuous analogue of work of Montalb\'an for countable…

Let f : X --> X be a dominant rational map of a projective variety defined over a number field. An important geometric-dynamical invariant of f is its (first) dynamical degree d_f= lim SpecRadius((f^n)^*)^{1/n}. For algebraic points P of X…

The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). We extend it here to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show…

Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After…

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…