Related papers: Differentially closed fields and universality on a…
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…
It was proved by Valenti and Zaicev, in 2011, that, if $G$ is an abelian group and $K$ is an algebraically closed field of characteristic zero, then any $G$-grading on the algebra of upper block triangular matrices over $K$ is isomorphic to…
Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary,…
In this survey we present the history and recent progress on several fundamental (quasi)conformal uniformization problems in the complex plane. Uniformization refers to the process of mapping a space to a canonical model by means of a…
The class of special generic maps is a natural class of smooth maps containing Morse functions on spheres with exactly two singular points and canonical projections of unit spheres. We find new restrictions on such maps on $6$-dimensional…
We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived…
Let $K$ be a Henselian, non-trivially valued field with separated analytic structure. We prove the existence of definable retractions onto an arbitrary closed definable subset of $K^{n}$. Hence directly follow definable non-Archimedean…
The purpose of this paper is to introduce a Zariski-like topology on the spectrum of all proper ideals of a ring. We show that the space is T_0, quasi-compact, and every irreducible closed subset has a unique generic point. Furthermore,…
All constructive methods employed in modern mathematics produce only countable sets, even when designed to transcend countability. We show that any constructive argument for uncountability -- excluding diagonalization techniques --…
We work over an o-minimal expansion of a real closed field R. Given a closed simplicial complex K and a finite number of definable subsets of its realization |K| in R we prove that there exists a triangulation (K',f) of |K| compatible with…
The Scott rank of a countable structure is a measure, coming from the proof of Scott's isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a sentence of $\mathcal{L}_{\omega_1 \omega}$)…
In this paper, we give a general axiomatization of anomalies in closed and open conformal field theories. In particular, we generalize Segal's notion of modular functor to a setting where the ``set of labels'' is a 2-vector space. In the…
This paper surveys topological results obtained from characteristic classes built from the two types of traces on the algebra of pseudodifferential operators of nonpositive order. The main results are the construction of a universal $\hat…
We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…
The purpose of this note is to observe that a homomorphism of discrete groups $f:\Gamma\to G$ arises as the induced map $\pi_0(\mathfrak{M})\to \pi_0(\mathfrak{X})$ on path components of some closed normal inclusion of topological groups…
Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at $0$, known to hold for bounded scalar type spectral…
We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric…
For an ordinary K3 surface over an algebraically closed field of positive characteristic we show that every automorphism lifts to characteristic zero. Moreover, we show that the Fourier-Mukai partners of an ordinary K3 surface are in…
We calculate the particle spectrum of the SSM which follows from the assumption that the commonly assumed universal form of the soft supersymmetry --breaking terms is invariant under renormalisation. It is argued that this ``strong''…
Let $k$ be a nonperfect separably closed field. Let $G$ be a connected reductive algebraic group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In particular, we present a…