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A semiclassical linear response theory based on the Vlasov equation is reviewed. The approach discussed here differs from the classical one of Vlasov and Landau for the fact that the finite size of the system is explicitly taken into…

Hyperbolic buildings are central objects in both hyperbolic geometry and geometric group theory, exhibiting a wide range of intriguing characteristics, especially with respect to group actions. In this paper, we develop the theory of…

We show that a locally Ahlfors 2-regular and locally linearly locally contractible metric surface is locally quasisymmetrically equivalent to the disk. We also discuss an application of this result to the problem of characterizing surfaces…

In the present paper we study the thermodynamical properties of finitely generated continuous subgroup actions. We address a notion of topological entropy and pressure functions that does not depend on the growth rate of the semigroup and…

In this paper we study numerical semigroups containing a given positive integer and closed with respect to the action of an affine map. For such semigroups we find a minimal set of generators, their embedding dimension, their genus and…

In this paper, we study stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. Such actions are known to exist only on one-dimensional manifolds. The aim of this paper is to introduce a geometric method to…

We study embeddings associated with oscillation functionals in rearrangement-invariant spaces. More precisely, given a positive function \(\psi\), we analyze how the interaction between the geometry of the underlying space and the growth of…

The fermion sign problem is often viewed as a sheer inconvenience that plagues numerical studies of strongly interacting electron systems. Only recently, it has been suggested that fermion signs are fundamental for the universal behavior of…

We define for every positive Anosov representation of a nonabelian free group into $\mathrm{SO}(2n,2n-1)$ a family of $\mathbb{R}^{4n-1}$-valued cocycles which induce proper affine actions on $\mathbb{R}^{4n-1}$. We construct fundamental…

It is shown that if the squeezing function tends to one at an h-extendible boundary point of a $\mathcal C^\infty$-smooth, bounded pseudoconvex domain, then the point is strictly pseudoconvex.

We give a complete description of partially wrapped Fukaya categories of graded orbifold surfaces with stops. We show that a construction via global sections of a natural cosheaf of A$_\infty$ categories on a Lagrangian core of the surface…

We identify type-preserving representations $\phi: \pi_1(\Sigma)\to \mathrm{PSL}(2,\mathbb{R})$ of the fundamental group of every punctured surface $\Sigma = \Sigma_{g,p}$ that are not Fuchsian yet send all non-peripheral simple closed…

We use a weak mean curvature flow together with a surgery procedure to show that all closed hypersurfaces in $\mathbb{R}^4$ with entropy less than or equal to that of $\mathbb{S}^2\times \mathbb{R}$, the round cylinder in $\mathbb{R}^4$,…

Let k be a number field, let E/k be an elliptic curve, and let S be a finite set of places of k contianing the archimedean places. Let F be an algebraic closure of k. We prove that if a point P in E(F) is nontorsion, then there are only…

We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least two whose Chern character represents a non-zero Hochschild homology class is quasi-isomorphic to a simple closed curve equipped with a…

Finite rank median spaces are a simultaneous generalisation of finite dimensional ${\rm CAT}(0)$ cube complexes and real trees. If $\Gamma$ is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of…

Suppose $ F $ is an integrand associated with a uniformly convex $ \mathscr{C}^{3} $-norm, and $ V $ is a $ n $-dimensional varifold in an open subset of $ \mathbf{R}^{n+1} $ such that $ \mathscr{H}^n \llcorner \operatorname{spt} \| V \| $…

An almost Fuchsian manifold is a hyperbolic 3-manifold of the type $S\times \mathbb{R}$ which admits a closed minimal surface (homeomorphic to $S$) with the maximum principal curvature $\lambda_0 <1$, while a weakly almost Fuchsian manifold…

An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) in $D$ spatial dimensions shows a violation of the…

Consider the action of $GL(n,\mathbb{Q_p})$ on the $p$-adic unit sphere $\mathcal{S}_n$ arising from the linear action on $\mathbb{Q}_p^n\setminus\{0\}$. We show that for the action of a semigroup $\mathfrak{S}$ of $GL(n,\mathbb{Q}_p)$ on…