Related papers: The Abhyankar-Moh theorem for plane valuations at …

We give a construction of the universal enveloping $A_\infty$ algebra of a given $L_\infty$ algebra, alternative to the already existing versions. As applications, we derive a higher homotopy algebras version of the classical Milnor-Moore…

Let $p$ be a prime. Tate and Voloch proved that a point of finite order in the algebraic torus cannot be $p$-adically too close to a fixed subvariety without lying on it. The current work is motivated by the analogy between torsion points…

In [3] it was proved that almost-greedy and semi-greedy bases are equivalent in the context of Banach spaces with finite cotype. In this paper we show this equivalence for general Banach spaces.

Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…

We study decay rates for bounded $C_0$-semigroups from the perspective of $L^p$-infinite-time admissibility and related resolvent estimates. In the Hilbert space setting, polynomial decay of semigroup orbits is characterized by the…

We show that the homotopy theories of differential graded categories and $\mathrm{A}_\infty$-categories over a field are equivalent at the $(\infty,1)$-categorical level. The results are corollaries of a theorem of Canonaco-Ornaghi-Stellari…

We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The…

The enhanced group classification of a semi-linear generalization of a general bond-pricing equation is carried out by employing the underlying equivalence and additional equivalence transformations. The knowledge of the sub classes with…

It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.

For each finite semisimple tensor category, we associate a quantum group (face algebra) whose comodule category is equivalent to the original one, in a simple natural manner. To do this, we also give a generalization of the Tannaka-Krein…

A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…

We classify integrable bounded simple weight modules over classical Lie superalgebras at infinity. We also study the categories of such modules, and we prove that for most of the classical Lie superalgebras at infinity the respective…

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found.

We describe dual notions of tangent bundle for an infinity-topos, each underlying a tangent infinity-category in the sense of Bauer, Burke and the author. One of those notions is Lurie's tangent bundle functor for presentable…

We revisit the quantum de Finetti theorem. We state and prove a couple of variants thereof. In parallel, we introduce an operator version of the Martin boundary on quantum groups and prove generalizations of Biane's theoresm. Our proof of…

In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…

In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.

We consider the space of all configurations of finitely many (potentially nested) circles in the plane. We prove that this space is aspherical, and compute the fundamental group of each of its connected components. It turns out these…