Related papers: Constructive Peter--Weyl Theory: What is Known and…
This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a.~ topological full groups). We determine that any piecewise full group that is locally compact in the compact-open topology…
We study a topology on a space of functions, called sticking topology, with the property to be the weakest among the topologies preserving continuity. In suitable frameworks, this topology preserves borelianity, local integrability, right…
We develop the homotopy theory of semisimplicial sets constructively and without reference to point-set topology to obtain a constructive model for $\omega$-groupoids. Most of the development is folklore, but for a few results the author is…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a…
In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…
In this paper, we introduce a persistent (co)homology theory for Cayley digraph grading. We give the algebraic structures of Cayley-persistence object. Specifically, we consider the module structure of persistent (co)homology and show the…
We develop a constructive theory of continuous domains from the perspective of program extraction. Our goal that programs represent (provably correct) computation without witnesses of correctness is achieved by formulating correctness…
We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of `peak projections', and in the…
The author was recently able to provide a cohomological interpretation of Tate's Riemann-Roch formula for number fields using some new harmonic analysis objects, ghost-spaces. When trying to investigate these objects in general, we realized…
We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…
Using the completed inductive, projective and injective tensor products of Grothendieck for locally convex topological vector spaces, we develop a systematic theory of locally convex Hopf algebras with an emphasis on Pontryagin-type…
The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of analysis, combinatorics, dynamics, logic, number theory, and…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to…
We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the…
The P versus NP problem is addressed in a context of provability and limitations on the possibility of finding sound axioms for formal theories. It is shown that if the term "constructible theory" is defined in a way which satisfies certain…
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commutative relationship. One application of Bialgebras is in the…