Related papers: An Algebraic Preservation Theorem for Aleph-Zero C…

We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for classifying the full Poisson automorphism groups of…

We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…

I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…

In this work we examine the stability of some classes of integrals, and in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing…

Given a G-structure with connection satisfying a regularity assumption we associate to it a classifying Lie algebroid. This algebroid contains all the information about the equivalence problem and is an example of a G-structure Lie…

We study the behaviors of cohomological Hall algebras and relevant subjects under an edge contraction. Given a quiver with potential and fix an arrow, the edge contraction is a way to construct a new quiver with potential. We show that…

In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra $H$, one can associate it to a Hopf algebroid $H_{par}$ which…

We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width…

Stable homotopy theory is governed by the principle that after inverting loop spaces, homotopy types become the representing objects for homology theories. We show that this principle extends to higher category theory: inverting…

Physical theories can be characterized in terms of their state spaces and their evolutive equations. The kinematical structure and the dynamical structure of finite dimensional quantum theory are, in light of the Choi-Jamio{\l}kowski…

We assign a relational structure to any finite algebra in a canonical way, using solution sets of equations, and we prove that this relational structure is polymorphism-homogeneous if and only if the algebra itself is…

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies…

Let G be a totally disconnected, locally compact group admitting a contractive automorphism f. We prove a Jordan-Holder theorem for series of f-stable closed subgroups of G, classify all possible composition factors and deduce consequences…

In the 1930s, H. Hopf conjectured that a closed, even-dimensional manifold of positive sectional curvature has positive Euler characteristic. We show this under the additional assumption of an isometric $T^4$-action on the manifold,…

Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others…

We find conditions on ideals of an algebra under which the algebra is dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the real numbers. We introduce a concept of bq-homomorphism (which is given by two linear maps $f,…

A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations…

We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It…

An equivalence structure is a set with a single binary relation, satisfying sentences stating that the relation is an equivalence relation. A computable structure A is said to be $\Delta^0_\alpha$ categorical if for any computable structure…

In this version small mistakes are corrected and the exposition is changed as suggested by the referee (to appear in Canadian Journal of Mathematics). The first main result of the paper is a criterion for a partially commutative group $\GG$…