Related papers: Monotone-light factorizations in coarse geometry
We first develop a general theory of Johnson filtrations and Johnson homomorphisms for a group $G$ acting on another group $K$ equipped with a filtration indexed by a "good" ordered commutative monoid. Then, specializing it to the case…
The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In…
We show that diagram groups can be viewed as fundamental groups of spaces of positive paths on directed 2-complexes (these spaces of paths turn out to be classifying spaces). Thus diagram groups are analogs of second homotopy groups,…
We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.
Linked-twist maps are area-preserving, piece-wise diffeomorphisms, defined on a subset of the torus. They are non-uniformly hyperbolic generalisations of the well-known Arnold Cat Map. We show that a class of canonical examples have…
This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the…
In this paper, we study three relative LS categories of a map and study some of their properties. Then we introduce the `higher topological complexity' and `weak higher topological complexity' of a map. Each of them are homotopy invariants.…
In this paper we study compact monotone tall complexity one $T$-spaces. We use the classification of Karshon and Tolman, and the monotone condition, to prove that any two such spaces are isomorphic if and only if they have equal…
We build a bridge between geometric group theory and topological dynamical systems by establishing a dictionary between coarse equivalence and continuous orbit equivalence. As an application, we give conceptual explanations for previous…
In this thesis we present an introduction to Soft-Collinear Effective Theory, which can be used to prove (or disprove) factorization theorems to all orders in the strong coupling constant for some B decays into light and energetic…
We prove that the mapping stack Map(Y,X) of topological stacks X and Y is again a topological stack if Y admits a compact groupoid presentation. If Y admits a locally compact groupoid presentation, we show that Map(Y,X) is a paratopological…
Generalized synchronization is plausibly the most complex form of synchronization. Previous studies have revealed the existence of weak or strong forms of generalized synchronization depending on the multi- or mono-valued nature of the…
Photonic resonances are a powerful tool for controlling light-matter interactions. However, unlocking many of the most scientifically intriguing and technologically promising phenomena requires entering the strong coupling regime, where…
We establish a correspondence between consistent comprehension schemes and complete orthogonal factorisation systems. The comprehensive factorisation of a functor between small categories arises in this way. Similar factorisation systems…
H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite…
After a brief introduction to the problem of subtraction of infrared divergences for high-order collider observables, we present a preliminary study of strongly-ordered soft and collinear multiple radiation from the point of view of…
It it shown that geometric morphisms between elementary toposes can be represented as adjunctions between the corresponding categories of locales. These adjunctions are characterised as those that preserve the order enrichment, commute with…
We propose a new notion called \emph{infinity-harmonic maps}between Riemannain manifolds. These are natural generalizations of the well known notion of infinity harmonic functions and are also the limiting case of $p$% -harmonic maps as…
Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic…
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…