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In this paper we take a look at compactly generated weak Hausdorff spaces equipped with an action of a compact Lie group $G$ together with their colimits and homotopy colimits. In particular, we investigate relations between (homotopy)…
Let $M$ be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno, Silva and Ruffino ($Stoch$. $Dyn$., 2013) it is shown that, up to a stopping time $\tau$, a stochastic flow of local…
One proves that the category of globular CW-complexes up to dihomotopy is equivalent to the category of flows up to weak dihomotopy. This theorem generalizes the classical theorem which states that the category of CW-complexes up to…
A locally compact group $ G $ is discrete if and only if the Fourier algebra $ A(G) $ has a non-zero (weakly) compact multiplier. We partially extend this result to the setting of ultraspherical hypergroups. Let $H$ be an ultraspherical…
A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie…
We study projectivity in the category of $G$-flows and affine $G$-flows for Polish groups $G$. We also introduce the notion of \emph{proximally irreducible} extensions between affine $G$-flows. Using this we provide a characterization of…
The description of the subgroup structure of a non-commutative division ring is the subject of the intensive study in the theory of division rings in particular, and of the theory of skew linear groups in general. This study is still so far…
In this paper we study the dynamics of Bernoulli flows and their subflows over general countable groups from the symbolic and topological perspectives. We study free subflows (subflows in which every point has trivial stabilizer), minimal…
We give explicit solutions to the two-component Hunter-Saxton system on the unit circle. Moreover, we show how global weak solutions can be naturally constructed using the geometric interpretation of this system as a re-expression of the…
Let $G$ be a matrix group. Topological $G$-manifolds with Palais-proper action have the $G$-homotopy type of countable $G$-CW complexes (3.2). This generalizes E Elfving's dissertation theorem for locally linear $G$-manifolds (1996). Also…
We investigate local regularity properties of weak solutions to a broad class of nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations. In particular, we focus on proving an interpolative apriori boundedness estimate for weak…
$p$-Adic compactifications of geometric loop and diffeomorphism groups of compact manifolds on finite-dimensional spaces over non-Archimedean fields are investigated. Weakened topology is introduced. The structure of newly constructed…
This is the first of a series of papers, where we introduce a new class of estimates for the Ricci flow, and use them both to characterize solutions of the Ricci flow and to provide a notion of weak solutions to the Ricci flow in the…
We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples are obtained by AbC constructions with several frequencies.
For any bounded, smooth domain $\Omega\subset \R^2$, %(or $\Omega=\R^2$), we will establish the weak compactness property of solutions to the simplified Ericksen-Leslie system for both uniaxial and biaxial nematics, and the convergence of…
We study types that appear in ultraproducts that have distributions which can be thought of as a sequence of graphs. The property of having distributions that are captured by graphs is motivated by a commonality of $\mathrm{SOP}_2$-types…
We investigate whether a class of models describing F-theory compactifications admits a specific type of flux vacua with an exponentially small vacuum expectation value of the superpotential, by generalizing a method recently developed in…
Starting from a higher Courant bracket associated to exceptional generalized geometry, we provide a systematic derivation of all types of fluxes and their Bianchi identities for four-dimensional compactifications of M-theory. We show that…
In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of…
A locally compact group G is called a WS-group if the double orbits of the weakly almost periodic functions on G are relatively weakly compact. It is known that Moore-groups are WS-groups. We will show that if a discrete FC-group is a…