We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...
Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...
In the nanoscale regime, flow behaviors for liquids show qualitative deviations from bulk expectations. In this work, we reveal by molecular dynamics simulations that plug flow down to nanoscale induces molecular friction that leads to a new flow structure ...
Single-chain nanoparticles (SCNPs) are a type of polymeric nanoparticles formed by collapsing/folding individual polymer chains via intra-molecular interactions. Their emergence holds promise to construct sub-20 nm polymeric nanoparticles with defined stru ...
Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...
We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and φ : G → GL(V ) is a non-trivial irreducible repres ...
Recent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge-invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday' ...
