Geodesic interpretation of the global quasi-geostrophic equations - Modin, Klas; Suri, Ali (Calculus of Variations and Partial Differential Equations)

Holomorphic induction beyond the norm-continuous setting, with applications to positive energy representations - Niestijl, Milan (Journal of Functional Analysis)

Infinite-dimensional Lie groups - Glöckner, Helge; Neeb, Karl-Hermann

Drinfeld correspondence in infinite dimensions - Rahangdale, Praful

Compact invariant random subgroups - Cohen, Tal; Glöckner, Helge; Goffer, Gil; Lederle, Waltraud

Diffeomorphism groups of compact locally polyhedral manifolds - Jakob, Johanna

Boundary values of diffeomorphisms of simple polytopes, and controllability - Glöckner, Helge; Grong, Erlend; Schmeding, Alexander (Differential Geometry and its Applications)

Stochastic Euler-Poincaré reduction for central extension - Suri, Ali (Differential Geometry and its Applications)

Stochastic Perturbation of Geodesics on the Manifold of Riemannian Metrics - Cruzeiro, Ana Bela; Suri, Ali

Poisson bivectors on infinite dimensional manifolds - Michor, P. W.; Rahangdale, Praful
We show that, on a smoothly paracompact convenient manifold $M$ modeled on a convenient space with the bornological approximation property, the dual map of a Poisson bracket factors as a smooth section of the vector bundle $L_{skew}^2(T^*M,\mathbb R)$.

Manifolds of continuous BV-functions and vector measure regularity of Banach–Lie groups - Glöckner, Helge; Schmeding, Alexander; Suri, Ali (Geometric Mechanics)

Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms - Janssens, Bas; Niestijl, Milan (Communications in Mathematical Physics)
Abstract Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations $$\overline{ρ }$$ ρ ¯ of the Lie group $${{\,Diff\,}}_c(M)$$ Diff c ( M ) of compactly supported diffeomorphisms of a smooth manifold M that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by $$\overline{ρ }$$ ρ ¯ . We show that if M is connected and $$\dim (M) > 1$$ dim ( M ) > 1 , then any such representation is necessarily trivial on the identity component $${{\,Diff\,}}_c(M)_0$$ Diff c ( M ) 0 . As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology $$H^2_ct(\mathcal {X}_c(M), \mathbb {R})$$ H ct 2 ( X c ( M ) , R ) of the Lie algebra of compactly supported vector fields. This is subtly different from Gelfand–Fuks cohomology in view of the compact support condition.

Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday (J. Lie Theory)

Manifold of mappings and regularity properties of half-Lie groups - Pinaud, Matthieu

Describing the nub in maximal Kac-Moody groups - Bischof, Sebastian; Marquis, Timothée
Let $G$ be a totally disconnected locally compact (tdlc) group. The contraction group $con(g)$ of an element $g\in G$ is the set of all $h\in G$ such that $g^n h g^{-n} → 1_G$ as $n → ∞$. The nub of $g$ can then be characterized as the intersection $nub(g)$ of the closures of $con(g)$ and $con(g^{-1})$. Contraction groups and nubs provide important tools in the study of the structure of tdlc groups, as already evidenced in the work of G. Willis. It is known that $nub(g) = \{1\}$ if and only if $con(g)$ is closed. In general, contraction groups are not closed and computing the nub is typically a challenging problem. Maximal Kac-Moody groups over finite fields form a prominent family of non-discrete compactly generated simple tdlc groups. In this paper we give a complete description of the nub of any element in these groups.

On flat groups in affine buildings - Bischof, Sebastian
In this article we work out the details of flat groups of the automorphism group of locally finite Bruhat-Tits buildings.

Lie groups of real analytic diffeomorphisms are L^1-regular - Glöckner, Helge (Nonlinear Analysis)
Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all real-analytic diffeomorphisms of $M$, which is modelled on the (DFS)-space ${\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of time-dependent real-analytic vector fields on $M$ which are integrable functions in time, and their dependence on the time-dependent vector field. Notably, we show that the Lie group $G$ is $L^1$-regular in the sense that each $[\gamma]$ in $L^1([0,1],{\mathfrak g})$ has an evolution which is an absolutely continuous $G$-valued function on $[0,1]$ and smooth in $[\gamma]$. As tools for the proof, we develop several new results concerning $L^p$-regularity of infinite-dimensional Lie groups, for $1\leq p\leq \infty$, which will be useful also for the discussion of other classes of groups. Moreover, we obtain new results concerning the continuity and complex analyticity of non-linear mappings on open subsets of locally convex direct limits.

Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups - Pinaud, Matthieu

Curvature and stability of quasi-geostrophic motion - Suri, Ali (Journal of Geometry and Physics)

Conjugate points along spherical harmonics - Suri, Ali (Journal of Geometry and Physics)