7 problems

Non-local exponentiality conjecture. The Lie group $C^\infty(M,{\mathbb{R}}) \rtimes_\alpha {\mathbb{R}}$ is not locally exponential. More specifically, there is a sequence…

Let ${\mathfrak S}_p({\mathcal H})$ be the Schatten operator ideal on a Hilbert space ${\mathcal H}$, with $1\leq p\leq\infty$. Consider the classical real Banach–Lie groups and al…

Analytic-structure conjecture. Every smooth $p$-adic Banach-Lie group admits a smoothly compatible $p$-adic analytic Lie group structure.

Let $({\mathcal{H}},\Sigma)$ be a combinatorial Hopf algebra, and consider its Lie group of controlled characters. Regularity conjecture. With better estimates, or a refinement of…

Let $\mathbf H\subset\mathbf G$ be an abstract Wiener group with Lie algebra $\mathbf h$, let $\mathbf H_0$ be the identity component of $\mathbf H$, and let…

Let $\mathbf H\subset\mathbf G$ be an abstract Wiener group with Lie algebras $\mathbf h\subset\mathbf g$, and let $\nu_{t/N}^{\mathbf h\subset\mathbf g}$ denote the corresponding…

Let $\mathbf H\subset\mathbf G$ be an abstract Wiener group, with Lie algebras $\mathbf h\subset\mathbf g$, and let $\mathbf H_0$ denote the identity component of $\mathbf H$. For…