Entropy, holomorphic convexity, and locally symmetric spaces

par William Sarem (Université de Grenoble)

jeudi 16 avr. 2026, 10:30 → 11:30 Europe/Paris

Let $X = G/K$ be a Hermitian symmetric space of noncompact type (in rank one, $X$ is the unit ball in $\mathbb{C}^n$ and $G$ is the group $\mathrm{PU}(n,1)$), and let $\Gamma$ be a discrete and torsion-free subgroup of $G$. Can we find criteria on $\Gamma$ implying that the quotient of $X$ by $\Gamma$ is holomorphically convex, or that it contains no compact analytic subvariety of positive dimension?
I will present criteria inspired by the work of Dey and Kapovich, which concern the critical exponent of the group (in rank one) or its entropy associated with some linear form (in higher rank). In both cases, the proofs involve Patterson–Sullivan measures, and the ultimate goal is to show that these quotients are Stein manifolds. The results in higher rank come from work in progress, in collaboration with Colin Davalo.