The standard convex closed hull of a subset of $\mathbb{R}^d$ is defined as the intersection of all images,

under the action of a group of rigid motions, of a half-space containing the given set. We propose

a generalisation of this classical notion, that we call a $(K,\mathbb{H})$-hull, and which is obtained from the

above construction by replacing a half-space with some other convex closed subset $K$ of the

Euclidean space, and a group of rigid motions by a subset $\mathbb{H}$ of the group of invertible affine

transformations. The above construction encompasses and generalises several known models in convex

stochastic geometry and allows us to gather them under a single umbrella. The talk is based on recent

works by Kalbuchko, Marynych, Temesvari, Thäle (2019), Marynych, Molchanov (2022) and Kabluchko,

Marynych, Molchanov (2023+).

**Date**: 23 October 2023, 14:00 (Monday, 3rd week, Michaelmas 2023)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L5**Speaker**: Oleksandr Marynych (National University of Kyiv)**Organising department**: Department of Statistics**Organisers**: Julien Berestycki (University of Oxford), Christina Goldschmidt (Oxford), James Martin (Department of Statistics, University of Oxford)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Members of the University only- Editor: Julien Berestycki