# Pol van Hoften: On the discrete part of the Hecke-orbit conjecture

**Time: **
Tue 2020-11-17 13.15 - 14.00

**Location: **
Zoom, meeting ID: 657 9019 8929

**Participating: **
Pol van Hoften, King's College London

### Abstract

The Hecke-orbit conjecture, proposed by Chai and Oort, gives strong restrictions on the shape of Hecke-invariant subvarieties of special fibers of Shimura varieties. It consists of a continuous part, which predicts the dimensions of Hecke orbits, and a discrete part, which predicts that certain subvarieties called central leaves are irreducible. In this talk I will give an introduction to the discrete part of the Hecke orbit conjecture, focussing mostly on explicit low-dimensional examples, and discuss a geometric proof for Shimura varieties of Hodge type.

**Zoom Notes: **The meeting ID is 657 9019 8929 and the passcode is 3517257.