# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Mass transport on aperiodic tilings"

Suppose that we have two mass distributions on a $d$-dimensional aperiodic tiling, each defined by a local rule such as "put 3 kg on every A tile and 1 kg on every B tile" or "put 5kg on every A tile that is next to a B tile". When is it possible to do a bounded transport from one distribution to the other? When is it possible to do that transport according to a local rule? When is it possible to do that transport in a way that is arbitrarily well approximated by a local rule? All of these questions boil down to questions about the top Cech cohomology of the continuous hull of our tiling. We answer those questions for a wide class of substitution tilings. This is joint work with Michael Kelly.