at the

American Institute of Mathematics, San Jose, California

organized by

Jozsef Balogh, Silvia Fernandez, and Gelasio Salazar

The main topics for the workshop are:

- Zarankiewicz's Crossing Number Conjecture (Turán's Brickyard Problem), including its weaker variants: rectilinear crossing number and 2-page crossing number.
- The Harary-Hill Conjecture on the crossing number of the complete graph.
- The rectilinear crossing number of the complete graph.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Bishellable drawings of $K_n$

by Bernardo M. Abrego, Oswin Aichholzer, Silvia Fernandez-Merchant, Dan McQuillan, Bojan Mohar, Petra Mutzel, Pedro Ramos, R. Bruce Richter and Birgit Vogtenhuber

Note on k-planar crossing numbers

by J. Pach, L.A. Szekely, Cs.D. Toth and G. Toth, *Comput. Geom. 68 (2018), 2–6 * MR3715039

Disjoint edges in topological graphs and the tangled-thrackle conjecture

by Andres J. Ruiz-Vargas, Andrew Suk and Csaba D. Toth, *Graph drawing (2016) 284-293 * MR3333234

Crossing numbers of complete tripartite and balanced complete multipartite graphs

by Ellen Gethner, Leslie Hogben, Bernard Lidický, Florian Pfender, Amanda Ruiz, and Michael Young, *J. Graph Theory 84 (2017), no. 4, 552–565 * MR3623394