Douglas Arnold is McKnight Presidential Professor of Mathematics at the University of Minnesota.

• 1. Low-rank tensor methods for partial differential equations Markus Bachmayr; 2. The virtual element method Lourenço Beirão da Veiga, Franco Brezzi, L. Donatella Marini and Alessandro Russo; 3. Floating-point arithmetic Sylvie Boldo, Claude-Pierre Jeannerod, Guillaume Melquiond and Jean-Michel Muller; 4. Compatible finite element methods for geophysical fluid dynamics Colin J. Cotter; 5. Control of port-Hamiltonian differential-algebraic systems and applications Volker Mehrmann and Benjamin Unger; 6. Overcoming the timescale barrier in molecular dynamics: transfer operators, variational principles and machine learning Christof Schütte, Stefan Klus and Carsten Hartmann; 7. Linear optimization over homogeneous matrix cones Levent Tunçel and Lieven Vandenberghe.