I will introduce the concept of a physical measure and discuss a new family of simple one-dimensional maps which may admit different kinds of physical measures and, in some cases, no physical measures.

Stefano Luzzatto is a Senior Research Scientist at the Abdus Salam International Centre for Theoretical Physics (ICTP), in Trieste Italy, a UNESCO institute with a mission to promote excellence in science in developing countries. He completed his PhD in Dynamical Systems in 1995 at the International School for Advanced Studies (SISSA) in Trieste, Italy and the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil, under the supervision of J. Palis and M. Viana. After a postdoc with S. Van Strien at Warwick University, he joined Imperial College London in 2000 as a permanent faculty member, where he co-founded the DynamIC research group with J. Lamb. In 2009 he moved to his current position at ICTP.

Prof Luzzatto's expertise is in Dynamical Systems and Ergodic Theory. He has published papers in top international journals, with collaborators from many different countries, and presented his research in seminars and conferences around the world. He has extensive teaching experience, including intensive mini-courses in international settings, and is writing a textbook based on an innovative “Socratic” approach to teaching. He has supervised more than 70 students at all levels, from Master’s to PhD to Postdoc. He is also very involved in international capacity building programmes and is the founder of the International Mathematics Master (IMM).