Expander graphs in general, and Ramanujan graphs in particular, have been a focus of a lot of research in the last five decades. It has been probably the area with the most fruitful interaction between mathematics and computer science, where applications went both ways. In recent years a high dimensional theory of expanders have started to emerge. We will survey some of its challenges and achievements and try to explain why this is not just a generalization but also a direction which leads to new horizons in pure math ( e.g. topological overlapping) and in CS ( "property testing").

Professor Alex Lubotzky holds a Maurice and Clara Weil Chair in mathematics at the Einstein Institute of Mathematics of the Hebrew University of Jerusalem.

He is known for contributions to geometric group theory, the study of lattices in Lie groups, representation theory of discrete groups and Kazhdan's property (T), the study of subgroup growth and applications of group theory to combinatorics and computer science (expander graphs) and error correcting codes.

He is a Fellow of the American Academy of Arts and Sciences, and the recipient of many distinguished international prizes.

In 2018 he received the Israel Prize, for mathematics and gave a Plenary lecture at the 2018 International Congress of Mathematicians at Rio de Janeiro, Brazil.

The Michael Erceg Senior Visiting Fellowship is made possible by generous support from the Margaret and John Kalman Charitable Trust

Refreshments will be served at 5pm, prior to the lecture in the level 4 Common Area (room 303.407).