The Indian Institute of Technology Bombay is organizing an Institute Colloquium (co-hosted by Infosys Science Foundation) on January 7, 2025.
The details of the Colloquium are provided below:

Title: "Ramanujan and Expander Graphs"

Speaker: Professor Peter Sarnak, Professor Emeritus, Institute for Advanced Study in Princeton and Eugene Higgins Professor of Mathematics at Princeton University.

About the Speaker:

Professor Peter SARNAK was born in Johannesburg, South Africa. He received his Bachelor’s degree in Mathematics from the University of Witwatersrand, South Africa in 1975 and PhD in Mathematics from Stanford University, USA in 1980. He was an Assistant Professor (1980–1983) and Associate Professor (1983) at New York University, USA. He then joined Stanford University, where he was successively an Associate Professor (1984–1987) and Professor (1987–1991). From 1991, he moved to Princeton University and was appointed H Fine Professor (1995–1996) and the Chair of the Mathematics Department (1996–1999). He was a member of the Institute for Advanced Study (1999–2002 and 2005–2007) and served as a Professor there from 2007 until moving to Emeritus status in 2024. He was also a Professor at the Courant Institute of Mathematical Sciences, New York University (2001–2005) and has been appointed as Eugene Higgins Professor of Mathematics at Princeton University (2002–) and Gopal Prasad Professor at the Institute for Advanced Study (2022-24).

Professor Sarnak is a member of the US National Academy of Sciences, a Fellow of the Royal Society of London and is the recipient of several awards including the Shaw Prize, the Sylvester Medal from the Royal Society and the Wolf Prize.

[Speaker's webpage: https://www.ias.edu/math/people/faculty/sarnak]

Abstract:

Expander graphs are highly connected sparse graphs. They have wide theoretical and practical applications in Computer Science and Engineering. Ramanujan Graphs are optimal expanders and as the name suggests they are constructed number theoretically. We review their construction as well as more recent constructions that use statistical physics. We highlight some recent applications in the reverse direction where combinatorial ideas are combined with arithmetical ones to establish expansion of graphs arising in diophantine analysis.

In this Institute Colloquium at IIT Bombay, Prof. Sarnak will speak about the Ramanujan and expander graphs and their connection to diverse topics not only in mathematics but to science and engineering in general. This fascinating story has its origins in the famous Ramanujan inequality on the tau function, proved by Pierre Deligne in 1974 as a consequence of the Riemann hypothesis for function fields, i.e., the Weil conjectures.