Summer 2019

A connection between optimal AG codes and LPS Ramanujan graphs.

Tuesday, Aug. 6, 2019 10:00 am11:30 am PDT

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Shai Evra (IAS)


Second-floor lounge

In the 90's, Garcia-Stichtenoth constructed excellent codes coming from algebraic curves over finite fields.  Later on, Elkies observed that these curves comes from modular curves, which are
objects of great importance in number theory. In the 80's, Lubotzky-Phillips-Sarnak and Margulis constructed excellent expander graphs (the famous Ramanujan graphs). The proof that these graphs are indeed Ramanujan passes through modular curves and modular forms. The purpose of this talk is to describe a connection between these optimal AG codes and these LPS Ramanujan graphs.

I will not assume any prior knowledge in algebraic geometry and number theory (for instance, you do not need to know what are modular curves and modular forms).