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Princeton Professor delivers Ramanujan Colloquium

Krishnaswami Alladi

Versatile mathematician connects variety of topics and provides global picture

Renowned mathematician Professor Peter Sarnak of Princeton University and the Institute for Advanced Study, delivered the Second Ramanujan Colloquium on March 19 at the University of Florida, Gainesville. He followed it up with two seminar lectures on March 20 and 21. His colloquium and lectures were on "Sieves, the generalised Ramanujan conjectures, and expander graphs."

Professor Sarnak, a versatile mathematician, was able to connect a variety of topics and provide a global picture. He explained the role of arithmetic combinatorics in treating such questions along with the abstract approaches involving modular forms.

The Colloquium is sponsored by Professor George Andrews of Pennsylvania State University, an authority on Ramanujan’s work. It was launched in March 2007, and the first speaker was the young mathematician, Professor Manjul Bhargava of Princeton University. Professor Sarnak, the second speaker, is one of Professor Bhargava’s teachers.

Number Theory has several long-standing problems such as the conjecture (yet unresolved) that there are infinitely many twin primes. Sieve methods which were originally devised to tackle such questions, have succeeded in establishing similar results for numbers with very few prime factors.

In his lectures, Professor Sarnak described how to view such problems in a general geometric and group theoretic setting. In doing so, he discussed Ramanujan’s celebrated conjecture on the size of the tau function that was proved by Pierre Deligne in the 1970s. He then described certain far-reaching generalisations of the original Ramanujan conjecture and the progress that has been achieved by him and other leading experts towards these generalised conjectures. Just as India released a stamp of Ramanujan, Belgium has released a stamp of Pierre Deligne in which Ramanujan’s inequality for the tau function is displayed next to the picture of Deligne. Professor Sarnak showed a slide of the Deligne stamp during his lectures.

Professor Krishnaswami Alladi is Chairman of the Mathematics Department at the University of Florida.

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