• Circle Method (March, 2011)

  • The circle method finds its genesis in the first letter of Srinivasa Ramanujan to G.H. Hardy written in January 1913. This method was developed in the celebrated paper of Hardy and Ramanujan on the partition function. It ws further developed in a series of papers by Hardy and Littlewood in their work on Waring's problem and Goldbach's conjecture. In the first lecture, we give a short survey of the method. In the second lecture, we show its application to Waring's problem. In the third lecture, we give a short sketch of Vinogradov's solution to Goldbach's problem that every odd number can be written as a sum of three primes.

  • Special values of zeta and L-functions (Dec, 2011)

  • We will survey known results concerning special values of zeta and L-functions and discuss several open questions in the area.

    Schedule of lectures for March, 2011, can be found here