Date & Time: Friday July 20, 4pm (Tea/Coffee at 3:45pm)
Location: Simons Centre, Ground Floor.
Speaker: Prof. Kaneenika Sinha, Mathematics group, IISER Pune.
Title : Ramanujan and the circle method
Abstract: This year, we celebrate 100 years of a phenomenal 1918 paper of G. H. Hardy and Srinivasa Ramanujan which outlined a method to estimate the number of "partitions" of large natural numbers, that is, the number of ways of writing a number as sums of smaller natural numbers. After Ramanujan's unfortunate early demise, this method was developed by Hardy and Littlewood into what is now called the circle method in common parlance. In fact, this method addresses several problems in mathematics which can be stated in elementary language, but which need to be converted into a study of points on acircle. In this talk, we will discuss the ideas behind the circle method and applications to some such ``elementary" problems.
https://www.ias.ac.in/article/fulltext/reso/009/06/0051-0055
2) Harald Helfgott's preprint on the proof of ternary Goldbach conjecture:
https://arxiv.org/abs/1312.7748
3) A nice blog post by Helfgott on his work:
https://valuevar.wordpress.com/2013/07/02/the-ternary-goldbach-conjecture/
4) An article by K Ramachandra on Ramanujan and circle method:
https://hal.archives-ouvertes.fr/hal-01104295/document
5) A mathematically (but not unnecessarily) technical treatment of the circle method:
https://web.williams.edu/Mathematics/sjmiller/public_html/BrownClasses/1/circlemethod.pdf
6) Unrelated: Since we had a small discussion on the twin prime conjecture, here is an article I wrote for The Hindu on it a few years ago
https://www.thehindu.com/sci-tech/science/Running-from-prime-to-prime/article16072971.ece