# SASTRA Ramanujan prize for Radziwill, Matomaki

Maksym Radziwill receives the 2016 SASTRA-Ramanujan award for mathematics and citation from Steven Weintraub, Lehigh University, at Kumbakonam, Ramanujan's birthplace. Photo: Special Arrangement

The 2016 SASTRA-Ramanujan award for mathematics was presented to Maksym Radziwill of McGill University, Canada, at the inauguration of the International Conference on Number Theory at SASTRA University at Kumbakonam.

The joint winner is Kaisa Matomaki of University of Turku, Finland.

The award citation and the shared prize money of \$5,000 was presented by Prof. Steven Weintraub from Lehigh University who is also the Associate Secretary of the American Mathematical Society. Prof. Radziwill will deliver the Srinivasa Ramanujan Birthday Commemorative Lecture on December 22.

SASTRA University presents the Ramanujan award to a leading mathematician under 32 years. This year the prize has been jointly given to Kaisa Matomaki and Maksym Radziwill for their ‘revolutionary’ collaborative work on short intervals in number theory. The second woman to receive the prize since it was instituted in 2005, Professor Matomaki (who will collect the award later) said in an email, “I was surprised and, of course, very happy to receive such a prestigious prize.”

Mathematics is generally seen as a lonely pursuit, but number theory has a lot more collaborative work. After meeting at a conference, Professors Matomaki and Radziwill started a collaboration mainly through email and occasionally in person. Their work dwells on properties of numbers in “short intervals.”

Prof. Radziwill told The Hindu: “If you take an integer at random, and take a few integers around it, for instance, we take a [large] number like 10100 and then I pick a thousand integers around it. My work with Matomaki shows that the way these [for instance, thousand] integers factor is the same way in which [all] the integers below 10100 factor. So factorization inside small boxes is like factorization inside all integers.” This is reminiscent of the self-similar behaviour within a fractal.

In number theory, understanding behaviour in short intervals is very important and also it is very difficult to prove this result. So what Matomaki and Radziwill have achieved was basically shocking. People did not expect such powerful results could be obtained,” said Prof. Krishnaswamy Alladi of Florida University, chairperson of the prize committee.

The two mathematicians worked with Fields medallist Terence Tao in making a breakthrough on the Chowla conjecture. “Terry Tao pointed out that our work is relevant to Chowla conjecture, and by using our results and some of his ideas, he could make the first advancement in Chowla conjecture,” said Prof. Radziwill. “In my opinion he has essentially proved it,” he added.

So far, the most challenging award choice was in 2005, when there was a tie between Manjul Bhargava and Kannan Soundararajan. Prof. Alladi advised the committee to take a leaf out of Indira Gandhi’s book. Faced with a tie for the first Kalidas Samman between Mallikarjun Mansur and Semmangudi Srinivasa Iyer, she decided to award both musicians. “I told the Vice-Chancellor, Dr. Sethuraman, these are the best candidates in Algebraic Number Theory and Analytic number theory and immediately The SASTRA prize will be on the world map. That was the most challenging decision,” Prof. Alladi said. Thus the first SASTRA Ramanujan prize was awarded to both mathematicians. The present year is the second time that two mathematicians have been selected for the prize.

Why is the age limit so low? It’s partly for the glamour of the challenge (What can you do in a time spanning the entire duration of Ramanujan’s life?). Prof Alladi adds,“We also wanted to give them the prize before they won other bigger prizes. If you get a Fields medallist and bestow on him/her an Indian honour, it is not all that great – It is okay, we should do it, I am not saying it should not be done, but to recognize them early.”