### Summer @TIFR

The monsoon is on its full flow, and it’s raining heavily outside, with the aroma of the wet soil incensing the atmosphere romantically. And I am here typing this blog post.

The VSRP program has ended and I have returned home. It happened to follow the KISS principle – Keep It Short, Silly; though I wasn’t very happy with it. The time when I had started enjoying the program, it came to an abrupt end. It was good though with dramatic twists in the starting and I enjoyed it thoroughly, learnt new things and made a lot of new friends. Let me share my experience with you, after I read a similar kind by Vipul Naik.

VSRP stands for Visiting Students Research Program, an initiative taken by Tata Institute of Fundamental Research (TIFR), Mumbai – India’s foremost research institute – to help expose students to some advanced topics. More detailed info can be found here. This year VSRP for mathematics was from 13 June to 8 July.

To those who don’t know me, I am majoring in mathematics, and I have completed three years in my 5 year integrated MSc program. The VSRP program started on 13th and after regular academic chores, we were assigned our respective guides by Prof. S. Subramanian who was the coordinator for Mathematics this year. Ankit Rai (ISI Bangalore) and I were placed under Prof. R.V. Gurjar who specialises in complex algebraic surfaces. We shared the common interest to study Riemann surfaces. He gave a short lecture on what Riemann surfaces are and advised us to follow the book of Otto Forster. We had to read the first few sections of the book. Thus my project kicked off.

TIFR has a beautiful campus. It is not that big compared to most academic institutes, but it is enough for not getting bored. It faces the sea on one side, and is an awesome place for a stroll in the evening with the waves clattering, with the wind blowing through hairs, and music flowing in the ears. The food is good, with three canteens to suit varied tastes.

The first week went good and I learnt some basic stuffs about Riemann surfaces. Let me give a layman idea. In an elementary study one notices that the elementary functions like square-root and logarithm are multi-valued, and therefore technically are not functions. But for doing analysis one needs the function to be single-valued, and hence one usually restricts the range so that the function is single-valued, and then we talk about analyticity and else. However, multi-valuedness is a basic nature of the complex functions, and therefore theory should incorporate this feature, instead of circumventing it. Riemann introduced the concept of Riemann surfaces as the proper setting to study such functions. A Riemann surface is a pair $(X,\Sigma)$, where $X$ is a connected two-dimensional manifold and $\Sigma$ is a complex structure on X. Locally a Riemann surface is simply an open set in the complex plane. Simple examples include the complex plane $\mathbb{C}$ and domains of a Riemann surface $X$. Two non-trivial examples are the Riemann sphere $\mathbb{P}^{1}$ and the torus $S^{1} \times S^{1}$, when equipped with a suitable complex structure. Maybe later, I’ll try to write a more detailed exposition.

Weekdays were spent on reading the book, and the weekends on trips and hanging out with friends. TIFR had also organised a trip to Giant Metrewave Radio Telescope (GMRT), Pune. It was fun getting acquainted with some basic Radio Astronomy. Besides, the views of the landscape during the trip was spectacular, and given that I am interested in photography, it was exciting experience to take photographs. The album can be seen here.

In contrast, this time there was no presentation kind of thing – which was both a relief as well as a disappointment. Relief, coz, I could read more freely, and a disappointment, coz, I wanted to hone my speaking skills. However, I did submit my one page report!

Altogether, it was a welcome experience. Making new friends, and learning about their curriculum and college life. Goodbye to them. Yeah! That’s life!!