We will be featuring different members of the Brilliant community, so that you can get to know them better. For the fifth issue, we are featuring Abhishek Sinha, who is currently a third year PhD student at MIT pursuing his dreams. It comes as no surprise that his problems and solutions tend to delve into the deeper aspects of mathematics, and highlight the underlying connections that you will get to explore as you further your studies in mathematics.
One of his problems that I really enjoyed seeing, is Continuous Coloring which serves as an introduction to topology and analysis. Just look at the colorful image, which motivates the problem :)
Amongst the solutions that he posted, the one to It's a Jelly Bean highlights the power of linear algebra, which turns an otherwise messy and boring calculus exercise into an application of a basic fact!
1. Tell us more about yourself.
Hi there! I am Abhishek Sinha, currently a third year PhD student at MIT, working at the intersection of Theoretical Computer Science and Electrical Engineering.
I was immensely motivated to pursue a doctoral degree during my stay at the Indian Institute of Science (IISc) when I did my Masters (It is a truly fantastic place!). I pursued an engineering degree there (Electrical Communication Engineering), where the emphasis was more on the fundamental aspects of the subject, e.g. Information Theory, Stochastic Processes and Game Theory, which I enjoyed thoroughly. MIT is traditionally very strong in this area in general and the current research by its faculty (especially in our lab, LIDS) seemed very exciting to me. Hence I decided to join MIT.
You may visit my homepage to know more about my research and academic activities. I hail from the beautiful Indian city of Kolkata, also known as the city of joy. I love Bengali literature, music, chess, Indian cuisine and of course, mathematics.
2. What was the process of applying to graduate school in the US like? The process of application for graduate studies in the US is fairly standard; you first write a few standardized tests (GRE, TOEFL) and then apply to the universities of your choice. For admission to top graduate programs, prior research experiences, publications and recommendations from your research advisor play a crucial role.
3. What is an interesting research problem that you are working on?
I am currently working on a classical problem called optimal broadcast, where we are interested in efficiently distributing messages, generated at a source node, to all other nodes in a graph with side constraints. The fundamental challenge that I am trying to address is to develop a distributed algorithm which is provably optimal. See this recent paper of ours for more information and analysis on this problem. To tackle this problem, we are using tools from Probability, Stochastic Control and Graph Theory, which makes the problem rich and exciting.
4. What is one fun fact about yourself that the Brilliant community doesn’t know about.
In my ninth grade, I developed a simple program in C-language which could simultaneously be used to encode a text file as well as to decode the encoded one. I used to amuse my friends by emailing them an encoded file, which looked nothing but garbage and then asking them to look at the file after executing the program once and twice!
5. What do you want to accomplish in the next few years?
I would like to complete my PhD and move on to the next phase of academia and continue solving interesting research problems. Moreover, I would like to explore the field of mathematics in breadth and in depth, as a professional exercise or just because it is fun to do.
6. What do you wish for Brilliant?
Brilliant is an excellent platform for the youngsters to get excited about the field of mathematics and physics. I am with Brilliant for almost two years and it gives me something new to look forward to everyday. Brilliant is definitely not restricted to another problem-solving website but is creating a fascinating and vibrant community of its own. I would like to congratulate the employees of Brilliant.org for doing such a wonderful job. I wish that Brilliant keeps on growing forever with new and exciting sets of mathematical problems everyday.