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Featured Member - Abhishek Sinha

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.

Note by Calvin Lin
2 years, 1 month ago

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Abhishek, nice to get to know a future MIT PhD better. Looking forward to hearing more from you. Chew-Seong Cheong · 2 years, 1 month ago

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What is that yellow book you have on your desk? Adarsh Kumar · 2 years, 1 month ago

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@Adarsh Kumar That's a book on basic topology :) Abhishek Sinha · 2 years, 1 month ago

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If you have any further questions about pursuing a PhD, you can ask them here! Calvin Lin Staff · 2 years, 1 month ago

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Congrats on being featured sir!!!

I heard rumors that we must not lose more than \(2\) marks in SAT to enter MIT, is it true? Sravanth Chebrolu · 2 years, 1 month ago

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@Sravanth Chebrolu Not really! Our marks in grade 9-12 and many other things affect impact the admission process too. Arulx Z · 2 years, 1 month ago

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Hello sir, can you please tell me what's your job after completing PhD ? Anish Harsha · 2 years, 1 month ago

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@Anish Harsha Doctoral degree holders join various jobs, e.g., faculty positions at research universities, scientists at industrial/ government labs etc. Abhishek Sinha · 2 years, 1 month ago

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@Abhishek Sinha For pursuing an engineering degree which is better IIT OR MIT ? Aakash Khandelwal · 2 years, 1 month ago

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@Abhishek Sinha I've a few questions about the eligibility criteria of MIT, M.S. (Maths) which are as follows:

  1. Can a person graduated from ignou (correspondence course) Maths (hons.) apply for that?

  2. What is the list of all the tests to pass to get qualified for admission in M.S. at MIT?

  3. Any other restrictions/requirements/additional documents for a student belonging to INDIA?

Sandeep Bhardwaj · 2 years, 1 month ago

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@Sandeep Bhardwaj I am not sure about MS program at Math. Most of the students are given admission to the PhD program and they complete their master's along the way. I am not very sure about either 1, 2 or 3 but I think standardized tests suffice. The emphasis is more (probably entirely) on original research contributions that the candidate already has. Abhishek Sinha · 2 years, 1 month ago

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Can you reveal that encoding -decoding program of yours ? Raven Herd · 2 years, 1 month ago

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@Raven Herd Actually it is very easy. I used a multiplicative group of sufficiently large size and I replaced each element by its inverse. So by running the program twice, you get back the original content. Abhishek Sinha · 2 years, 1 month ago

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@Abhishek Sinha See ,I have never learnt c++ .I only know Java.Can there be a method using it? Raven Herd · 2 years, 1 month ago

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@Raven Herd What I described above is a general algorithmic procedure and could be implemented in any language. You may also use the additive group. For example, take the ASCII value of each character and then negate it. Abhishek Sinha · 2 years, 1 month ago

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@Raven Herd Based on the comments, here's how it might have been -

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s = 'some string'

def codecode(n):
    return ''.join([chr(159 - ord(x)) for x in n])

r = codecode(s)
q = codecode(r)

print r, q

Arulx Z · 1 year, 9 months ago

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@Arulx Z Is this python ? I am sorry if I am too much demanding but is there any Java version of this code.(I haven't started python yet) Raven Herd · 1 year, 9 months ago

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@Raven Herd No problem :)

Here's the Java code -

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String n = "some string";
String codecode = "";

for(char x : n.toCharArray()) // Convert string to character array and iterate over it
{
  codecode += (char) (158 - ((int) x));
  // Convert the character to ASCII. Let it be n
  // Compute 158 - n. The number achieved will have a value between 32 to 126
  // This range contains all commonly used ASCII characters
  // Now convert the value 158 - n back to a character and concatenate it to the string codecode  
  // If you repeat the process, you'll get the same character because 158 - (158 - n) = n
}

System.out.println(codecode);

Arulx Z · 1 year, 9 months ago

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@Arulx Z Awesome . Hey , try my new set Hall of fame. I wanted to know that is there any olympiad concerning computer programming(in India or online). Raven Herd · 1 year, 9 months ago

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@Raven Herd Yes! Try ZCO/ZIO to qualify for INOI and IOI. There are numerous programming contests available online. This page will guide you.

I am not sure if I'll be able to solve the problems in the set because most of them are based on Geometry (and my Geometry skills aren't that good). But I'll try for sure! Arulx Z · 1 year, 9 months ago

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@Arulx Z AWESOME WIKI . You don't worry I'll post numerous algebra problems too . After all ,the song's too long. Raven Herd · 1 year, 9 months ago

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How was your experience with iisc. Satvik Choudhary · 2 years, 1 month ago

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@Satvik Choudhary Entirely fascinating! I'll encourage everyone to visit IISc if they have a chance. Abhishek Sinha · 2 years, 1 month ago

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Congratulations Abhishek Refaat M. Sayed · 2 years, 1 month ago

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Congratulations and best wishes for your future. Niranjan Khanderia · 2 years, 1 month ago

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@Abhishek Sinha First of all congratulations. Can you please share your job preferences after completing PhD. Rajdeep Das · 1 year, 1 month ago

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did u enter iisc through kvpy or by giving paper from later stage Aakash Sidhwani · 1 year, 9 months ago

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For pursuing an engineering degree which is better: IIT OR MIT ? Rahul Sethi · 2 years, 1 month ago

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Congratulations Abhishek! Even I look forward to join MIT after grade 12. Arulx Z · 2 years, 1 month ago

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Hello Sir, congratulations for being featured!

Just a question, how is the physics faculty of MIT? Can we students get there? Swapnil Das · 2 years, 1 month ago

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@Swapnil Das Physics faculty at MIT is very good. You can definitely get there. Abhishek Sinha · 2 years, 1 month ago

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@Abhishek SinhaSir what r the things they look for undergraduate admissions is there any age limit ??Also I have alimca record topper in a physics olympiad at bachelors level in the country .Will it help as a transfer student thank you !! Tejas Suresh · 1 year, 2 months ago

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Congrats Bryan Lee Shi Yang · 2 years, 1 month ago

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Hi i myself Arijit Dutta.I don't just love maths I love to eat maths,sleep maths and talk maths.now a days I m taking preparation for bank po exams.is there any competition for maths on internet or anywhere globally on quantitative aptitude? Arijit Dutta · 2 years, 1 month ago

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Is it true that a PhD thesis needs to be 250< pages? (Just asking) Hetansh Mehta · 2 years, 1 month ago

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@Hetansh Mehta Not really; e.g., John Nash's thesis was merely \(26\) page long. Abhishek Sinha · 2 years, 1 month ago

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@Abhishek Sinha In response also to Mehta: don't worry! Really, do not!!! By the time you are writing your dissertation, 250 pgs will seem either a) impossibly few or b) a generous allowance within which you'll easily be able to articulate (or prove, or establish as possible, etc.) your claim. No worries....just do what you love! Sam Floyd · 2 years, 1 month ago

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