I had my TIFR PhD interview today. Inspired by the Princeton Generals, where students who get through their Qualifying exam write about the questions asked, even I am writing here describing my interview experience. But I am not very enthusiastic about writing this, since the questions were very basic and not from all subjects, a very unlikely event during a Maths PhD interview. Nevertheless, here is the interview–

Chair: Prof. A. Sankaranarayanan

Other interviewers: Prof. Indranil Biswas, Prof. Raja Sridharan, Prof. Ravi Rao

I do not remember who asked which question, so in much of what follows, I am referring to all as “interviewer”. Most questions were asked by RR.

AS: So you work at Larsen & Toubro?

Me: No sir, I was working at L&T for an year from 2007 to 08. Then I joined IIT Bombay in 2008 till now.

RR: Under whom have you taken courses at IIT?

(I name Limaye sir and other teachers)

IB: What are your interests?

Me: Sir I do not have a particular interest as such, but I do like Algebra.

RR: is a field. Is a UFD when considered as a subring of ?

Me: Yes sir, zerodivisors in would mean zerodivisors in which is a domain. (Mistake.)

RR: So it is a domain. But is it a UFD?

Me: Ohh.. Yes.. I mean no. Consider , it can be factored in two ways. (I proved that the two were irreducibles and not unit-times-each-other.)

RS: is smooth and Then can you say if ?

(I tried for a long time to prove, then tried to give a counter-example. didn’t work. He suggested and it worked, though I goofed up in differentiating and taking limits)

(In the meanwhile, there was an interesting discussion among them if they should finish off Algebra before switching to Analysis.)

RR: Is a domain?

Me: If it is to be a domain, then the polynomial should be prime, hence irreducible. (thinking) Eisenstein.. won’t work!

Interviewer: Hint — The polynomial is homogeneous.

(Solved it.)

Interviewer: A linear transformation sends straight lines to themselves. What can you say about ?

(I wrote, wrongly, a diagonal matrix with different diagonal entries. Later corrected the mistake after they asked me to repeat the question.)

Interviewer: is a -dimensional vector space and is its subspace such that for every isomorphism , we have . What can you say about ?

(Proved that the dimension must be .)

Interviewer: Consider , the symmetric group on -symbols and an element of order in it.

(I wrote the element as a -cycle. There followed a long discussion as to why it should be a -cycle, and orders of commuting elements, their lcm’s etc. It finally ended with me group-acting on those -symbols and ‘proving’ that order of disjoint cycle types is the lcm of their orders.)

RR: Find a -subgroup of .

(This took the longest time of all. The question was interesting, involving some fundoo linear algebra. In spite of many hints from them, I was not able to solve it. Finally, RS told the answer.)

Me: (excitedly) Ohk, not just the elements of order -power, I have found the group of order !!

RS: No, I have found it!

Me: (embarassed) yes sir..

(There followed a discussion if they should ask more questions. Finally, RS asked me to prove that the additive group of a field of characteristic zero is not cyclic. I was halfway done when I was told to go.)

Note: The interview lasted for an hour. The interviewers were pleasant but and did give subtle hints when I got stuck up. But they stopped me whenever they thought I was not giving the right justification or hand-waving proofs.

PS: I was not offered the fruit juice the others before me were offered. 😛

## 9 comments

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November 27, 2011 at 15:17

pankajthanks for info…..

March 8, 2012 at 00:42

NachiketThanks for describing your interview experience, I’ve never given an interview before so it was nice to read something about it. I am a BSc student and have my TIFR maths interview next week, so I had a few queries.

1) In your interview, majority of the questions seem to be from algebra, is this because you said you liked algebra, or do they ask questions from all topics(topology, analysis etc) regardless and you weren’t able to mention all the questions here?

2) I had to qualify a written exam for the interview, so in the interview will they ask questions from the written paper?

3) Any particular/special topics that one has to prepare for the interview?

Thanks a lot.

March 8, 2012 at 10:36

Abhishek ParabSee this link – https://abhishekparab.wordpress.com/2011/03/04/a-brief-advice-for-mathematics-interviews/

June 22, 2012 at 14:40

ankurSir, My marks in Bsc. are pretty much bad. So, does that make a large difference in me getting selected in TIFR? but i cross the IIT JAM 2012 cutoff

PLZ. reply

February 18, 2013 at 11:28

aniketphysicsDid this interview get you selectd at TIFR?

February 22, 2019 at 00:30

GautamHello! How long did you have to wait before the results got out?

November 20, 2013 at 07:45

ankitI am from different background so i want to know that from where one should get prepare for algebra ? is there any standard book for algebra maths ? kindly help me out… reply ASAP

October 26, 2014 at 05:01

fapturboA motivating discussion is definitely worth comment.

I think that you need to publish more on this topic, it may not be a

taboo matter but generally people don’t talk about such issues.

To the next! All the best!!

December 1, 2014 at 00:43

SarmaHi,

Thanks for the information. My Duaghter completed B.Sc and appearing for TIFR in next 10 days. What is the cut off mark for TIFR interview last 2 years (out of 30). Is there any weightage for B.Sc marks?

Please help