I am transferring into the "Applied Mathematics and Statistics" PhD. program at the Johns Hopkins university. I started off as a graduate student in physics at UIUC where I worked on these projects, http://arxiv.org/abs/1512.01226, http://arxiv.org/abs/1307.7714

Since summer 2014, I started pursuing complexity theory and I am interested in theory of Ramanujan expanders, spectral graph theory, polytope extension complexity, Lasserre hierarchy and matrix norm sketching. I am particularly interested in questions in complexity theory which have an interface with physics.

Jan
28
awarded Yearling
Jan
28
awarded Yearling
Jan
4
comment How does one sample uniformly at random from an uncountably infinite set?
@SashoNikolov By the second option you mean coming up with some probability distribution on some other finite set which could be close in Wasserstein metric to the uniform distribution on the uncountably infinite set? Any examples/reference you know of doing this? Do you have any example of how one constructs an uniform probability distribution in the probability theorists' sense? (..apart from may be "trivial" examples like specifying that the PDF is identically 11 for say an uniform distribution on a line..)
Jan
3
comment What papers should everyone read?
Did the notions of BQP and QMA exist when Feynman wrote this paper? Or is there a recent paper which draws this connection? Any reference/exposition of this fact that k-local Hamiltonian is QMA complete?
Dec
26
comment How does one sample uniformly at random from an uncountably infinite set?
@SashoNikolov What does a probability theorist mean when he/she says, "I know how to sample uniformly at random from this given uncountably infinite set?"
Dec
23
comment How does one sample uniformly at random from an uncountably infinite set?
@usul Could you kindly give a reference which may be demonstrates what you are saying?
Dec
23
comment How does one sample uniformly at random from an uncountably infinite set?
@PeterShor Thanks for the suggestions! Could you kindly elaborate on your comment? (...When talking to a probability theorist they would tend to use the phrase that say for a given uncountable infinite set they "know how to sample uniformly at random". I wonder if such an assertion by a probability theorist is equivalent to having a polynomial time algorithm or are they meaning something different? How does one represent an uniform probability distribution on say a Lie group?...)
Dec
23
asked How does one sample uniformly at random from an uncountably infinite set?
Oct
30
comment What are the recent research directions in the topic of circuit lower bounds from derandomization?
@vzn Thanks for the link! Your list is interesting! Can you share some thoughts about how/if you see these developments in arithmetic complexity being related to the progress in the direction of pseudorandomness and extractors as in the recent works of Raghu Meka, Xin Li etc ?
Oct
30
comment What are the recent research directions in the topic of circuit lower bounds from derandomization?
@D.W. Ofcourse I have seen a lot of papers on this topic! But I don't have a big-picture of this pursuit. What was I was hoping is if some expert can give a short high-level view of what are the big themes and directions of work currently being pursued in this particular field.
Oct
30
awarded Student
Oct
30
awarded Editor
Oct
30
revised What are the recent research directions in the topic of circuit lower bounds from derandomization?
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Oct
30
asked What are the recent research directions in the topic of circuit lower bounds from derandomization?
Oct
30
awarded Autobiographer
Oct
5
revised A question about using Herbst' theorem
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Oct
5
asked A question about using Herbst' theorem
Sep
26
comment About some possible optimality properties of Ramanujan graphs
Thanks for these insights!
Sep
25
awarded Autobiographer
Sep
23
revised About some possible optimality properties of Ramanujan graphs
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