I am currently a
Harry Bateman Research instructor in Mathematics at Caltech. I did my Phd in Mathematics at The
Ohio State University under the supervision of Dr. Dijen Ray-Chaudhuri.
I also hold a
Bachelors(B. Stat.(Hons)) and Masters degree(M. Stat.) in Statistics from The Indian
Statistical Institute (Kolkata and Bangalore),
Here is my CV. And here is a summary of my research.
Research Interests: Combinatorics.
My current research interests include Extremal Combinatorics,
Probabilistic methods, and Design theory. I have
more recently become very interested in the applications
of Probabilistic methods in Combinatorics especially
in Graph-theoretic applications such as coloring problems.
Teaching: I taught Math 121 during Fall 09. I taught the same course in Fall and Spring in 2008 as well. I also taught Ma/CS 6b during Winter 09 and Winter 2010 though I covered different topics. As for Math 121c, I taught a course in Design theory in 2009, and a course on Probabilistic methods in
Combinatorics in 2010. Here is a link to lecture notes (This should see some changes soon as some parts of it are not complete) from this course, thanks to the students of this
course who consented to act as scribes. The nature of the notes is attempt to solve the corresponding 'Exposition Problem'
(see this blog
of Gowers for a definition of this term, not to mention a fantastic
exposition of Razborov's magical theorem!) for the Probabilistic
method. Two important features of this course
that are not covered in other texts/lecture notes are the result of
Pippenger and Spencer on chromatic index of uniform hypergraphs, and
Jeff Kahn's asymptotic solution to the Erdős-Faber-Lovász conjecture. This is my Teaching philosophy.
Check the Teaching
page for more information. Also, see an update on the upcoming course for Winter, Ma/CS6b.
Some of my talks:
Rooted Forest Set Systems and Steiner Designs.
(2005 AMS Spring Eastern Sectional Meeting, Newark, DE, April 2-3, 2005)
Steiner 3-designs: Results Old and New (28th Ohio State -
Denison Mathematics conference, May 19-21, 2006)
Simple $3$-designs and $PSL(2,q)$, $q\equiv 1\pmod 4$ (Wright State
University, Dayton, OH,
November 6, 2006). Additional results in this direction were later
presented at the Nanyang
Technological University, Singapore and National
University of Singapore (NUS) on the 26th and 27th of September,
Infinite families of Steiner $3$-designs with block size $6$
GrapH TheorY conference, Wright State University, Dayton OH, May
$ \lambda$ -Large Type Theorem for Candelabra Systems: ( OSU-Denison
29 conference), The Ohio State University, Columbus, May 17, 2008.
Towards a Lambda-large Theorem for Candelabra Systems: At the 5-day workshop on Combinatorial design theory at The Banff International Research Station (BIRS), November 13, 2008, Banff, Canada.
Graphs with Bounded degree and matching size: Combinatorics Seminar, Caltech, Pasadena, December 4, 2008.
Simple Forbidden Configurations and Steiner designs: Combinatorics Seminar, Caltech, Pasadena, May 11, 2010.
Some coloring and packing problems for Graphs: 3 SURFs of Summer 2010, Combinatorics Seminar, Caltech, Pasadena, October 19, 2010.
Forbidden configurations, extremal set systems, and Steiner designs,
Mathematics Seminar, Indian Institute of Sciences (IISc), Bangalore,
December 14, 2010.
3-designs and PSL(2,q) (Jointly with Dijen Ray-Chaudhuri) : Designs, Codes, and Cryptography, Volume 44 (2007) .
with restricted valency and matching number (jointly with Niraj
Khare) : Discrete
Math., Volume 309, Issue 12, (2009).
infinite families of Candelabra systems with block size 6 and Steiner
designs : J.
Comb. Inform. Sys. Sci., Volume 34, (2009).
A transform of complementary aspects with applications to entropic uncertainty (with P. Mandayam, S Wehner) :
J. Math.Phy., Volume 51, Issue 8,(2010). Also here (online journal copy).
Forbidden Configurations and Steiner Designs : submitted.
A lambda-large theorem for Candelabra systems, preprint.
A Short Proof of Brooks' theorem for List Colorings, preprint.
Baranyai's theorem: An exposition, in preparation.
On optimal planar packings of some trees, (with E. Cohen), in preparation.
On a list coloring problem for graphs embedded on the torus, in preparation.
Over the past two years, I have had the occasion of mentoring undergrad students for a Summer Research Fellowship (SURF). I mentored one student in 2008, and 4 in 2009.
The Electronic Journal of Combinatorics.
MathWorld (a quick
reference in case you forget the definition of something!)
Design Theory : A very
interesting site for design theorists.
Alon's papers: I
find most of his papers extremely well organised, lucidly presented and
very interesting combinatorially-especially some of his survey papers.
Gowers: Apart from his own very exciting material, he also has a link
to some very interesting webpages of equally interesting Combinatorists!
Terrence Tao's Blog:
What can I say - Everything he writes is fantastic!
The Papers of Paul Erdős:
The Renyi Institute seems to be doing a great service to all
Combinatorists by having an online repository of all(all? well, perhaps
not all!) the papers of Paul Erdos. As far as I see, the list looks
pretty comprehensive till 1989.
Douglas West' Open Problem Page.
How to give a talk:
I saw this link on the homepage of Paul Nevái; I have tried to find the
original article but all the links I have found online seem dead
or lead elsewhere. This is apparently based on a talk delivered by
Gian-Carlo Rota on the occasion of the
Rotafest in April, 1996.
I think this
is a vastly superior game to baseball, though my American friends may
Other (Non-mathematical) Interests:
Music: I have now moved samples of my work here
My Blog: I wrote more regularly at one point of time. Some of them were just
random rants/musings. But some of them were written purely for form and structure
rather than content.