Original filename: sop.pdf
Title: Soumyo Biswas- Statement of Purpose
Author: Soumyo Biswas
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Statement of Purpose
of Soumyo Biswas (SFB F50: PhD applicant for 2017)
Motivation: Combinatorics became my major field of interest since the time I was able to make significant progress independently in a formerly open conjecture proposed by Martin J Erickson (the conjecture can be found on http://www.openproblemgarden.org/op/a_sequence_defined_on_multisets).
This was done as my summer project in May 2015-July 2015 under the mentorship of Professor Arvind
Ayyer, faculty at maths department, Indian Institute of Science.
Project of Interest and Goals: The project F50-02: Shape Characteristics of Planar Maps and
Planar Graphs has particularly caught my interest; the use of generating functions, as done in Tutte’s
paper (which was mentioned in the notes related to this particular project by Professor Drmota) for
counting the number of rooted maps with n edges is in general of interest to me and I would like to
make similar contributions to the research.
In addition to the above, the notes by Professor Drmota as referred above mention a particular open
problem, viz, whether a planar map has a continuous limit to a Brownian map. This has also particularly caught my interest as Brownian motion is more or less familiar to me (in the context of graduate
level) and a topic of interest, as I have taken a related course-Topics in Probability and Stochastic
Processes (Martingales and Brownian Motion), and am currently doing a reading course on Stochastic Calculus (the instructor for both these courses being Professor Manjunath Krishnapur, faculty at
maths department, Indian Institute of Science).
My expectation is to be able to work on the above open conjecture using principles from combinatorics
as well as those from stochastic calculus which would be fascinating to me as these two fields are ones
that I am the most familiar with and have the most interest in.