My Mathematical Interests

I received my doctorate in mathematics at Queen's University, Kingston. My supervisor is Professor Ram Murty and my thesis was on "Effective equidistribution of eigenvalues of Hecke operators".

I received my Bachelor's degree with honours in mathematics from Lady Shriram College for Women, University of Delhi. Ours was a small department, but very active. LSR was the first college in Delhi to organize an inter-university Mathematics festival in 1997, my freshman year. We had many interesting activities like quizzes, mathematical extempore, dumb-charades(based on mathematical terms) and "Just-A-Minute" sessions. I was actively involved in the festival during the three years that I spent there.

We also had annual presentation sessions, in which participants would give talks on interesting topics that were not covered in our course. I gave talks on the following topics:

• Fermat's Last Theorem
• Analysis in military decision-making
• Category Theory

As an undergraduate, I got a chance to spend a few months in Tata Institute of Fundamental Research, Bombay as a visiting student. I studied algebra under Professor S.M. Bhatawadekar. It was a very motivating experience. Before coming to Queen's, I spent a year at I.I.T. Bombay.

I completed my master's degree at Queen's under the supervision of Professor Murty. My master's thesis was on Generalized Hurwitz zeta functions.

I have presented my MSc thesis in

• Student session of CNTA meeting in Montreal in May, 2002
• ISM 2002 Quebec-Wide Graduate Student Conference
• Connecting Women in Mathematics across Canada, University of Alberta, June 2003

I have given talks in Queen's on the following subjects :

• Analytic continuation of the Riemann Zeta Function via partial summation
• Binomial theorem and the Riemann zeta function
• From prime numbers to irreducible polynomials
• Quadratic Reciprocity via linear algebra
• The sign of the Gaussian Sum for the quadratic character
• Eichler-Selberg Trace Formula
• Continued fractions and Orthogonal Polynomials
• Counting Elliptic Curves with conductor N
• Pell's Equation-from Brahmagupta to Lagrange
• Approaching the large sieve via Fourier Analysis
• Effective Poisson Summation Formula
• Equidistribution of points in a few sequences
• Counting Hecke Eigenforms with Integer Fourier Coefficients
• Fourier Analysis of periodic arithmetic functions
• Capturing primes with a sieve
• Selberg-Beurling polynomials and the large sieve inequality
• A classic function of Ramanujan
• Averages of exponents in factoring integers
• The classic paper of Riemann on the zeta function
• Counting elliptic curves of conductor less than N
• Dirichlet's Class Number Formula revisited

Here are details of my current research work.

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