Here’s the maths page!

Papers

  1. On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy, with O.E. Gonzalez, C.H. Kwan, S.J. Miller, R. Van Peski. Journal of Number Theory, 183C (2018) pp. 407-427. Journal ArXiv

  2. Biases in prime factorizations and Liouville functions for arithmetic progressions, with P. Humphries and S. Shekatkar. Journal de théorie des nombres de Bordeaux, 31 no. 1 (2019), p. 1-25. Journal ArXiv

  3. Eisenstein cocycles over imaginary quadratic fields and special values of L-functions, with J. Flórez and C. Karabulut. Journal of Number Theory. Volume 204, November 2019, pp. 497-531. Journal ArXiv

  4. On the balanced Voronoi formula for GL(n). To appear in Functiones et Approximatio. Journal ArXiv

  5. Universal Fourier expansions for Bianchi modular forms. To appear in International Journal of Number Theory. Journal ArXiv

  6. Shifts of the sum of prime divisor function of Alladi and Erdős, with S. Shekatkar. To appear in Integers. Journal ArXiv

  7. Explicit formulas for the spectral side of the trace formula of SL(2). To appear in Acta Arithmetica. Journal ArXiv

Preprints

  1. Lattice points in quadratic irrational polytopes, with Y. Gaur. ArXiv

  2. Mock automorphic forms and the BPS index. ArXiv

  3. On stable orbital integrals and the Steinberg-Hitchin base. Preprint

  4. On the computational complexity of MSTD sets, with T. Mathur. ArXiv

  5. Refinements of the trace formula for GL(2). ArXiv

  6. Endoscopic points on Siegel eigenvarieties, with B. Balasubramanyam. Preprint

  7. The three gap theorem and periodic functions, with A. Suki Dasher and A. Hermida.

Some past teaching:

I organized the Langlands Program Seminar at the CUNY GC from 2014–2016. Find the notes here.

  • Spring 2018: Stochastic Processes - IISER Pune

    This course assumes a background in measure theoretic probability. We develop the basics of continuous martingales, then move on to Brownian motion, which sets the stage for stochastic integration, or Itô calculus. We then develop the theory of stochastic differential equations, and discuss applications to PDEs and also mathematical finance. Find the notes here.

  • Spring 2016: Topics in Geometry - Vassar College

    The first half of the course introduces Galois theory through famous problems in geometry; the second half of the course hints at modular forms through the problem of sums of squares, from Fermat to Jacobi. Find the notes here.

  • Fall 2012: Thinking Mathematically - Brooklyn College

    The first half of the course develops mathematical thinking in the sense of logic and proof; the second half of the course approaches social justice through matehmatical tools, considering how numbers can be used and misused. Text: Rethinking Mathematics: Teaching Social Justice by the Numbers, Eric Gutstein and Bob Peterson Eds., 2013