Here’s the maths page! First, a professional photo (©MFO):

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Preprints

  1. Shifts of the sum of prime divisor function of Alladi and Erdős, (with S. Shekatkar). Submitted.

  2. Mock automorphic forms and the BPS index. Submitted.

  3. Heights of CM-cyles and derivatives of L-series, (with Y. Elias). Submitted.

  4. Biases in prime factorizations and Liouville functions for arithmetic progressions, (with P. Humphries and S. Shekatkar). Submitted. Latest

  5. Eisenstein cocycles over imaginary quadratic fields I: Values of L-functions, (with J. Flórez and C. Karabulut). Submitted.

  6. Lower bounds for Weil’s Explicit Formula via Selberg’s Trace Formula. Submitted.

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). To appear in Journal of Number Theory.

Past teaching:

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

  • Fall 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