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

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

Mock automorphic forms and the BPS index. Submitted.

Heights of CMcyles and derivatives of Lseries, (with Y. Elias). Submitted.

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

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

Lower bounds for Weil’s Explicit Formula via Selberg’s Trace Formula. Submitted.
Papers
 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
Links
 The Liberated Mathematician the webpage of woke mathematician Piper Harron
 Alice’s Adventures in Numberland stories of gender discrimination in mathematics by Alice Silverberg