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I'm currently a postdoctoral fellow at the Indian Institute of Science Education and Research (IISER), Pune; previously at the Max Planck Institut für Mathematik (MPIM), Bonn. My work focuses on the interplay between trace formulae and L-functions in the theory of automorphic forms and representation theory. I also like to think about interactions between homotopy theory and number theory.

In progress

  1. From binary Hermitian forms to Bianchi modular forms, (with C. Karabulut and D. Zagier).

  2. Eisenstein cocycles over imaginary quadratic fields II: p-adic L-functions (with J. Flórez and C. Karabulut).

  3. The balanced Voronoi formula for GL(n,F), (with G. Cherubini).

Preprints

  1. Overconvergent L-packets and eigenvarieties, (with B. Balasubramanyam). Preprint available upon request.

  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.

Loose ends

  • An idea on connecting Bernstein’s ‘Stacks in Representation Theory’ to infinity categories. Slides, PDF.

  • An attempt to formulate the tensor product lift of GL(n) x GL(m) representations in terms of the Hitchin fibration PDF

  • Generalizing work of Fouvry, Kowalski, Michel, on bilinear sums at AWS 2016. (with S. Chow, A. Gafni, D. Lowry-Duda, and T. Mao) PDF

  • An attempt to formulate the notion of a multiplicative genus for Levine’s algebraic cobordism. (with E. Elmanto) PDF

  • Problem session at Sarnak 61 conference – I was a scribe for the problem session held at Peter Sarnak’s 61st birthday conference. PDF

I organized the Langlands Program Seminar at the CUNY GC. Find the notes here.

Some interesting courses I’ve taught:

  • 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

Past teaching:

  • IISER Pune
    • Summer 2017: IISER Pune Summer Student Programme project mentor
  • Williams College
    • Summer 2016: SMALL REU project mentor
  • Vassar College
    • Spring 2016: Multivariable calculus, 2 sections; Topics in geometry
  • Hunter College
    • Fall 2015: Calculus II; Precalculus
    • Spring 2015: Calculus II
    • Fall 2014: Calculus II
    • Summer 2014: Calculus IV
    • Spring 2014: Calculus II; Calculus III
    • Fall 2013: Calculus I; Algebra
  • Brooklyn College - Summer 2013: Pre-Calculus
    • Spring 2013: Thinking Mathematically; Precalculus
    • Fall 2012: Thinking Mathematically, 2 sections
    • Summer 2012: Pre-Calculus
  • Bronx Community College
    • Spring 2012: Arithmetic and Algebra
    • Fall 2011: Arithmetic and Algebra