Levent Alpöge

Levent Alpöge (NSF postdoc, levent.alpoge@columbia, arXiv, cv)


  1. Points on curves. (My PhD thesis at Princeton.)
    [Standalone papers coming soon! Recent recorded talks on some of the chapters: Ch. 7, Ch.s 9 and 11.]

  2. The average elliptic curve has few integral points. (My senior thesis at Harvard.)


  1. (with Wei Ho) The second moment of the number of integral points on elliptic curves is bounded.

  2. The average number of rational points on odd genus two curves is bounded.

  3. Square-root cancellation for the signs of Latin squares. Combinatorica.

  4. The average number of integral points on elliptic curves is bounded.

  5. van der Waerden and the primes. Amer. Math. Monthly 122 (2015), no. 8, 784-785.

  6. Proof of a conjecture of Stanley-Zanello. J. Combin. Theory Ser. A. 125 (2014), 166-176.

  7. Self-conjugate core partitions and modular forms. J. Number Theory 140 (2014), 60-92.

  8. (with Steven J. Miller) Low-lying zeroes of Maass form L-functions. Int. Math. Res. Not. (2015), no. 10, 2678-2701.

  9. (with Nadine Amersi, Geoffrey Iyer, Oleg Lazarev, Steven J. Miller, and Liyang Zhang) Maass waveforms and low-lying zeros. In: C. Pomerance, M. Rassias (eds.), Analytic Number Theory: in Honor of Helmut Maier's 60th Birthday, 19-56, Springer, 2015.

  10. (with Thomas Ang, Luke Schaeffer, and Jeffrey Shallit) Decidability and shortest strings in formal languages. Descriptional Complexity of Formal Systems, Lecture Notes in Comput. Sci. 6808 (2011), 55-67.

  11. (with Alark Joshi, Dustin Scheinost, John Onofrey, Xiaoning Qian, and Xenios Papademetris) A vtk-based, CUDA-optimized non-parametric vessel detection method. VTK Journal. (My Intel STS project from high school.)

  12. Analytic number theory and quadratic reciprocity. Harvard College Mathematics Review.
              (I once thought I'd discovered a new and "purely analytic" proof of quadratic reciprocity. In fact the argument was known to Dirichlet! So I turned it into a little expository article.
               See the fun!! section for a non-expository version, which amounts to a few lines.)


  1. (with Dennis Gaitsgory and Gurbir Dhillon) Math 123 (= Algebra II) notes.

  2. (with Dennis Gaitsgory) Math 122 (= Algebra I) notes.


my generals

My mathematical hero was sure "analytic number theory is not number theory"! :)

solve for x!
(you may assume char. ≠ 2.)

article XXXIII!