Levent Alpöge (NSF postdoc / junior fellow, alpoge@fas, arXiv, cv)

Theses:

  1. Points on curves. (My PhD thesis at Princeton.)

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

Papers:

  1. Un peu d'effectivité pour les variétés modulaires de Hilbert-Blumenthal.

  2. Quadrics in arithmetic statistics.

  3. Note on a theorem of Professor X.

  4. Modularity and effective Mordell I.

  5. A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so (with Manjul Bhargava and Ari Shnidman).

  6. A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so (with Manjul Bhargava and Ari Shnidman).

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

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

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

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

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

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

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

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

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

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

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

  18. 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.)

Some talks:

    recent recorded talks

"Book":

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

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




fun!!




my generals




some amusing math history links