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

Theses:

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

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

Papers:

20. Integers expressible as the sum of two rational cubes (with Manjul Bhargava and Ari Shnidman).

19. Local systems and Suzuki groups (with Nick Katz, Gabriel Navarro, Eamonn O'Brien, and Pham Huu Tiep).

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

17. Quadrics in arithmetic statistics.

16. Note on a theorem of Professor X.

15. Modularity and effective Mordell I.

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

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

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

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

10. Square-root cancellation for the signs of Latin squares.

9. Nagell-Lutz, quickly.

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

7. van der Waerden and the primes.

6. Analytic number theory and quadratic reciprocity.*

5. Proof of a conjecture of Stanley-Zanello.

4. Self-conjugate core partitions and modular forms.

3. Low-lying zeroes of Maass form L-functions (with Steven J. Miller).

2. Maass waveforms and low-lying zeros (with Nadine Amersi, Geoffrey Iyer, Oleg Lazarev, Steven J. Miller, and Liyang Zhang).

1. Decidability and shortest strings in formal languages (with Thomas Ang, Luke Schaeffer, and Jeffrey Shallit).

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

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

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

fun!!