Levent Alpöge (anthropic capabilities / junior fellow, alpoge@fas, arXiv, cv, my minor planet!! :D)

i have paused my appointment at the society of fellows and am now at anthropic i have paused my appointment at the society of fellows and am now at anthropic, an obvious choice for me (given that i was no longer interested in remaining on the sidelines) given their focus on safety --- at the moment i am most interested in testing my many ideas relevant to pretraining and more generally trying to make breakthroughs in capabilities research, and in my view it would be unethical for me to try to do so in an organization giving safety less primacy


me at intel's 2010 sts talking about cuda and moore's law!
behind my hand is the then-canonical image showing the organization of memory on an nvidia gpu
(registers, caches, sram, dram, threads, warps, blocks, grids, etc.)
time flies!

in fact this field switch is a return to my "childhood" work --- in 2009, before i knew what a vector space was, i was writing cuda kernels for (medical) computer vision applications (see e.g. my first paper below)! that work was unprestigious then, so i concluded that i should work on more "serious" topics instead of trying to parallelize everything i could find. hint: prestige is stupid

[it is amusing to wonder what might have been had i remained on that track given how early that work was (i even had a side project in which i attempted to produce style-transferred language output through "gofai" methods, since i knew nothing about neural networks --- it failed)!! --- i conclude that i am glad i gave mathematics my full focus]

in any case my priority now is supporting safety work, though my interests lie in capabilities --- hence anthropic. if you are a mathematician interested in learning the core of the field, especially to either work on safety research or else support it as i am, please let me know! after all, though i was witness to terrible behaviour in the math community (it is large and full of humans :) ), i found the modal member of such to be exactly the kind of person who would have a positive (in my opinion) influence on this field's developments

my papers and such are below, and expect more (non-ai, naturally --- no secrets :) ) to come!

i also hope to throw together a quick video series for math experts trying to quickly learn the field's basics (again no chance of secrets of course :) ) --- but nothing below yet!

finally, and unrelated to anthropic, my dream with this technology has long been to finally make the journal system in mathematics obsolete (i stopped giving my solo works over to journals a year before graduate school --- the arXiv clearly suffices for mathematicians uninterested in politics or ranking others' work) by making formalization practical --- indeed even easy! (imagine a world where it is the norm to upload formalizations along with pdfs to the arXiv! or one where there is a new bourbaki-like push to formalize works like ega...!) whether that is a priority during these rapid developments is unclear, but if you have ideas related to this please let me know :)!

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:

21. Conditional algorithmic Mordell (with Brian Lawrence).

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!!

human languages: english (native), turkish (native), spanish, french, russian, german

through my own laziness the last four are in varying states of disuse

i have started making real progress in ottoman and hope to learn (spoken) latin and (spoken) ancient / modern greek!

i also have character-colour synesthesia!

this includes numbers and other scripts e.g. cyrillic and greek, though not (yet?) ottoman (script or numbers)...!