This is my research on other topics.
Fun fact: My first successful research was related to the card
game SET. In particular, I showed that in a game of SET with 6
attributes rather than 4, the maximum number of cards that you can
have without having a set is 112.
Papers:
- On the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices.
Dominik Beck, Zelin Lv, and Aaron Potechin. arXiv
- Hardness of sampling for the anti-ferromagnetic Ising model on random graphs.
Neng Huang, Will Perkins, and Aaron Potechin. arXiv
- On induced subgraphs of H(n,3) with maximum degree 1.
Aaron Potechin and Hing Yin Tsang. arXiv
- Clique Is Hard on Average for Unary Sherali-Adams.
Susanna F. de Rezende, Aaron Potechin, and Kilian Risse. FOCS
2023. arXiv
- Ellipsoid Fitting Up to a Constant. Jun-Ting
Hsieh, Pravesh Kothari, Aaron Potechin, and Jeff Xu. ICALP
2023. arXiv
- Near-optimal fitting of ellipsoids to random points.
Aaron Potechin, Paxton Turner, Prayaag Venkat, and Alex Wein.
COLT 2023. arXiv
- The Sixth Moment of Random Determinants. Dominik
Beck, Zelin Lv, and Aaron Potechin. Journal of Integer
Sequences, Vol. 26, Article 23.6.3. 2023. arXiv
- Bounds on the Total Coefficient Size of
Nullstellensatz Proofs of the Pigeonhole Principle and the
Ordering Principle. Aaron Potechin and Aaron Zhang. ICALP 2024. arXiv
- Almost-Orthogonal Bases for Inner Product Polynomials.
Chris Jones and Aaron Potechin. ITCS 2022. arXiv
- Expander Random Walks: The General Case and
Limitations. Gil Cohen, Dor Minzer, Shir Peleg, Aaron
Potechin, and Amnon Ta-Shma. ICALP 2022. ECCC
- A Conjecture on Induced Subgraphs of Cayley Graphs.
Aaron Potechin and Hing Yin Tsang. arXiv
Note: Our conjecture was quickly refuted, see this paper.
- Lengths of Words Accepted by Nondeterministic Finite
Automata. Aaron Potechin and Jeffrey Shallit.
Information Processing Letters Volume 162, October 2020. arXiv
- A note on a problem of Erdos and Rothschild. Aaron
Potechin. arXiv
- The critical group of a line graph. Andrew Berget,
Andrew Manion, Molly Maxwell, Aaron Potechin, and Victor
Reiner. Annals of Combinatorics Volume 16 (2012) Issue 3
p.449-488. arXiv
- Proof of Han's hook expansion conjecture. Kevin
Carde, Joe Loubert, Aaron Potechin, and Adrian Sanborn. arXiv
- Maximal Caps in AG(6,3). Aaron Potechin. Designs,
Codes, and Cryptography. Volume 46 (2008) Issue 3 p.243-259.