Polymath Jr. results from summer of 2020
â€‹ Papers produced during this summer:â€‹

Consequences of the packing problem, Journal of Algebraic Combinatorics 54 (2021), 1095–1117 .

Lp Regularity of Toeplitz Operators on Generalized Hartogs Triangles, European Journal of Mathematics, to appear.

Convex geometries representable by at most 5 circles on the plane, submitted to a journal. â€‹

Distinct Distances with L_p metrics, Computational Geometry: Theory and Applications 100 (2022): 101785. Young Researchers Award.

Filtering cohomology of ordinary and Lagrangian Grassmannians, Involve, a Journal of Mathematics 152 (2022), 271288.

Computing Rational Powers of Monomial Ideals, Journal of Symbolic Computation 116 (2023), 3957.

When Life Gives You Lemons, Make Mathematicians, Notices of the AMS 68 (2021), 375478.

Extending Zeckendorf's Theorem to a Nonconstant Recurrence and the Zeckendorf Game on this Nonconstant Recurrence Relation, Fibonacci Quarterly 58 (2020), 5576.

Winning strategy for the multiplier and multialliance Zeckendorf games, Fibonacci Quarterly 59 (2021), 308318.

Convex bodies and asymptotic invariants for powers of monomial ideals, Journal of Pure and Applied Algebra 226 (2022), 107089.

Bounds on Zeckendorf Games, Fibonacci Quarterly, to appear.

Walking to Infinity on the Fibonacci Sequence, Fibonacci Quarterly, to appear.
 Modeling Random Walks to infinity along some number theory sequences, the Journal of Integer Sequences 25 2022, Article 22.6.1.

Walking to Infinity on primes in $\mathbb{Z}[\sqrt{2}]$, submitted to a journal

The ExplorerDirector Game on Graphs, submitted to a journal.

Convex geometries representable with colors, by ellipses on the plane, and impossible by circles, submitted to a journal.
 Approaches to the Generalized Alternating Sign Matrix Conjecture, in preparation.
â€‹â€‹
Projects and Mentors:â€‹

Zeckendorf Games, Walking to Infinity on Special Sequences: Steven Miller*, Clayton Mizgerd, Fei Peng, Tudor Popescu, Nawapan Wattanawanichkul.

QBinomials and the Grassmannian: Victor Reiner, Galen DorpalenBarry.

Convex Geometries: Kira Adaricheva*, Madina Bolat, Gent Gjonbalaj.

Toepliz operators on Bergman spaces, Rearrangement of Series, Weaktype (1,1) Estimates for Riesz Transforms: Yunus Zeytuncu*, Cody Stockdale, Nathan Wagner.

Distinct distances: Adam Sheffer*, Nóra Frankl, Surya Mathialagan, Jonathan Passant.

Monomials, Convex Bodies, and Optimization: Alexandra Seceleanu*, Ben Drabkin, Tingting Tang.

Generalized Alternating Sign Matrices: Ben Brubaker*, Claire Frechette, Elizabeth Kelley, Eric Nathan Stucky.

Explorer Director Game, Hat Guessing Number of Graphs: Pat Devlin*, Erin Meger, Abigail Raz.