​       Papers produced during this summer:​

• 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. ​

• 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 15-2 (2022), 271--288.

• Computing Rational Powers of Monomial Ideals, Journal of Symbolic Computation 116 (2023), 39-57.

• When Life Gives You Lemons, Make Mathematicians, Notices of the AMS 68 (2021), 375--478.

• Extending Zeckendorf's Theorem to a Non-constant Recurrence and the Zeckendorf Game on this Non-constant Recurrence Relation, Fibonacci Quarterly 58 (2020), 55--76.

• Winning strategy for the multiplier and multialliance Zeckendorf games, Fibonacci Quarterly 59 (2021), 308--318.

• 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 Explorer-Director 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.

​​

Projects and Mentors:​

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

• Q-Binomials and the Grassmannian: Victor Reiner, Galen Dorpalen-Barry.

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

• Toepliz operators on Bergman spaces, Rearrangement of Series, Weak-type (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.