​       Papers produced during this summer:​

• A Pair of Diophantine Equations Involving the Fibonacci Numbers, X. Chen, H. V. Chu, F. K. Kesumajana, D. Kim, L. Li, S. J. Miller, J. Yang, C. Yao, The Fibonacci Quarterly 63.3 (2025): 542-553.

• Constructions of Macaulay Posets and Macaulay Rings Penelope Beall, E. Boyali, N. Chen, E. Chlachidze, T. T. Dao, F. Garvey, M. Johnson, Y. O. Li, N. Kuzmanovski, K. Ma, T. Mal, R. M. Mudiyanselage, Q. Mayo, N. Minsky-Primus, A. Seceleanu, S. Veerapaneni, Electronic Journal of Combinatorics 33 (2026).

• ​Generalizations of the M&M Game, S. Das, S. J. Miller, G. Polanco, Y. Wu, X. Wang, A. Yang, C. Yao, The PUMP Journal of Undergraduate Research, to appear.

• The MacaulayPosets package for Macaulay2, P. Beall, N. Kuzomanovski, Y. O. Li, and A. Seceleanu.

• Affine Equivalence of Subsets of Fn2 via Venn Diagrams and Applications to Sidon Sets, K. Calta, S. Covey, T. E. Goldberg, L. L. Rose, D. Rose-Levine, submitted.

• Weak-Type Regularity of the Bergman Projection on Generalized Hartogs Triangles in Cn, C. Kurzenknabe and S. Sundar, The PUMP Journal of Undergraduate Research 9 (2026): 223-241.

• Generalized Infinite Skolem Sequences, S. Mneimneh, S. Farhat, B. Gildea, J. Rosenthal, S. Ganesan, A. Chatterjee, in preparation.

• Quad-packing in the game Evenquads, T. Aiba, D. Català, T. Goldberg, H. Gopalakrishnan, D. Harrelson, L. Rose, and R. Watson, in preparation.

• More to Appear!

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Projects and Mentors: ​

• Asymmetric Colorings of Graphs: Calum Buchanan, Daniel Johnston, Van Magnan, Jeremy Quail, Puck Rombach.

• Dessins d'enfants and complete regular maps: Lisa Berger, Connor Stewart Ajmain Yamin

• Doing Algebra and Analysis with Graphs: Zhanar Berikkyzy, Lisa Naples, Daniel van Wyk, H.G. Siewert.

• Games and Finite Geometry: Timothy Goldberg, Daniel Rose-Levine, Lauren Rose.

• Games and Tools for Math Education: Jyoti Arora, Siddharth Darapuri, Anup Bishnoi.

• Generative machine learning models for data assimilation: Ricardo Baptista, Giulio Trigila, Tanya Wang

• Infinite Skolem Sequences: Saad Mneimneh, Chanel, Saman Farhat, Benjamin Garrett, Paul Cesaretti, Ryan Vaz.

• Macaulay rings and Macaulay posets: Nik Kuzmanovski, Alexandra Seceleanu.

• Nonlocal Models: Petronela Radu, Mikil Foss, Alex Heitzman, Animesh Biswas.

• Probability and Number Theory: Steven J. Miller, Chris Yao, M.Tip Phaovibul, Hung Viet Chu, Diego Garcia, Thomas Rascon, Jingkai (Carl) Ye

• Ribbon knots: Erin Grimes, Sam Lewis-Monkman, Jeffrey Meier, Alex Zupan

• Toeplitz and Hankel Operators on Bergman Spaces: Zhenghui Huo, Duke Kunshan University Nathan Wagner, Brown University Yunus Zeytuncu, Adam Christopherson.