​       Papers produced during this summer:​

• A generative flow for model conditional sampling via optimal transport, J. Alfonso, R. Baptista, A. Bhakta, N. Gal, A. Hou, I. Lyubimova, D. Pocklington, J. Sajonz, R. Tsai, and G. Trigila, NeurIPS 2023 Workshop Optimal Transport and Machine Learning.

• R(K6−e,K4)=30, D. Jones, E. Kahan, and E. Rauer, Graphs and Combinatorics (2025) 41:27.

• Bounds in simple hexagonal lattice and classification of 11-stick knots, Y. Bao, A. Benveniste, M. Campisi, N. Cazet, A. Goh, J. Liu, and E. Sherman, Journal of Knot Theory and Its Ramifications, 32(14), 2350097.

• Solving the n-color ice model, P. Addona, E. Bockenhauer, B. Brubaker, M. Cauthorn, C. Conefrey-Shinozaki, D. Donze, W. Dudarov, J. Dukes, A. Hardt, C. Li, J. Li, Y. Liu, N. Puthanveetil, Z. Qudsi, J. Simons, J. Sullivan, and A. Young, Annals of Combinatorics (2025). 

• Winning Strategies for the Generalized Zeckendorf Game, S. J. Miller, E. Sosis, J. Ye, the Fibonacci Quarterly 60 (2022), 270-292.

•  Schreier Multisets and the s-step Fibonacci Sequences, H. Viet Chu, N. Irmak, S. J. Miller, L. Szalay, S. X. Zhang, to appear in the Proceedings of the 2023 Integers Conference.

• Avoiding 3-Term Geometric Progressions in Hurwitz Quaternions, M. Asada, B. Fang, E. Fourakis, S. Manski, N. McNew, S. J. Miller, G. Moreland, A. Yamin, S. Zhang, Journal of Integer Sequences 27 (2024), Article 24.7.7. 

• Exploring a Geometric Conjecture, some Properties of Blaschke Products, and the Geometry of Curves Formed by Them, M. Celik, M. Duguin, J. Guo, D. Luo, K. Spinelli, Y. E. Zeytuncu, and Z. Zhu, Computational Methods and Function Theory.

• Rainbow common graphs must be forests, Yihang Sun, The Electronic Journal of Combinatorics (2025): P3-7.

• Linear Recurrences of Order at Most Two in Nontrivial Small Divisors and Large Divisors, H. V. Chu, K. H. Le, S. J. Miller, Y. Qiu, and L. Shen, in Combinatorial and Additive Number Theory 2022 & 2023, CANT VI (Melvyn B. Nathanson, editor), Springer.

• A note on integration by parts, M. Logala and V. H. Moll, Scientia Series A: Mathematical Sciences, 2022.

• The Accelerated Zeckendorf Game, Diego Garcia-Fernandezsesma,
  Steven J. Miller, Thomas Rascon, Risa Vandegrift, and Ajmain Yamin,
  the Fibonacci Quarterly 62 (2024), 3-14.

• v-Palindromes: An Analogy To The Palindromes, C. Bispels, M. Boran, S. J. Miller, E. Sosis, and D. Tsai, PUMP 7, 186-206.

• Colorings of symmetric unions and partial knots, B. Clingenpeel, Z. Dai, G. Diraviam, K. Jaber, K. Kar, Z. Liu, T. Miklethun, H. Nagampoozhy, M. Perry, M. Samuelson-Lynn, E. Seamans, N. Xie, A. Wright, R. Zou, A. Zupan, Journal of Knot Theory and Its Ramifications (2025).
• Uniform convergence is not just for Real Analysis, V. H. Moll and S. Saha, Scientia Series A: Mathematical Sciences 33 (2023): 35-37.
• A characterization of prime v-palindromes, M. Boran, G. Choi, S. J. Miller, J. Purice, and D. Tsai.
• Bounds for Rainbow-uncommon Graphs, B. Bates, G. Elvin, Z. Berikkyzy, R. Fines, I. Reiter, M. Lie, N. Chiem, H. Mikulas, K. Zhou. 
• The integrals in Gradshteyn and Ryzhik. Part 32: Powers of trigonometric functions, D. Chen, T. Dunaisky, A. R. McCurdy, V. H. Moll, C. Nguyen, and V. Sharma, Scientia Series A: Mathematical Sciences 32 (2022): 71-98.

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Projects and Mentors:​

• Machine Learning: Ricardo Baptista, Giulio Trigila, David Gomez, Aimee Maurais.

• Finding Ellipses: Yunus Zeytuncu, Mehmet Celik, Kamryn Spinelli

• Large-scale Ramsey project: Anurag Bishnoi, Zhanar Berikkyzy, Luis Garcia Puente, Adam Sheffer, Natasha Morrison, Sherry Sarkar, Eduardo Torres Davila, Gabriel Elvin, George Santellano, Daniel Hathcock, David Narvaez, Lauren Nelsen, Ferdinand Ihringer, Shival Dasu, Surya Mathialagan, Karthik Nataraj, Yaqian Tang.

• Lattice Models: Ben Brubaker, Andy Hardt.

• Combinatorial knot theory: Marion Campisi, Nicholas Cazet.

• Kolmogorov complexity: Johanna Franklin, Michael Chen

• Commutative Algebra: Ananthnarayan Hariharan, Aryaman Maithani.

• Number Theory: Steven J Miller, Ajmain Yamin, Daniel Tsai, Hung Chu.

• Integral Evaluation: Victor Moll, Peter Marcus, Caleb Fong

• Harmonic Analysis: Cody Stockdale, Michael Penrod, John-Oliver MacLellan.

• Ribon Links: Alex Zupan, Ana Wright