​       Papers produced during this summer:​

• Axial constants and sectional regularity of homogeneous ideals, M. DeBellevue, A. Lebovitz, Y. Li, M. Lotfi, S. Mohite, X. Pan, M. S. Pathak, S. R. Zamir, A. Seceleanu, S. X. Zhang, Proceedings of the AMS 151 (2023), 1363–1378.

• Vertex Distortion Detects the Unknot, M. Campisi, N. Cazet, D. Crncevic,  T. Fellman, P. Kessler, N. Rieke, V. Srivastava, L. Torres, Journal of Knot Theory and Its Ramifications 31 (2022): 2250074.

• Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triples, T. Jaklitsch, T. C. Martinez, S. J. Miller, S. Mukherjee, Rocky Mountain Journal of Mathematics, to appear.

• On Benford’s Law and the Coefficients of the Riemann Mapping, F. Beretta, J. Dimino, W. Fang, T. C. Martinez, S. J. Miller, D. Stoll, Fractal and Fractional, to appear. 

• The lexicographically least square-free word with a given prefix, S. Berera, A. Gómez-Colunga, J. Lakerdas-Gayle, J. López, M. Matin, D. Roebuck, E. Rowland, N. Scully, and J. Whidden, Electronic Journal of Combinatorics 30 (2023) #P3.11.

• k-Diophantine m-tuples in finite fields, T. Hammonds, S. Kim, S. J. Miller, A. Nigam, K. Onghai, D. Saikia, International Journal of Number Theory 19 (2023), 891-912.

• On the cardinality of minimal presentations of numerical semigroups, C. Elmacioglu, K. Hilmer, C. O'Neill, M. Okandan, and H. Park-Kaufmann, Algebraic Combinatorics, to appear.

• On faces of the Kunz cone and the numerical semigroups within them, L. Borevitz, T. Gomes, J. Ma, H. Niergarth, C. O'Neill, D. Pocklington, R. Stolk, J. Wang, S. Xue, submitted. 

• The integrals in Gradshteyn and Ryzhik. Part 31: Forms containing binomials, D. Chen, S. Choudhry, A.-R. Corcau, T. Dunaisky, B. Larson, D. Leahy, X. Li, M. Logal, A. R. McCurdy, Q. Miao, P. Mohapatra, V. H. Moll, C. Nguyen, O. Peterson, N. Ragunathan, V. Sharma, B. Sisler, R. Tarsala, and H. Zayour, submitted.

• Benfordness of the Generalized Gamma Distribution, Z. Bi, I. Durmić, S. J. Miller, PUMP Journal of Undergraduate Research, to appear. 

• 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, submitted.

• Tri-plane diagrams for simple surfaces in S^4, W. Allred, M. Aragon, Z. Dooley, A. Goldman, Y. Lei, I. Martinez, N. Meyer, D. Peters, S. Warrander, A. Wright, and A. Zupan, submitted to a journal. 

• Class Numbers and Pell's Equation x^2+105y^2=z^2, T. Jaklitsch, T. C. Martinez, S. J. Miller, S. Mukherjee, Proc. of International Conference on Class Groups of Number Fields and Related Topics, 2021.

• Distinct Distances in R^3 Between Quadratic and Orthogonal Curves, T. Aldape, J. Liu, G. Pylypovychm, A. Sheffer, and M.-Q. Vo, submitted.

• On faces of the Kunz polyhedron and the semigroups within them, L. Borevitz, T. Gomes, J. Ma, C. O'Neill, D. Pocklington, R. Stolk, J. Wang, Shuhang Xue, in preparation. 

• Betti numbers of quadratic ideals of low embedding dimension, A. Agarwal, M. Batavia, Z. Lihn, H. Lu, A. Maithani, A. Pradhan, S. Rath, A.Seceleanu, in preparation.

• On preferential sampling from urns, J. Burden, C. Chakraborty, Q. Fang, L. Lin, N. Malibari, S. Matoush, I. Milbank, M. Prado, R. Ren, Q. Rong, M. Sánchez Garza, E. Sun, E. Treviño, in preparation.

• Analyses of Tapatan and Picaria, A. G. Adams, L. P. Arceneaux, H. Benham, A. Bhartari; M. Cruz-Larios, Q. Dong, L. F. Estrada, J. Franklin, A. Gangal, Z. J. Hercher, K. J. Martindale, H. P. Neveux, Y. Qiu, X. Shi, M. S. Sun, M. W. Sunseri, H. Tiwari, H. Verma, W. Wang, E. Worrell, and J. Wu, in preparation.

• More to come?

​

Projects and Mentors:​

• Expanding Polynomials: Adam Sheffer, Sara Fish, Sam Mansfield, Sophie Stevens, Audie Warren.

• Benford's Law: Steven J. Miller, Thomas C. Martinez, Danny Stoll.

• Number Theory: Steven J. Miller, Thomas C. Martinez.

• Markov Games: Johanna Franklin, Heidi Benham.

• Computational Algebra: Alexandra Seceleanu, Michael DeBellevue, Shah Roshan Zamir.

• Finding Ellipses: Yunus Zeytuncu, Gabe Udell.

• Gelfand–Tsetlin Polytopes: Ben Brubaker, Andy Hardt.

• Square-free Words: Eric Rowland, John Jairo Lopez.

• Lattice Knots and Links: Marion Campisi, Nicholas Cazetemail, Luis Torres.

• Numerical Semigroups and Polyhedra: Christopher O'Neill, Tara Gomes, Rene Ardila.

• Diophantine m-tuples and elliptic curves: Seoyoung Kim, Steven J. Miller, Trajan Hammonds. 

• Knotted surfaces in dimension four: Alex Zupan, Nicholas Meyer, Ana Wright.

• Selecting balls from urns: Enrique Treviño, Maximiliano Sánchez Garza.

• Schreier graphs of self-similar groups: Zoran Sunic, John Connell.

• Anti-Ramsey multiplicities of graphs: Zhanar Berikkyzy, Gabriel Elvin.

• Evaluating Integrals: Victor Moll, Vaishavi Sharma.

• Erdos-Ko-Rado Problems: Pat Devlin, Erin Meger, and Luis Perez.