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Students and faculty in the Mathematics Department collaborate on research and pedagogy in numerous ways. Examples include:

• 700-level senior seminar, a capstone experience for every mathematics major,
• research with faculty as an independent study project (MATH 500), and
• semester or summer paid research assistantship. 

Students also have the opportunity to give presentations on their work in our weekly seminars, school-wide spring and summer research symposia, or at regional and national conferences such as the annual Hudson River Undergraduate Math Conference and the Joint Math Meetings.

John Schmitt and Henry Zhan (‘26.5): Combinatorial Nullstellensatz

Henry Zhan (‘26.5) and Professor John Schmitt collaborated with Professor Erhard Aichinger (Johannes Kepler University in Linz, Austria) in writing a manuscript entitled Structured and Punctured Nullstellensätze.  Submitted for publication at the end of Professor Schmitt’s research visit to JKU’s in June 2025, the manuscript generalizes Noga Alon’s Combinatorial Nullstellensätze in various ways and becomes another useful tool for the Polynomial Method.  It is available here, .  Their journeys also took them twice to in Berkeley, California; the photo shows them on one of these trips at the Golden Gate Bridge.

John Schmitt, Seunghwan Oh ’25, and Xianzhi Wang ’23: polynomial method

Seunghwan Oh (’25) and Xianzhi Wang (’23) recently co-authored a manuscript with Professor John Schmitt which addresses a 48-year-old conjecture of Martin Gardner. They use the polynomial method to show that any placement of queens on a chessboard that is maximal with respect to the property of no-3-in-a-line must have size at least n+1 in the case that n>1 is congruent to 1 modulo 4. Their paper will be published by the European Journal of Combinatorics in March 2025 and is available at .  (Pictured left-to-right: Seunghwan and Xianzhi at a celebratory moment.)

Michaela Kubacki, Ran Brown ‘24, Hugh Easton ‘23, and Tao You ‘23: Computational Fluid Dynamics and Machine Learning

In Summer 2021, Ran Brown ‘24, Hugh Easton, and Tao You worked with Professor Michaela Kubacki to explore applications of machine learning on problems in computational fluid dynamics. This project involved a literary search to build a bibliography database of existing research combining machine learning with computational fluid dynamics. The students then completed two exploratory projects recreating and further exploring results from selected literature: (1) predicting steady-state laminar flow around a object given boundary data and (2) predicting drag on an immersed object in laminar flow. 

John Schmitt, Bryan Currie ‘22, Seamus Turco ’21.5 and Chris Hauptfeld ’21: graph theory

Bryan Currie ’22 and Professor John R. Schmitt collaborated with Professor Jill Faudree (U. Alaska Fairbanks) in writing a revised and greatly expanded survey paper in the field of graph theory. The 98-page paper was published in October 2021 by the  and is titled A Survey of Minimum Saturated Graphs. As of January 2025, the paper has garnered close to 100 citations on GoogleScholar. Currie was supported by the College’s Undergraduate Collaborative Research Fund during the summer of 2020. Seamus Turco ’21.5 and Chris Hauptfeld ’21 assisted in preparing the bibliography and gathering resources. Bryan is now a Ph.D. student at New Jersey Institute of Technology studying applied mathematics.

Alex Lyford, Thomas Rahr ’20, and Tina Chen ’18: using Camels to teach probability

Alex Lyford, along with research assistants Thomas Rahr ’20 and Tina Chen ’18 published an article titled in the journal Teaching Statistics. This article was the culmination of a project where Alex, Tom, and Tina developed 1) a classroom activity designed to teach students how to reason about probability in the context of the board game Camel Upand 2) an app designed to help students better understand probability through the use of simulation. In Camel Up, players place bets on various camel races, and the player with the most money at the end of the game wins! Players with a developed knowledge of probability and expected value typically outperform those without such knowledge, and this activity is designed to teach that knowledge in a way that can be transferred to other situations such as making decisions about jobs or insurance. Alex loves using this activity in MATH 116 - Introduction to Statistical Science.

John Schmitt and Tommaso Monaco ’20: polynomial method

During the 2019 summer, Prof. Schmitt worked with Tommaso Monaco ’20 on a problem arising in combinatorial design theory. A conjecture posed by Marco Buratti (U. Perugia, Italy) states that for the cyclic group of order p and any multi-set of ±è–1 elements coming from the first (p–1)/2 elements of the group, there exists a Hamiltonian path in the complete graph on the cyclic group of order p where the edge lengths of the path are the elements of the given multiset.

Tommaso and Prof. Schmitt showed how one can use the polynomial method to formulate a solution to this problem. They shared this progress with their collaborators whom they met for the first time during the ninth Slovenian International Conference on Graph Theory, held in Bled, Slovenia, in June 2019. Together they are writing a manuscript containing a collection of results with Simone Costa (U. Brescia, Italy), Matt Ollis (Marlboro College, Vermont), Anita Pasotti (U. Brescia, Italy), and Marco Pellegrini (U. Cattolica del Sacro Cuore, Italy).

Steve Abbott and Jingyi Wu ’17: interpolation of triangular numbers

A Bohr Mollerup Theorem for Interpolating the Triangular Numbers recently appeared in the Journal of Complex Analysis. This project grew out of Wu’s interest in learning more about the gamma function as part of an independent study project she initiated in her junior year. Wu is starting a PhD program in Logic and Philosophy of Science at University of California, Irvine. .