Marcus’s talk, “A philosophical account of mathematics that won’t make you hate philosophers,” was hosted by the Mathematical Association of America’s special interest group on the philosophy of mathematics.
Marcus said that in general, knowing about something requires sense experience – but that mathematics seems to evade sense experience in that much of what we know about it cannot not be perceived by our senses. He discussed how a theory of knowledge for mathematics called autonomy Platonism can make use of intuition in a way that does not challenge our confidence in mathematics.
Several faculty members also presented research at the JMM. Professor of Mathematics Sally Cockburn and Debra Boutin, the Samuel F. Pratt Professor of Mathematics, discussed their work in a session on “Women in Graph Theory.”
Cockburn’s presentation, “Edge Determining Sets and Determining Index,” was based on a 2022 summer research project with Sean McAvoy ’23 in which they investigated a new way of quantifying the symmetry of a network. Knowing that a given drawing of a network can look very symmetric and that different drawings of the same network can look very different, they examined how symmetric the actual underlying system of nodes and connections is by using edges, the connections between nodes.
Boutin’s talk addressed work that was similar to that of Cockburn and McAvoy but raised different questions to ask (parameters to find) that tell different stories about the symmetries of a given network using their nodes.
Also in that session, “Breaking Symmetries of Mycielskian Graphs,” a paper on which Cockburn and Boutin were co-authors, was presented by Sarah Loeb of Hampton Sydney College.
Visiting Professor of Mathematics Saber Ahmed gave two papers at the meetings. In a session on the Mathematical Sciences Research Institute Undergraduate Program (MSRI-UP), he presented “Highest Weight Modules Over The Quantum Periplectic Superalgebra of Type P.” He also discussed “Periplectic q-Brauer algebra” in a session featuring papers by recent doctoral recipients. Both papers were co-authored with Dimitar Grantcharov of the University of Texas at Arlington, and N. Guay of the University of Alberta.
In addition to the faculty presentations, several students discussed their research. Awildo Gutierrez ’23 presented “The Effect of Operations on the Deficiency of Chemical Reaction Networks” in the MRSI-UP session. Gutierrez participated in the MRSI program last summer. The paper was co-authored with Elijah Leake, a 2022 graduate of DePaul University, and Caelyn Sobie, a student at Arizona State University.
Austin Pineau ’23 presented research on “Geometric characteristics of symmetric numerical semigroups in the Kunz cone” both in a poster session and as a paper in a session on math research by undergraduates and students in post-baccalaureate programs. Pineau co-authored the paper with students from Wellesley College, Rutgers University, and Scripps College.
“Bond Lattices, Parking Functions, and Unimodal Forests,” a paper on which Sophie Rubenfeld ’23 was a co-author, was presented in a session on women in graph theory.
Mathematics and Statistics
Math majors at Hamilton explore both the abstract, theoretical aspects of mathematics and its applications to a variety of topics.