Members of the Math Association of America gathered Friday and Saturday at Hillsdale College for the first time for the Michigan chapter’s annual meeting.
Associate Professors of Mathematics David Gaebler and David Murphy, chair members of the Michigan MAA’s 2016 local arrangements committee, organized the event. The gathering drew 120 students and faculty from 17 schools.
Murphy and three other Michigan faculty members each gave a lecture. Over 20 students, including senior Daniel Slonim, presented their research on various topics, ranging from mathematical proofs to educational programs.
Most of the students at the meeting attended Michigan colleges. Faculty from the University of Michigan, The Ohio State University, Loyola Marymount University, and University of Northern Colorado delivered lectures.
Murphy’s lecture, “Desingularizations of Some Nilpotent Orbit Closures,” summed up three years of research, beginning before he joined Hillsdale’s faculty in 2007.
“This is work that was actually started while I was at Kalamazoo,” he said. “It is in some sense, a preliminary report. It’s still ongoing work. We don’t have all the results we wanted.”
His main goal, he said, was to “make progress.”
He conducted his work with Professor Terrell L. Hodge of Western Michigan University. Murphy said he was unfazed by his research’s missing solutions.
“It’s the case with math,” he said. “Generally, we have far more questions than answers.”
Slonim spoke on “Interleaving of Path Sets” and discussed combining infinite sequences of numbers. He assisted Assistant Professor of Mathematics William Abram, Artem Bolshakov of the University of Texas at Dallas, and Professor Jeffrey Lagarias from the University of Michigan.
“They’ve been working on this project for a while now,” Slonim said. “I just joined them this summer and have been working on it through the year.”
Slonim’s work dealt with path sets, which he described as, “a set of infinite sequences over a given finite alphabet,” where the alphabet defined the set of symbols or numbers used in a sequence.
The researchers used labeled graphs of arrows and numbers to show the patterns of the sequences. The infinite sequences, Slonim said, could be woven together to form new sequences. This could also occur between sets of sequences, which formed new sets. These combinations assist mathematicians in the study of fractals, but scientists have found a new use for them, as well.
“Interleaving of path sets also has applications to neural networks,” Slonim said. “There is a group of scientists in Taiwan who are working on that right now. That was an application that nobody who was working on this anticipated.”
Despite the scientific advances being made overseas, Slonim explained he only researched path sets to understand them better.
“We’re mostly studying them because they’re interesting in their own right,” he said.
