Explaining a Mathematics problem

Mathematics Department

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Mid-Hudson Mathematics Consortium

The Mid-Hudson Mathematics Consortium brings together colleges and universities from across the Hudson Valley to strengthen connections among faculty and students. Our goal is to create opportunities to explore mathematics through shared events, collaborative projects, and professional networks. By strengthening these connections, the Consortium enhances students’ educational experiences and builds lasting relationships within the local mathematics community.

Our first initiative is to create a shared list of faculty members who are interested in giving research talks at nearby institutions. Each entry in the list includes a brief bio, talk title, abstract, and contact info, making it easy for departments to invite local speakers and bring new mathematical perspectives to their campuses. This resource is designed to encourage cross-campus engagement, expose students to a wide range of research areas, and strengthen community among mathematics departments in the region. If you are interested in inviting a speaker from the list below to give a talk, please reach out to them directly.

Speaker: Joseph Kirtland
Affiliation: Marist University

Abstract
Identification numbers, such as credit card numbers, ISBNs, UPCs, and vehicle identification numbers, are used to identify individual items, specific products, people, accounts, and documents.  Each time an identification number is transmitted, there is a chance that an error in the number will occur.  To combat this problem, many identification number systems include a check digit and a mathematical calculation to determine if the number received was the number sent.  This talk will present the mathematics behind and the reliability of a variety of schemes used today, including one developed by IBM, and end with a scheme that will find and automatically correct errors.

Bio
Joseph Kirtland received his Ph.D. from the University of New Hampshire and his B.S. from Syracuse University. His professional interests are finite and infinite group theory, linear algebra, mathematics education, and mathematical computing. He also enjoys poetry (Philip Larkin and Mary Oliver are two of his favorite poets), hiking (he and his wife have hiked all the peaks over 3,500 feet in the Catskills), and cycling (his road bike can be often seen in Northern Dutchess County).

Speaker: Andy Borum
Affiliation: Vassar College

Abstract 
The next time you tie your shoes, unravel a charging cable, or twirl a noodle around a fork, think about how this problem could be described mathematically. Here is one possible description, continuing with the noodle example—given two shapes of a three-dimensional curve, one representing the noodle’s starting shape and one representing the goal shape, how should the curve’s endpoints be moved so that the curve deforms from the starting shape into the goal shape? During this process, we should avoid self-intersections of the curve, since the noodle can’t pass through itself, and ensure that the curve remains in stable equilibrium so that the noodle doesn’t slide off of the fork. These two constraints—avoiding self-intersections and remaining stable—make this problem seem particularly challenging. In this talk, I will describe an example of this problem from robotics—manipulation of a thin flexible cable—and I will show how a careful analysis of the equations describing the cable’s shape can lead to a closed-form solution.

Bio
Andy Borum is an Assistant Professor in the Mathematics and Statistics Department at Vassar College, and he was previously a Visiting Assistant Professor in the Department of Mathematics at Cornell University. He received his B.S. in Mathematics and his B.S. in Engineering Science and Mechanics from Virginia Tech in 2012, and his M.S. in 2014 and Ph.D. in 2018, both in Aerospace Engineering, from the University of Illinois at Urbana-Champaign. His research is in applied mathematics and focuses on problems in elasticity, robotics, and control theory.