Assistant Professors of Mathematics Courtney Gibbons and Andrew Dykstra presented invited research talks at the fall southeastern sectional meeting of the American Mathematical Society. The conference, held Oct. 5-6 at the University of Louisville, featured a broad range of sessions organized by research area.
Gibbons presented in a session on “Commutative Rings, Ideals, and Modules.” Her presentation, “Non-simplicial decompositions of Betti diagrams of complete intersections,” highlighted her work with several co-authors on a paper of the same title.
The paper describes the utility of abandoning certain conventions in Betti diagram decompositions in certain special cases. The authors propose a new decomposition algorithm that, unlike existing algorithms, preserves algebraic information encoded in the tensor product of Tor-independent modules over polynomial rings.
The paper is freely available on the mathematics arXiv maintained by Cornell University and will appear in the Journal of Commutative Algebra later this year.
Dykstra presented “Kakutani Equivalence in the Nearly Continuous Category: Part 2,” the second of two talks summarizing joint work with Ayse Sahin from DePaul University, in a session on “Topological Dynamics and Ergodic Theory.”
Dykstra presented research showing that two specific dynamical systems (the Morse minimal system and the binary odometer) are equivalent in a new category. This category, called “measured topological dynamics,” was introduced in the late 1970s and has seen a surge of new developments since 2000. Dykstra and Sahin’s most recent work, in addition to providing new examples, opens the door to new questions. Because this area of research is so new, the landscape is still far from being fully understood.