The Mathematics Seminar typically meets on Thursdays at 12:45-1:45PM in Adel 163. Any faculty, students, or friends of the department are welcome to attend. Contact the organizers John Neuberger or Dana Ernst or if you have questions.
Note that talks are listed in reverse chronological order.
Dates: Thursday, November 2; Thursday, November 16; Thursday, November 30
Speaker: Dana Ernst (NAU)
Abstract: In combinatorics, the theory of species is a beautiful abstract, systematic method for deriving the generating functions of discrete structures. In this series of talks, we will introduce species, explore various properties, and tinker with a variety of examples.
Dates: Thursday, October 12
Speaker: Jim Swift (NAU)
Dates: Thursday, October 5
Speaker: Samuel Harris (NAU)
Abstract: Some of the nicest unitary matrices to use are permutation matrices—these are square matrices with exactly one “1” in every row and column, and zeros everywhere else. When you relax this condition of “0’s and 1’s” to involve matrices instead, you get magic unitaries: these are block unitary matrices, where each block is a self-adjoint matrix equal to its own square (an “orthogonal projection”), and summing blocks over any row or column gives the identity matrix. In this talk I’ll introduce magic unitaries, why they matter, and an important problem involving their stability.
Dates: Thursday, September 28
Speaker: Rachel Neville (NAU)
Abstract: A classical statistical problem is determining whether data is samples from the same probability distribution. When data is high dimensional, this can prove particularly challenging. I’ll discuss an approach this problem using summaries of topological information about the data. Along the way, I’ll note some interesting connections with work on minimal spanning trees and fractal dimensions. This culminates in a proposed persistence-based test for comparing samples. Some of this is joint work with John Leland.
Dates: Thursday, September 14; Thursday, September 21
Speaker: Michael Falk (NAU)
Abstract: I’ll give an update on the current state of our project to the classify Orlik-Solomon algebras using 2-isomorphism of hypergraphs, a joint project with Geoff Whittle. There will be an appearance of the (exterior) Stanley-Reisner ring of a simplicial complex. I’ll focus on recent developments that involve the Grassmannian of $p$-planes in $n$-space and linear line complexes.
Date: Thursday, September 7
Speaker: Lina Ellis (NAU grad student)
Abstract: We discuss basic potentials of the nonrelativistic and relativistic quantum mechanics that can be integrated in the Nikiforov and Uvarov paradigm with the aid of a computer algebra system. This consideration may help the readers to study analytical methods of quantum physics.