Graduate Mentoring Seminar- Dr. Dane Taylor
Mathematics of Multilayer Networks for Data Science and Complex Systems
5:00PM, Tue Feb 19 2019, 250 Mathematics Building
Networks are a natural representation for datasets arising in biology (neuroscience, microbiomes and genetics), social systems (reality mining, politics and online social networks) and critical infrastructures (internet, power grid, and transportation system). Due in part to the diversity of applications, there remains a significant gap between the popular heuristics that are widely used for these systems and the development of rigorous techniques grounded on first principles in mathematics and statistics. I will describe my analyses of multilayer networks in which different layers encode different types of edges, such as complementary datatypes or a network at different instances in time. This research involves a variety of techniques (e.g., linear algebra, perturbation theory, random matrix theory, and computational topology/geometry) and is both applied and theoretical. For example, I will discuss the ranking of U.S. Mathematics Departments using data from the Mathematics Genealogy Project as well as describe the information-theoretic limitations on the detectability of communities in networks. I will focus on situations in which applied mathematics can have significant impact in network science as well as describe situations where the applications are demanding new mathematical methods.
Colloquium- Dr. Steven Mackey, Western Michigan University
"Inverse Problems for Matrix Polynomials and Rational Matrices"
4:00PM, Thu Mar 7 2019, 250 Mathematics bldg.
Matrix polynomials arise in a variety of application areas,
including the vibration analysis of mechanical structures, optimal control,
and linear systems theory. The key structural data of a matrix polynomial
in many such applications are its eigenvalues and elementary divisors (both
finite and infinite), together with its left and right minimal indices. A
fundamental inverse problem for matrix polynomials, then, is to characterize
the combinations of structural data that are realizable by some matrix polynomial.
And when a list of structural data is realizable in principle, is it possible to simply
construct a realization in such a way that the given structural data is transparently
visible, in a manner analogous to the Jordan canonical form for matrices, or the
Kronecker canonical form for matrix pencils? In this talk we discuss recent work
on these questions, and as time permits the analogous questions for rational
Levi Sledd (Vanderbilt)
4:00PM, Fri Mar 8 2019, Math 122
Ruth Charney (Brandeis)
4:00PM, Fri Apr 19 2019, Math 122
Catherine Pfaff (Queen's University)
4:00PM, Fri May 3 2019, Math 122