Title: Computing the Witten-Reshetikhin-Turaev Invariant of 3-Manifolds
Applied Mathematics in Action through Biostatistics
Gideon K. D. Zamba, PhD.
Professor of Biostatistics
Professor of Radiology and Nuclear Medicine
The University of Iowa
Applied mathematics is a field of constant adaptability to the world’s contingencies. Such
adaptability requires a solid training and a keen understanding of theoretical and pure
mathematical thinking—as the activity of applied thinking is vitally connected to research
in pure mathematics. One such applied mathematical field is the field of statistics. As the
world continues to rely more on data for inference and decision making, statistics and
associated data-driven fields have gained an increased recognition. The purpose of this talk
is to educate the audience about the field of statistics, about statistical involvements, and
provide examples of settings where statistical theory finds an application and where real-
world applications call for new statistical developments. The presentation further provides
some general guidance on the mathematical and computational skills needed for a
successful graduate work in Statistics or Biostatistics.
Title: Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras
Abstract: I will review results on classiﬁcation of quantum superintegrable systems on two-dimensional Euclidean space allowing separation of variables in Cartesian coordinates and possessing an extra integral of third or fourth order. The exotic quantum potential satisfy a nonlinear ODE and have been shown to exhibit the Painlevé property. I will also present diﬀerent constructions of higher order superintegrable Hamiltonians involving Painlev´e transcendents using four types of building blocks which consist of 1D Hamiltonians allowing operators of the type Abelian, Heisenberg, Conformal or Ladder. Their integrals generate ﬁnitely generated polynomial algebras and representations can be exploited to calculate the energy spectrum. I will point out that for certain cases associated with exceptional orthogonal polynomials, these algebraic structures do not allow to calculate the full spectrum and degeneracies. I will describe how other sets of integrals can be build and used to provide a complete solution.