Title: Conditional Positive Definiteness and Complete Monotonicity in Subnormal Operator Theory

Abstract: On a Hilbert space H, a subnormal operator S is the restriction, to an invariant subspace, of a normal operator N (i.e., N∗N = NN∗). Born in the 1950’s, subnormal operator theory has developed into one of the central areas of modern operator theory, sitting at the intersection of complex function theory and functional analysis. Powered by S. Brown’s 1978 discovery of nontrivial invariant...

Title: Metric lattices

Abstract: A lattice is a partially ordered set so that each pair of elements has a least upper bound and greatest lower bound. I'll describe a class of lattices which admit natural compatible metric structures and give an attempt at what it means to construct continuous limits of sequences of finite metric lattices.

Title: Fibonacci and related numbers in determinants

Abstract: There are many references to matrices or determinants that have Fibonacci numbers as elements. In this talk, we show several determinants expressing the Fibonacci and related polynomials. This method is well-applicable to other numbers or polynomials too. In addition, these results, based on the form of the Hessenberg matrix, allow for many applications such as inverse formulas, explicit expressions, and continued fraction...