Geometric aspects of multiparameter spectral theory

Aspects of Geometric Model Theory

In this paper (based on my tutorial in Utrecht) I want to discuss some themes from contemporary model theory, mainly originating in stability theory and classification theory, and point out some mathematical implications. Model theory has become largely the study of definable sets (or the category of definable sets and functions) in given structures, as well as the study of interpretability and...

Algebraic Aspects of Spectral Theory

We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of n× n matrices with entries that are polynomials or more general analytic functions. Short title: Algebraic Spectral Theory MSC subject classification: 47A56, 47C05, 15A22, 16Sxx, 16Bxx

Geometric Aspects of Heine - Stieltjes Theory

The goal of the paper is to develop a Heine-Stieltjes theory for univariate linear differential operators of higher order. Namely, for a given linear ordinary differential operator d(z) = P k i=1 Q i (z) d i dz i with polynomial coefficients set r = max i=1,...,k (deg Q i (z) − i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) deg Q k (z) = k + r we call it a non-degenerate higher Lamé ope...

Algebro-geometric aspects of Heine-Stieltjes theory

The goal of the paper is to develop a Heine-Stieltjes theory for univariate linear differential operators of higher order. Namely, for a given linear ordinary differential operator d(z) = Pk i=1Qi(z) d dzi with polynomial coefficients set r = maxi=1,...,k(degQi(z)− i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) degQk(z) = k + r we call it a non-degenerate higher Lamé operator. Following...

Some Geometric Aspects in Diffusion Theory