4 papers
A Non-Abelian Approach to Riemann Surfaces
Mehrzad Ajoodanian
We develop a non-abelian, gauge-theoretic framework for the Schwarzian derivative and for second-order differential equations on Riemann surfaces. As applications, we extend Dedeki…
A Non-Abelian Approach to Riemann Surfaces Part I: Wronskian Geometry
Mehrzad Ajoodanian
We study projectively flat holomorphic vector bundles over Riemann surfaces. To each such bundle, we naturally assign a Wronskian line bundle. The main idea is a notion of the divi…
On Abel's Identity
Mehrzad Ajoodanian
We provide a natural duality that matches, in reverse order, the coefficients of the characteristic polynomial of the Maurer-Cartan of the Wronskian matrix with the coefficients of…
Gauge theory and foliations I; germ cords versus quantum cords
Mehrzad Ajoodanian, Eaman Eftekhary
We apply gauge theory to study the space of smooth codimension- framed foliations on a smooth manifold . The quotient of Maurer-Cartan elements by the action of an i…