9 papers
Explicit Poincaré duality in the cohomology ring of the SU(2) character variety of a surface
Lisa Jeffrey, Aidan Lindberg, Steven Rayan
We provide an explicit description of the Poincaré dual of each generator of the rational cohomology ring of the character variety for a genus surface with central exte…
Toric co-Higgs bundles on toric varieties
Indranil Biswas, Arijit Dey, Mainak Poddar +1
Starting from the data of a nonsingular complex projective toric variety, we define an associated notion of toric co-Higgs bundle. We provide a Lie-theoretic classification of thes…
Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces
Indranil Biswas, Steven Rayan
We define homogeneous principal Higgs and co-Higgs bundles over irreducible Hermitian symmetric spaces of compact type. We provide a classification for each type of object up to is…
Nonabelian Hodge theory and vector valued modular forms
Cameron Franc, Steven Rayan
We examine the relationship between nonabelian Hodge theory for Riemann surfaces and the theory of vector valued modular forms. In particular, we explain how one might use this rel…
Principal co-Higgs bundles on
Indranil Biswas, Oscar García-Prada, Jacques Hurtubise +1
For complex connected, reductive, affine, algebraic groups , we give a Lie-theoretic characterization of the semistability of principal -co-Higgs bundles on the complex proje…
The Calogero-Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem
Steven Rayan, Thomas Stanley, Jacek Szmigielski
We review the Calogero-Françoise integrable system, which is a generalization of the Camassa-Holm system. We express solutions as (twisted) Higgs bundles, in the sense of Hitchin,…