15 citations · 25 across the 15 of their papers we have counts for
15 papers
Symmetric spaces for groups over involutive algebras and applications to Higgs bundles
Pengfei Huang, Georgios Kydonakis, Eugen Rogozinnikov +1
We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras . In the case when the algebra is Hermitian, or the…
Level structures on parahoric torsors and complete integrability
Georgios Kydonakis, Lutian Zhao
For a smooth complex algebraic curve and a reduced effective divisor on , we introduce a notion of -level structure on parahoric -torsors…
Spectral Networks: Bridging higher-rank Teichmüller theory and BPS states
Clarence Kineider, Georgios Kydonakis, Eugen Rogozinnikov +2
This book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories. It provides the…
Conformal limits in Cayley components and -positive opers
Georgios Kydonakis, Mengxue Yang
We study Gaiotto's conformal limit for the -Hitchin equations, when is a simple real Lie group admitting a -positive structure. We identify a fa…
Fock bundles and Hitchin components
Georgios Kydonakis, Charlie Reid, Alexander Thomas
We introduce the concept of a Fock bundle, a smooth principal bundle over a surface equipped with a special kind of adjoint-valued 1-form, as a new tool for studying character vari…
Tame parahoric nonabelian Hodge correspondence on curves
Pengfei Huang, Georgios Kydonakis, Hao Sun +1
The nonabelian Hodge correspondence for vector bundles over noncompact curves is adequately described by implementing a weighted filtration on the objects involved. In order to est…
Logahoric Higgs Torsors for a Complex Reductive Group
Georgios Kydonakis, Hao Sun, Lutian Zhao
In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group , we introduce a notion of sta…
From hyperbolic Dehn filling to surgeries in representation varieties
Georgios Kydonakis
Hyperbolic Dehn surgery and the bending procedure provide two ways which can be used to describe hyperbolic deformations of a complete hyperbolic structure on a 3-manifold. Moreove…
Poisson Structures on Moduli Spaces of Higgs Bundles over Stacky Curves
Georgios Kydonakis, Hao Sun, Lutian Zhao
We demonstrate the construction of Poisson structures via Lie algebroids on moduli spaces of twisted stable Higgs bundles over stacky curves. The construction provides new examples…
Monodromy of Rank 2 Parabolic Hitchin Systems
Georgios Kydonakis, Hao Sun, Lutian Zhao
We study the monodromy of the Hitchin fibration for moduli spaces of parabolic G-Higgs bundles in the cases when G=SL(2,R), GL(2,R) and PGL(2,R) A calculation of the orbits of the…
The Beauville-Narasimhan-Ramanan correspondence for twisted Higgs -bundles and components of parabolic -Higgs moduli Spaces
Georgios Kydonakis, Hao Sun, Lutian Zhao
We generalize the classical Beauville-Narasimhan-Ramanan correspondence to the case of parabolic Higgs bundles with regular singularities and Higgs -bundles. Using this correspo…
Topological invariants of parabolic -Higgs bundles
Georgios Kydonakis, Hao Sun, Lutian Zhao
For a semisimple real Lie group , we study topological properties of moduli spaces of polystable parabolic -Higgs bundles over a Riemann surface with a divisor of finitely ma…
Model Higgs bundles in exceptional components of the -character variety
Georgios Kydonakis
We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the -Hitchin equations…
Demonstrating research subcommunities in mathematical networks
Steven B. Bradlow, Konstantinos Kapenekakis, Georgios Kydonakis +2
We propose a method for demonstrating sub community structure in scientific networks of relatively small size from analyzing databases of publications. Research relationships betwe…
Opers versus nonabelian Hodge
Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis +3
For a complex simple simply connected Lie group , and a compact Riemann surface , we consider two sorts of families of flat -connections over . Each family is determine…