activity
20162025
most citedOpers versus nonabelian Hodge

15 citations · 25 across the 15 of their papers we have counts for

collaborators

15 papers

math.DG2025

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…

math.AG2025

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…

math-ph2024

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…

math.DG2024

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…

math.DG2023

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…

math.AG2022

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…

math.AG2021★ 1 cited

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…

math.DG2021

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…

math.AG2020★ 1 cited

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…

math.AG2019★ 1 cited

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…

math.AG2019★ 6 cited

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…

math.AG2018

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…

math.DG2018★ 1 cited

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…

cs.SI2017

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…

math.DG2016★ 15 cited

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…