Sebastian Heller

activity

20092026

most citedBranes through finite group actions

21 citations · 115 across the 37 of their papers we have counts for

collaborators

43 papers

math.DG2026

Embedded special Legendrian surfaces in $S^{5}$

Sebastian Heller, Franz Pedit, Charles Ouyang

We construct the first smooth embedded compact special Legendrian surfaces in $\mathbb S^5$ of genus greater than one. More precisely, for every sufficiently large integer $k$,…

math.DG2023

On the monodromy of holomorphic differential systems

Indranil Biswas, Sorin Dumitrescu, Lynn Heller +2

First we survey and explain the strategy of some recent results that construct holomorphic $sl (2, C)$ -differential systems over some Riemann surfaces $Σ_{g}$ of genus…

math.DG2023

Holomorphic Higgs bundles over the Teichmüller space

Indranil Biswas, Lynn Heller, Sebastian Heller

We study which representations $ρ$ of the fundamental group of a compact oriented surface $X$ admit Higgs data that depend holomorphically on the Riemann surface $Σ = (X, J)$ …

math.AG2023

Parabolic opers and differential operators

Indranil Biswas, Niels Borne, Sorin Dumitrescu +2

Parabolic SL(r,C)-opers were defined and investigated in [BDP] in the set-up of vector bundles on curves with a parabolic structure over a divisor. Here we introduce and study holo…

math.DG2022

Real Slices of $SL (r, C)$ -Opers

Indranil Biswas, Sebastian Heller, Laura P. Schaposnik

Through the action of an anti-holomorphic involution $σ$ (a real structure) on a Riemann surface $X$ , we consider the induced actions on $SL (r, C)$ -opers and study th…

math.DG2022

Loop group methods for the non-abelian Hodge correspondence on a 4-punctured sphere

Lynn Heller, Sebastian Heller, Martin Traizet

The non-abelian Hodge correspondence is a real analytic map between the moduli space of stable Higgs bundles and the deRham moduli space of irreducible flat connections mediated by…

math.DG2022

Higgs bundles and SYZ geometry

Sebastian Heller, Charles Ouyang, Franz Pedit

Using non-Abelian Hodge theory for parabolic Higgs bundles, we construct infinitely many non-congruent hyperbolic affine spheres modeled on a thrice-punctured sphere with monodromy…

math.DG2022

Fuchsian DPW potentials for Lawson surfaces

Lynn Heller, Sebastian Heller

The Lawson surfaces $ξ_{1, g}$ of genus $g$ are constructed by rotating and reflecting the Plateau solution $f_{t}$ with respect to a particular geodesic $4$ -gon $Γ_{t}$ along its bound…

math.AG2022

Infinitesimal deformations of parabolic connections and parabolic opers

Indranil Biswas, Sorin Dumitrescu, Sebastian Heller +1

We compute the infinitesimal deformations of quadruples $(X, S, E_{*}, D)$ , where $(X, S)$ is a compact Riemann surface with $n$ marked points, $E_{*}$ is a parabolic vector bundle on…

math.AG2022

On the monodromy map for the logarithmic differential systems

Marian Aprodu, Indranil Biswas, Sorin Dumitrescu +1

We study the monodromy map for logarithmic $g$ -differential systems over an oriented surface $S_{0}$ of genus $g$ , with $g$ being the Lie algebra of a complex red…

math.AG2021

On the existence of holomorphic curves in compact quotients of $SL (2, C)$

Indranil Biswas, Sorin Dumitrescu, Lynn Heller +1

We prove the existence of a pair $(Σ, Γ)$ , where $Σ$ is a compact Riemann surface with $genus (Σ) \geq 2$ , and $Γ \subset S L (2, C)$ is a cocompact…

math.AG2021

Branched SL(r,C)-opers

Indranil Biswas, Sorin Dumitrescu, Sebastian Heller

We define the branched analog of SL(r,C)-opers and investigate their properties. For the usual SL(r,C)-opers, the underlying holomorphic vector bundle is independent of the opers.…

math.DG2021★ 1 cited

Complete families of embedded high genus CMC surfaces in the 3-sphere (with an appendix by Steven Charlton)

Lynn Heller, Sebastian Heller, Martin Traizet

For every $g ≫ 1$ , we show the existence of a complete and smooth family of closed constant mean curvature surfaces $f_{φ}^{g},$ $φ \in [0, \frac{π}{2}],$ in the round $3$ -sphere defo…

math.AG2021

Holomorphic $sl (2, C)$ -systems with Fuchsian monodromy (with an appendix by Takuro Mochizuki)

Indranil Biswas, Sorin Dumitrescu, Lynn Heller +1

For every integer $g \geq 2$ we show the existence of a compact Riemann surface $Σ$ of genus $g$ such that the rank two trivial holomorphic vector bundle ${\mathcal O}^{\oplus…

math.DG2021★ 6 cited

Constant mean curvature surfaces based on fundamental quadrilaterals

Alexander I. Bobenko, Sebastian Heller, Nicholas Schmitt

We describe the construction of CMC surfaces with symmetries in $S^{3}$ and $R^{3}$ using a CMC quadrilateral in a fundamental tetrahedron of a tessellation of the spac…

math.DG2021

Uniformization of branched surfaces and Higgs bundles

Indranil Biswas, Steven Bradlow, Sorin Dumitrescu +1

Given a compact Riemann surface $Σ$ of genus $g_{Σ} \geq 2$ , and an effective divisor $D = \sum_{i} n_{i} x_{i}$ on $Σ$ with $degree (D) < 2 (g_{Σ} - 1)$ , there is a unique co…

math.AG2020

On certain Tannakian categories of integrable connections over Kaehler manifolds

Indranil Biswas, João Pedro dos Santos, Sorin Dumitrescu +1

Given a compact Kaehler manifold X, it is shown that pairs of the form (E, D), where E is a trivial holomorphic vector bundle on X, and D is an integrable holomorphic connection on…

math.AG2020

Branes and moduli spaces of Higgs bundles on smooth projective varieties

Indranil Biswas, Sebastian Heller, Laura P. Schaposnik

Given a smooth complex projective variety $M$ and a smooth closed curve $X \subset M$ such that the homomorphism of fundamental groups $π_{1} (X) \to π_{1} (M)$ is surjective, we…

math.DG2020

Willmore spheres in the 3-sphere revisited

Sebastian Heller

Bryant \cite{Bryant84} classified all Willmore spheres in $3$ -space to be given by minimal surfaces in $R^{3}$ with embedded planar ends. This note provides new explicit form…

math.AG2020★ 1 cited

Irreducible flat SL(2,R)-connections on the trivial holomorphic bundle

Indranil Biswas, Sorin Dumitrescu, Sebastian Heller

We construct an irreducible holomorphic connection with SL(2,R)-monodromy on the trivial holomorphic vector bundle of rank two over a compact Riemann surface. This answers a questi…

math.DG2019★ 1 cited

Area Estimates for High genus Lawson surfaces via DPW

Lynn Heller, Sebastian Heller, Martin Traizet

Starting at a saddle tower surface, we give a new existence proof of the Lawson surfaces $ξ_{m, k}$ of high genus by deforming the corresponding DPW potential. As a byproduct, we ob…

math.DG2019★ 4 cited

Real projective structures on Riemann surfaces and new hyper-Kähler manifolds

Sebastian Heller

The twistor space of the moduli space of solutions of Hitchin's self-duality equations can be identified with the Deligne-Hitchin moduli space of $λ$ -connections. We use real proje…

math.DG2019

Stability properties of 2-lobed Delaunay tori in the 3-sphere

Lynn Heller, Sebastian Heller, Cheikh Birahim Ndiaye

We show that the of 2-lobed Delaunay tori are stable as constrained Willmore surfaces in the 3-sphere.

math.DG2019

Isothermic constrained Willmore tori in 3-space

Lynn Heller, Sebastian Heller, Cheikh Birahim Ndiaye

We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore energy below $8 π$ . In parti…

Embedded special Legendrian surfaces in S5

On the monodromy of holomorphic differential systems

Holomorphic Higgs bundles over the Teichmüller space

Parabolic opers and differential operators

Real Slices of SL(r,C)-Opers

Loop group methods for the non-abelian Hodge correspondence on a 4-punctured sphere

Higgs bundles and SYZ geometry

Fuchsian DPW potentials for Lawson surfaces

Infinitesimal deformations of parabolic connections and parabolic opers

On the monodromy map for the logarithmic differential systems

On the existence of holomorphic curves in compact quotients of SL(2,C)

Branched SL(r,C)-opers

Complete families of embedded high genus CMC surfaces in the 3-sphere (with an appendix by Steven Charlton)

Holomorphic sl(2,C)-systems with Fuchsian monodromy (with an appendix by Takuro Mochizuki)

Constant mean curvature surfaces based on fundamental quadrilaterals

Uniformization of branched surfaces and Higgs bundles

On certain Tannakian categories of integrable connections over Kaehler manifolds

Branes and moduli spaces of Higgs bundles on smooth projective varieties

Willmore spheres in the 3-sphere revisited

Irreducible flat SL(2,R)-connections on the trivial holomorphic bundle

Area Estimates for High genus Lawson surfaces via DPW

Real projective structures on Riemann surfaces and new hyper-Kähler manifolds

Stability properties of 2-lobed Delaunay tori in the 3-sphere

Isothermic constrained Willmore tori in 3-space

Embedded special Legendrian surfaces in $S^{5}$

Real Slices of $SL (r, C)$ -Opers

On the existence of holomorphic curves in compact quotients of $SL (2, C)$

Holomorphic $sl (2, C)$ -systems with Fuchsian monodromy (with an appendix by Takuro Mochizuki)