Publications (39)
Degeneration of torsors over families of del Pezzo surfaces
Ulrich Derenthal, Norbert Hoffmann
Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE-singularities. Let G be the reducti…
Torsion-free rank one sheaves over del Pezzo orders
Norbert Hoffmann, Fabian Reede
Let A be a del Pezzo order on the projective plane over the field of complex numbers. We prove that every torsion-free A-module of rank one can be deformed into a locally free A-mo…
Energy harvesting below the onset of flutter
Merten Stender, Merten Tiedemann, Norbert Hoffmann
This work demonstrates preliminary results on energy harvesting from a linearly stable flutter-type system with circulatory friction forces. Harmonic external forcing is applied to…
The line bundles on moduli stacks of principal bundles on a curve
Indranil Biswas, Norbert Hoffmann
Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G-bundles on any smooth projectiv…
Data assimilation and parameter identification for water waves using the nonlinear Schrödinger equation and physics-informed neural networks
Svenja Ehlers, Niklas A. Wagner, Annamaria Scherzl +3
The measurement of deep water gravity wave elevations using in-situ devices, such as wave gauges, typically yields spatially sparse data. This sparsity arises from the deployment o…
SU(5) Heterotic Standard Model Bundles
Bjorn Andreas, Norbert Hoffmann
We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free…
Physics-informed neural networks for phase-resolved data assimilation and prediction of nonlinear ocean waves
Svenja Ehlers, Norbert Hoffmann, Tianning Tang +5
The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employ…
Stability of Arakelov bundles and tensor products without global sections
Norbert Hoffmann
This paper deals with Arakelov vector bundles over an arithmetic curve, i.e. over the set of places of a number field. The main result is that for each semistable bundle E, there i…
New Examples of Stable Bundles on Calabi-Yau Threefolds
Bjorn Andreas, Norbert Hoffmann
In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefol…
Einstein-Hermitian connection on twisted Higgs bundles
Indranil Biswas, Tomas L. Gomez, Norbert Hoffmann +1
Let be a smooth projective variety over . We prove that a twisted Higgs vector bundle $(\calE\, ,θ)$ on admits an Einstein--Hermitian connection if and only if…
Independent parameters for special instanton bundles on P^{2n+1}
Norbert Hoffmann
Motivated by Yang-Mills theory in 4n dimensions, and generalizing the notion due to Atiyah, Drinfeld, Hitchin and Manin for n=1, Okonek, Spindler and Trautmann introduced instanton…
Torelli theorem for the Deligne--Hitchin moduli space, II
Indranil Biswas, Tomás L. Gómez, Norbert Hoffmann
Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components …
A Torelli theorem for moduli spaces of principal bundles over a curve
Indranil Biswas, Norbert Hoffmann
Let X and X' be compact Riemann surfaces of genus at least 3, and let G and G' be nonabelian reductive complex groups. If one component M_G^d(X) of the moduli space for semistable…
The Boden-Hu conjecture holds precisely up to rank eight
Norbert Hoffmann
Consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the…
The Peregrine breather on the zero-background limit as the two-soliton degenerate solution: An experimental study
Amin Chabchoub, Alexey Slunyaev, Norbert Hoffmann +5
Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine bre…
On the essential dimension of coherent sheaves
Indranil Biswas, Ajneet Dhillon, Norbert Hoffmann
We characterize all fields of definition for a given coherent sheaf over a projective scheme in terms of projective modules over a finite-dimensional endomorphism algebra. This yie…
The Picard group of a coarse moduli space of vector bundles in positive characteristic
Norbert Hoffmann
Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M_{r,L}^{ss} denote the projective coarse moduli scheme of semistable rank r…
Galilean-transformed solitons and supercontinuum generation in dispersive media
Yuchen He, Guillaume Ducrozet, Norbert Hoffmann +2
The Galilean transformation is a universal operation connecting the coordinates of a dynamical system, which move relative to each other with a constant speed. In the context of ex…
Rationality and Poincare families for vector bundles with extra structure on a curve
Norbert Hoffmann
Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, followi…
Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data
Svenja Ehlers, Marco Klein, Alexander Heinlein +4
Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wa…
Stability of the Poincaré bundle
Indranil Biswas, Tomás L. Gómez, Norbert Hoffmann
Let X be an irreducible smooth projective curve, of genus at least two, over an algebraically closed field k. Let denote the moduli stack of principal G-bundles o…
On the rationality problem for forms of moduli spaces of stable marked curves of positive genus
Mathieu Florence, Norbert Hoffmann, Zinovy Reichstein
Let (respectively, ) be the moduli space of smooth (respectively stable) curves of genus with marked points. Over the field of complex numbe…
Dissipative solitons in forced cyclic and symmetric structures
Filipe Fontanela, Aurelien Grolet, Loic Salles +4
The emergence of localised vibrations in cyclic and symmetric rotating structures, such as bladed disks of aircraft engines, has challenged engineers in the past few decades. In th…
Deep-water waves: On the nonlinear Schr{ö}dinger equation and its solutions
Nikolay K. Vitanov, Amin Chabchoub, Norbert Hoffmann
We present a brief discussion on the nonlinear Schr{ö}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather s…
Bridging ocean wave physics and deep learning: Physics-informed neural operators for nonlinear wavefield reconstruction in real-time
Svenja Ehlers, Merten Stender, Norbert Hoffmann
Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation metho…
Directional Soliton and Breather Beams
Amin Chabchoub, Kento Mozumi, Norbert Hoffmann +7
Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, includi…
Moduli stacks of vector bundles on curves and the King-Schofield rationality proof
Norbert Hoffmann
This mainly expository text translates into stack language the proof of King and Schofield for the rationality of moduli schemes of vector bundles on a curve in the coprime case. A…
Some moduli stacks of symplectic bundles on a curve are rational
Indranil Biswas, Norbert Hoffmann
Let C be a smooth projective curve of genus at least 2 over a field k. Given a line bundle L on C, we consider the moduli stack of rank 2n vector bundles E on C endowed with a nowh…
Extreme wave excitation from localized phase-shift perturbations
Yuchen He, Andy Witt, Stefano Trillo +2
The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear disp…
Exploring localization in nonlinear oscillator systems through network-based predictions
Charlotte Geier, Norbert Hoffmann
Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure…
Surface Similarity Parameter: A New Machine Learning Loss Metric for Oscillatory Spatio-Temporal Data
Mathies Wedler, Merten Stender, Marco Klein +2
Supervised machine learning approaches require the formulation of a loss functional to be minimized in the training phase. Sequential data are ubiquitous across many fields of rese…
Homological algebra with locally compact abelian groups
Norbert Hoffmann, Markus Spitzweck
In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders.…
Nonlinear vibration localisation in a symmetric system of two coupled beams
Filipe Fontanela, Alessandra Vizzaccaro, Jeanne Auvray +4
We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bi…
Moduli schemes of generically simple Azumaya modules
Norbert Hoffmann, Ulrich Stuhler
Let A be an Azumaya algebra over a smooth projective variety X or more generally, a torsion free coherent sheaf of algebras over X whose generic fiber is a central simple algebra.…
A birational Torelli theorem with a Brauer class
Norbert Hoffmann, Fabian Reede
Let denote the coarse moduli space of semistable vector bundles of rank with trivial determinant over a smooth projective cur…
Poincaré families of G-bundles on a curve
Indranil Biswas, Norbert Hoffmann
Let G be a reductive group over an algebraically closed field k. Consider the moduli space of stable principal G-bundles on a smooth projective curve C over k. We give necessary an…
Establishing a common data base of ice experiments and using machine learning to understand and predict ice behavior
Leon Kellner, Merten Stender, Hauke Herrnring +4
Machine learning and statistical tools are applied to identify how parameters, such as temperature, influence peak stress and ice behavior. To enable the analysis, a common and sma…
G-torsors and universal torsors over nonsplit del Pezzo surfaces
Ulrich Derenthal, Norbert Hoffmann
Let S be a smooth del Pezzo surface that is defined over a field K and splits over a Galois extension L. Let G be either the split reductive group given by the root system of …
Torelli theorem for the Deligne--Hitchin moduli space
Indranil Biswas, Tomas L. Gomez, Norbert Hoffmann +1
Fix integers and , with if . Given a compact connected Riemann surface of genus , let $\MDH(X)$ denote the corresponding $\text{SL}(r, {\ma…