Christian Sevenheck

research interests

Hodge theory, non-commutative and irregular aspects
D-modules, hypergeometric systems, Bernstein polynomials
Applications to mirror symmetry
Non-isolated singularities
Frobenius manifolds
Twistor structures, tt*-geometry
Deformation theory

Publications and Preprints

Hypergeometric systems from groups with torsion, with Thomas Reichelt and Uli Walther, arXiv:2402.00762, 16 pages, 2024
Tautological systems, homogeneous spaces and the holonomic rank problem, with Paul Görlach, Thomas Reichelt, Avi Steiner and Uli Walther, arXiv:2211.05356, 57 pages, 2022
Betti structures of hypergeometric equations, with Davide Barco, Marco Hien and Andreas Hohl "International Mathematics Research Notices", volume 2023, issue 12, pages 10641–10701, 2023
Algebraic aspects of hypergeometric differential equations, with Thomas Reichelt, Mathias Schulze and Uli Walther, "Beiträge zur Algebra und Geometrie", volume 62, number 1, p. 137-203, 2021
Hodge ideals of free divisors, with Alberto Castaño Domínguez and Luis Narváez Macarro, "Selecta Mathematica", volume 28, article number 57, 2022
Tautological systems and free divisors, with Luis Narváez Macarro, "Advances in Mathematics", volume 352, p. 372-405, 2019
Examples of hypergeometric twistor D-modules, with Alberto Castaño Domínguez and Thomas Reichelt, "Algebra & Number Theory", volume 13, number 6, p. 1415-1442, 2019
Irregular Hodge filtration of some confluent hypergeometric systems, with Alberto Castaño Domínguez, "Journal de l'Institut mathématique de Jussieu" volume 20, number 2, p. 627-668, 2021
On the b-functions of hypergeometric systems, with Thomas Reichelt and Uli Walther, "International Mathematics Research Notices", volume 2018, issue 21 pages, p. 6535–6555
Hypergeometric Hodge modules, with Thomas Reichelt, Algebraic Geometry, volume 7, number 3, p. 263-345, 2020
Non-affine Landau-Ginzburg models and intersection cohomology, with Thomas Reichelt, "Annales scientifiques de l'École Normale Supérieure", volume 50, number 3, p. 665-753, 2017
Mirror symmetry, singularity theory and non-commutative Hodge structures, "Jahresbericht der DMV", volume 114, number 3, p. 131-162, 2012
Duality of Gauß-Manin systems associated to linear free divisors, "Mathematische Zeitschrift", volume 274, issue 1, p. 249-261, 2013
Logarithmic Frobenius manifolds, hypergeometric systems and quantum D-modules, with Thomas Reichelt, "Journal of Algebraic Geometry", volume 24, issue 2, 201-281, 2015
Summary of scientific work: Frobenius manifolds and variation of twistor structures in singularity theory, 22 pages, 2009
Bernstein polynomials and spectral numbers for linear free divisors, "Annales de l'Institut Fourier", volume 61, issue 1, p. 379-400, 2011
Twistor structures, tt*-geometry and singularity theory, with Claus Hertling, in "From Hodge theory to Integrability and tQFT: tt*-geometry", p. 49-73, 2008, Proceedings of Symposia in Pure Mathematics, American Mathematical Society
Limits of families of Brieskorn lattices and compactified classifying spaces, with Claus Hertling, "Advances in Mathematics", volume 223, p. 1155-1224, 2010
Linear free divisors and Frobenius manifolds, with Ignacio de Gregorio and David Mond, "Compositio Mathematica", volume 145, issue 5, p. 1305-1350, 2009
Curvature of classifying spaces for Brieskorn lattices, with Claus Hertling, "Journal of Geometry and Physics", volume 58, issue 11, p. 1591-1606, 2008
Nilpotent orbits of a generalization of Hodge structures, with Claus Hertling, "Journal für die reine und angewandte Mathematik", volume 609, p. 23-80, 2007
Unobstructed lagrangian deformations, "Comptes Rendus Mathématiques", volume 338, issue 8, p. 617-622, 2004
Rigid and Complete Intersection Lagrangian Singularities , with Duco van Straten, "manuscripta mathematica", volume 114, number 2, p. 197-209, 2004
Deformation of singular lagrangian subvarieties, with Duco van Straten, "Mathematische Annalen", Volume 327, number 1, p. 79-102, 2003
Ph.D. thesis: Lagrangian singularities, Cuvillier-Verlag Göttingen, 2003

Reports, Lecture Notes and non-refereed papers

D-modules and isolated hypersurface singularities (Handwritten notes), 6 lectures, summer school Madrid, june 2011
Singularitäten und Hodgetheorie (in german), Nachrichten der DMV, 2012
Toric geometry, hypergeometric D-modules and mirror symmetry, Oberwolfach Report, volume 9, number 3, S. 2852-2854, 2012
Landau-Ginzburg models for complete intersections, Oberwolfach Report, volume 9, number 2, S. 1388-1389, 2012
Gauß-Manin systems and Frobenius manifolds for linear free divisors, Oberwolfach Report, volume 6, number 3, S. 2432-2433, 2009
Variation of twistor structures and hypersurface singularities, Oberwolfach Report, volume 3, number 3, S. 2531-2533, 2006

address

Technische Universität Chemnitz
Fakultät für Mathematik
09107 Chemnitz
Germany
email: christian.sevenheck@mathematik.tu-chemnitz.de