Prof. Dr. Frederik Witt

Lehrstuhlleiter

Forschung

Theoretische Mathematik / Differential- und algebraische Geometrie

Preprints:   arXiv | iNSPIRE

Datenbanken:   MathSciNet | zbMATH | ORCID

Veranstaltungen im SoSe 25

Forschungsfreisemester

05 Combinatorics
  • 05E14 Combinatorial aspects of algebraic geometry
06 Order, lattices, ordered algebraic structures
  • Algebraic aspects of posets
14 Algebraic geometry
  • 14A20 Generalizations (algebraic spaces, stacks)
  • 14C20 Divisors, linear systems, invertible sheaves
  • 14D20 Algebraic moduli problems, moduli of vector bundles
  • 14F06 Sheaves in algebraic geometr
  • 14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
  • 14M25 Toric varieties, Newton polyhedra, Okounkov bodies
  • 14H60 Vector bundles on curves and their moduli
  • 14J32 Calabi-Yau manifolds (algebro-geometric aspects)
  • 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
18 Category theory; homological algebra
  • 18G10 Resolutions; derived functors (category-theoretic aspects)
32 Several complex variables and analytic spaces
  • 32Q25 Calabi-Yau theory
35 Partial differential equations
  • 35G25 Initial value problems for nonlinear higher-order PDEs
  • 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
  • 35J56 Boundary value problems for first-order elliptic systems
  • 35K55 Nonlinear parabolic equations  
  • 35R01 Partial differential equations on manifolds
52 Convex and discrete geometry
  • 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) 
  • 52C05 Lattices and convex bodies in 2 dimensions (aspects of discrete geometry)
53 Differential geometry
  • 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
  • 53C10 G-structures
  • 53C20 Global Riemannian geometry, including pinching
  • 53C24 Rigidity results
  • 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
  • 53C26 Hyper-Kähler and quaternionic Kähler geometry, "special'' geometry 
  • 53C27 Spin and Spinc geometry
  • 53C29 Issues of holonomy
  • 53C38 Calibrations and calibrated geometries 
  • 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 
  • 53C50 Lorentz manifolds, manifolds with indefinite metrics
  • 53C80 Applications of global differential geometry to the sciences
  • 53D05 Symplectic manifolds (general theory)
  • 53D18 Generalized geometries (à la Hitchin) 
  • 53D35 Global theory of symplectic and contact manifolds
55 Algebraic topology
  • 55N05 Čech types
58 Global analysis, analysis on manifolds
  • 58D17 Manifolds of metrics (esp. Riemannian)
  • 58D27 Moduli problems for differential geometric structures
  • 58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
  • 58E30 Variational principles in infinite-dimensional spaces
  • 58J32 Boundary value problems on manifolds
  • 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)
81 Quantum theory
  • 81T13 Yang-Mills and other gauge theories in quantum field theory
  • 81T30 String and superstring theories; other extended objects (e.g., branes)
  • 81T60 Supersymmetric field theories
83 Relativity and gravitational theory
  • 83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
  • 83E30 String and superstring theories in gravitational theory
  • 83E50 Supergravity

Veröffentlichungen

  1. 25. Altmann, K., Hochenegger, A., Witt, F.: Toric sheaves and polyhedra, https://arxiv.org/abs/2412.03476, (2024).
  2. 24. Altmann, K., Witt, F.: The structure of exceptional sequences on toric varieties of Picard rank two. Algebr. Comb. 7, 1039--1074 (2024). https://doi.org/10.5802/alco.371.
  3. 23. Altmann, K., Hochenegger, A., Witt, F.: Exceptional sequences of line bundles on projective bundles, https://arxiv.org/abs/2303.10924, (2023).
  4. 22. Altmann, K., Witt, F.: Toric co-Higgs sheaves. J. Pure Appl. Algebra. 225, 20 (2021). https://doi.org/10.1016/j.jpaa.2020.106634.
  5. 21. Ammann, B., Kröncke, K., Weiss, H., Witt, F.: Holonomy rigidity for Ricci-flat metrics. Math. Z. 291, 303--311 (2019). https://doi.org/10.1007/s00209-018-2084-3.
  6. 20. Mazzeo, R., Swoboda, J., Weiss, H., Witt, F.: Asymptotic geometry of the Hitchin metric. Commun. Math. Phys. 367, 151--191 (2019). https://doi.org/10.1007/s00220-019-03358-y.
  7. 19. Mazzeo, R., Swoboda, J., Weiss, H., Witt, F.: Ends of the moduli space of Higgs bundles. Duke Math. J. 165, 2227--2271 (2016). https://doi.org/10.1215/00127094-3476914.
  8. 18. Ammann, B., Weiss, H., Witt, F.: A spinorial energy functional: critical points and gradient flow. Math. Ann. 365, 1559--1602 (2016). https://doi.org/10.1007/s00208-015-1315-8.
  9. 17. Ammann, B., Weiss, H., Witt, F.: The spinorial energy functional on surfaces. Math. Z. 282, 177--202 (2016). https://doi.org/10.1007/s00209-015-1537-1.
  10. 16. Mazzeo, R., Swoboda, J., Weiß, H., Witt, F.: Limiting configurations for solutions of Hitchin’s equation. In: Actes de Séminaire de Théorie Spectrale et Géométrie. Année 2012--2014. pp. 91--116. St. Martin d’Hères: Université de Grenoble I, Institut Fourier (2014). https://doi.org/10.5802/tsg.296.
  11. 15. Fino, A., Semmelmann, U., Wiśniewski, J., Witt, F. eds: Mini-workshop: Quaternion Kähler Structures in              Riemannian and Algebraic Geometry. Oberwolfach Rep. 10, 3115--3145 (2013). https://doi.org/10.4171/OWR/2013/53.
  12. 14. Weiß, H., Witt, F.: A heat flow for special metrics. Adv. Math. 231, 3288--3322 (2012). https://doi.org/10.1016/j.aim.2012.08.007.
  13. 13. Weiss, H., Witt, F.: Energy functionals and soliton equations for G_2-forms. Ann. Global Anal. Geom. 42, 585--610 (2012). https://doi.org/10.1007/s10455-012-9328-y.
  14. 12. Hochenegger, A., Witt, F.: On complex and symplectic toric stacks. In: Contributions to algebraic geometry. Impanga lecture notes. Based on the Impanga conference on algebraic geometry, Banach Center, Bedlewo, Poland, July 4--10, 2010. pp. 305--331. Zürich: European Mathematical Society (EMS) (2012). https://doi.org/10.4171/114-1/11.
  15. 11. Gayet, D., Witt, F.: Deformations of associative submanifolds with boundary. Adv. Math. 226, 2351--2370 (2011). https://doi.org/10.1016/j.aim.2010.09.014.
  16. 10. Jeschek, C., Witt, F.: Generalised geometries, constrained critical points and Ramond-Ramond fields. Fortschr. Phys. 59, 494--517 (2011). https://doi.org/10.1002/prop.201000097.
  17. 9. Witt, F.: Gauge theory in dimension 7. In: Special metrics and supersymmetry. Lectures given in the workshop on geometry and physics: special metrics and supersymmetry, Bilbao, Spain, 29--31 May 2008. pp. 180--195. Melville, NY: American Institute of Physics (AIP) (2009). https://doi.org/10.1063/1.3089202.
  18. 8. Witt, F.: Metric bundles of split signature and type II supergravity. In: Recent developments in pseudo-Riemannian geometry. pp. 455--494. Zürich: European Mathematical Society (2008).
  19. 7. Witt, F.: Special metrics and triality. Adv. Math. 219, 1972--2005 (2008). https://doi.org/10.1016/j.aim.2008.07.017.
  20. 6. Witt, F.: Calabi-Yau manifolds with B-fields. Rend. Semin. Mat., Univ. Politec. Torino. 66, 1--21 (2008).
  21. 5. Gmeiner, F., Witt, F.: Calibrations and T-duality. Commun. Math. Phys. 283, 543--578 (2008). https://doi.org/10.1007/s00220-008-0571-9.
  22. 4. Witt, F.: Generalised G_2-manifolds. Commun. Math. Phys. 265, 275--303 (2006). https://doi.org/10.1007/s00220-006-0011-7.
  23. 3. Witt, F.: Special metric structures and closed forms, D.Phil. thesis, University of Oxford. (2005).
  24. 2. Jeschek, C., Witt, F.: Generalised G_2-structures and type IIB superstrings. J. High Energy Phys. 053, 15 (2005). https://doi.org/10.1088/1126-6708/2005/03/053.
  25. 1. Witt, F.: Conformal properties of harmonic spinors and lightlike geodesics in signature (1,1). J. Geom. Phys. 46, 74--97 (2003). https://doi.org/10.1016/S0393-0440(02)00151-1.
  • seit 2015: Lehrstuhl für Differentialgeometrie, Universität Stuttgart
  • 2010-2015: Tenure-Track-Professur für theoretische Mathematik, Universität Münster
  • 2009-2010: Juniorprofessor für Theoretische und Mathematische Physik LMU München
  • 2005-2009: PostDoc (FU Berlin, École Polytechnique, Universität Regensburg)
  • 2005: Promotion (University of Oxford)
Ph.D.
  • Torische Ko-Higgsbündel, U Stuttgart, 2024
M.Sc.
  • Multidimensional nowhere-zero flows on graphs, U Stuttgart, 2025
  • Algorithmen für Chevalleys Theorem (kobetreut), U Stuttgart, 2023
  • Ko-Higgsbündel über projektiven Räumen, U Stuttgart, 2022
  • Proteinsequenzen und tropische Geometrie, U Stuttgart, 2022
  • Torische Co-Higgsbündel und prä-bewertete Vektorräume, U Stuttgart, 2021
  • Quotienten algebraischer Varietäten, U Stuttgart, 2017
  • Limes-Konfigurationen vom hermitschen Standpunkt, U Stuttgart, 2016
  • Hodge-Theorie auf nichtkompakten Mannigfaltigkeiten, U Stuttgart, 2016
  • Die Momentenabbildung in der symplektischen und torischen Geometrie (kobetreut), FU Berlin, 2008
B.Sc.
  • Algebraische Kodierungstheorie, U Stuttgart, 2024
  • Der Satz von Riemann-Roch, U Stuttgart, 2023
  • Das NTRU-Kryptosystem, U Stuttgart, 2023
  • Topologische Datenanalyse mit dem Vietoris-Rips-Komplex, U Stuttgart, 2022
  • Mathieu-Gruppen (kobetreut), U Stuttgart, 2021
  • Die tropische Grassmansche Varietät, U Stuttgart, 2020
  • Der Satz von Mordell-Weil für elliptische Kurven, U Stuttgart, 2020

  • Reguläre algebraische Kurven, U Stuttgart, 2019

  • Über die Klassifikation komplexer Flächen, U Stuttgart 2019
  • Torische Ideale, Gröbner Basen und das Rucksackproblem, U Stuttgart 2016
  • Hirzebruch-Flächen - Konstruktion und Untersuchung einer symplektischen Mannigfaltigkeit, WWU Münster, 2014
  • Symplectic toric manifolds, LMU München, 2010
Staatsexamen / B.A. / M.Ed.
  • Elliptische Kurven und Galoiserweiterungen von Q, U Stuttgart, 2022
  • Die Sätze von Desargues und Pappus in der projektiven Geometrie, U Stuttgart, 2021
  • Platonische Körper in der Theorie und Praxis, U Stuttgart, 2020
  • Neuronale Netze und Gröbnerbasen, U Stuttgart, 2019
  • Die Picard- und Jacobi-Varietät einer Riemannschen Fläche, U Stuttgart, 2019
  • Public-Key Kryptographie, WWU Münster, 2014
  • Elliptische Kurven über endlichen Körpern, WWU Münster, 2014
  • Das Gruppengesetz einer kubischen Kurve, WWU Münster, 2014
  • Die Grad-Genus-Formel, WWU Münster, 2014
  • Minimalflächen und harmonische Abbildungen, WWU Münster, 2013

Universität Stuttgart

WWU Münster

  • Skalarkrümmung und Minimalflächen (SoSe 15)
  • Differentialgeometrie 1 (WiSe 14)
  • Geometrische Variationsrechnung (SoSe 14)
  • Mathematische Grundlagen der String-Theorie (SoSe 13)
  • Geometrische Analysis (WiSe 12)
  • Holomorphe Vektorbündel (SoSe 12)
  • Riemannsche Flächen (SoSe 11)
  • Komplexe Geometrie (WiSe 10)

LMU München

  • Yang-Mills-Theorie (SoSe 10)
  • Symplektische Geometrie 2 (WiSe 09)
  • Symplektische Geometrie 1 (SoSe 09)
Fachbereich Mathematik IDSR Institut Forschung Lehre Seminar Algebra und Geometrie Kontakt und Anfahrt
Dieses Bild zeigt Frederik Witt

Frederik Witt

Prof. Dr.

Professor - Lehrstuhl für Differentialgeometrie

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