Prof. Dr. Frederik Witt

Head of chair


Theoretical Mathematics / Differential- and algebraic geometry

Preprints:   arXiv | iNSPIRE

Databases:   MathSciNet | zbMATH


  1. 21. Altmann, K., Witt, F.: Toric co-Higgs sheaves. J. Pure Appl. Algebra. 225, 20 (2021).
  2. 20. Ammann, B., Kröncke, K., Weiss, H., Witt, F.: Holonomy rigidity for Ricci-flat metrics. Math. Z. 291, 303--311 (2019).
  3. 19. Mazzeo, R., Swoboda, J., Weiss, H., Witt, F.: Asymptotic geometry of the Hitchin metric. Commun. Math. Phys. 367, 151--191 (2019).
  4. 18. Mazzeo, R., Swoboda, J., Weiss, H., Witt, F.: Ends of the moduli space of Higgs bundles. Duke Math. J. 165, 2227--2271 (2016).
  5. 17. Ammann, B., Weiss, H., Witt, F.: A spinorial energy functional: critical points and gradient flow. Math. Ann. 365, 1559--1602 (2016).
  6. 16. Ammann, B., Weiss, H., Witt, F.: The spinorial energy functional on surfaces. Math. Z. 282, 177--202 (2016).
  7. 15. 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).
  8. 14. 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).
  9. 13. Weiß, H., Witt, F.: A heat flow for special metrics. Adv. Math. 231, 3288--3322 (2012).
  10. 12. Weiss, H., Witt, F.: Energy functionals and soliton equations for \(G_2\)-forms. Ann. Global Anal. Geom. 42, 585--610 (2012).
  11. 11. 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).
  12. 10. Gayet, D., Witt, F.: Deformations of associative submanifolds with boundary. Adv. Math. 226, 2351--2370 (2011).
  13. 9. Jeschek, C., Witt, F.: Generalised geometries, constrained critical points and Ramond-Ramond fields. Fortschr. Phys. 59, 494--517 (2011).
  14. 8. 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).
  15. 7. 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).
  16. 6. Witt, F.: Special metrics and triality. Adv. Math. 219, 1972--2005 (2008).
  17. 5. Witt, F.: Calabi-Yau manifolds with \(B\)-fields. Rend. Semin. Mat., Univ. Politec. Torino. 66, 1--21 (2008).
  18. 4. Gmeiner, F., Witt, F.: Calibrations and T-duality. Commun. Math. Phys. 283, 543--578 (2008).
  19. 3. Witt, F.: Generalised \(G_2\)-manifolds. Commun. Math. Phys. 265, 275--303 (2006).
  20. 2. Jeschek, C., Witt, F.: Generalised $G_2$-structures and type IIB superstrings. J. High Energy Phys. 053, 15 (2005).
  21. 1. Witt, F.: Conformal properties of harmonic spinors and lightlike geodesics in signature (1,1). J. Geom. Phys. 46, 74--97 (2003).
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)
  • 14D20 Algebraic moduli problems, moduli of vector bundles
  • 14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
  • 14M25 Toric varieties, Newton polyhedra 
  • 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
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
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
  • since 2015: Chair of differential geometry, University Stuttgart
  • 2010-2015: Tenure-Track for theoretical mathematics, University of Münster
  • 2009-2010: Assistant professor for theoretical und mathematical physics LMU Munich
  • 2005-2009: PostDoc (FU Berlin, École Polytechnique, University of Regensburg)
  • 2005: Doctoral dissertation (University of Oxford)
  • Toric Co-Higgs bundles, U Stuttgart, 2024
  • Algorithms for Chevalley's Theorem (co-supervised), U Stuttgart, 2023
  • Co-Higgs bundles on projective spaces, U Stuttgart, 2023
  • Protein Sequences and tropical geometry, U Stuttgart, 2022
  • Elliptic curves and Galois extensions of Q, U Stuttgart, 2022
  • Toric Co-Higgs bundles and prevalued vector spaces, U Stuttgart, 2021
  • Quotients of algebraic varieties, U Stuttgart, 2017
  • Limiting configurations from a hermitian point of view, U Stuttgart, 2016
  • Hodge theory on noncompact manifolds, U Stuttgart, 2016
  • The moment map in symplectic and toric geometry (co-supervised), FU Berlin, 2008
  • The theorem of Riemann-Roch, U Stuttgart, 2023
  • The NTRU cryptosystem, U Stuttgart, 2022
  • Topological data analysis with the Vietoris-Rips complex, U Stuttgart, 2022
  • Mathieu groups (co-supervised), U Stuttgart, 2021
  • The tropical Grassmannian variety, U Stuttgart, 2020
  • The Mordell-Weill Theorem on elliptic curves, U Stuttgart, 2020
  • Regular algebraic curves, U Stuttgart, 2019

  • On the classification of complex surfaces, U Stuttgart 2019
  • Toric ideals, Gröbner bases and the knapsack problem, U Stuttgart 2016
  • Hirzebruch surfaces  - construction and investigation of a symplectic manifold, WWU Münster, 2014
  • Symplectic toric manifolds, LMU München, 2010
State Examination / B.A. / M.Ed.
  • Elliptic curves and Galois extensions of Q, U Stuttgart, 2022
  • Desargues' and Pappus' Theorem in Projective Geometry, U Stuttgart, 2021
  • Platonic solids in theory and practice, U Stuttgart, 2020
  • Neural networks and Gröbner bases, U Stuttgart, 2019
  • The Picard- and Jacobi variety of a Riemann surface, U Stuttgart, 2019
  • Public key cryptography, WWU Münster, 2014
  • Elliptic curves over finite fields, WWU Münster, 2014
  • The group law of a cubic curve, WWU Münster, 2014
  • The genus-degree formula, WWU Münster, 2014
  • Minimal surfaces and harmonic maps, WWU Münster, 2013

University of Stuttgart

WWU Münster

  • Scalar Curvature and Minimal Surfaces (ST 15)
  • Differential Geometry 1 (WT 14)
  • Geometric Variational Calculus (ST 14)
  • Mathematical Foundations of String Theory (ST 13)
  • Geometric Analysis (WT 12)
  • Holomorphic Vector Bundles (ST 12)
  • Riemann Surfaces (ST 11)
  • Complex Geometry (WT 10)

LMU Munich

  • Yang-Mills-Theory (ST 10)
  • Symplectic Geometry 2 (WT 09)
  • Symplectic Geometry 1 (ST 09)
This image shows Frederik Witt

Frederik Witt

Prof. Dr.

Professor - Chair of Differential Geometry

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