Prof. Dr. Frederik Witt

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