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Doctoral School / UAM


Programa de Doctorado en Matemáticas
Our PhD program offers:
A broad range of research subjects covering many relevant areas in theoretical and applied mathematics: differential equations and applications, functional and complex analysis, harmonic analysis, inverse problems, number theory, group theory, algebraic and differential geometry, statistics and probability, numerical methods, mathematical logic, mathematical finance, etc.
An increasingly international orientation, both in the number of students coming from abroad and in the collaboration (via co-advisoring, courses and short visits) with worldwide researchers.
A well-established prestige, as confirmed by several international academic rankings (see for example the Academic Ranking of World Universities).
Research lines:

Partial derivative equations   

  •        Partial differential equations (PDE’s)
  •        Non-local equations
  •        Numerical methods for PDE’s
  •        Applications to fluid and solid mechanics
  •        Inverse problems
  •        Calculus of variations


Mathematical analysis

  •        Harmonic analysis (abstract and in Euclidean spaces)
  •        Fourier analysis
  •        Geometric measure theory
  •        Measure end integration
  •        Functions of a complex variable
  •        Functional analysis
  •        Theory of operators
  •        Potential theory
  •        Approximation theory


Number theory

  •         Elliptic curves
  •         Applications to cryptography
  •         Multiplicative number theory
  •         Arithmetic combinatorics



  •          Riemannian, sub-riemannian and semi-riemannian geometry
  •          Analysis and geometry in metric spaces
  •          Differential topology
  •          Algebraic topology
  •          Hyperbolic geometry
  •          Moduli spaces
  •          Complex geomertry



  •         Commutative algebra  
  •         Group theory
  •         Ring theory
  •         Algebraic geometry
  •         Arithmetic geometry
  •         Mathematical logic


Statistics and probability

  •          Functional data analysis
  •          Non-parametric statistics, set estimation
  •          Computational statistics   
  •          Classification problems
  •          Empirical processes
  •          Branching processes and their applications
  •          Statistics applied to environmental problems





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