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Research Areas
Mathematics
Algebra
Additive Categories
Additive, Abelian and Grothendieck Categories
Triangulated and Derived Categories
Group Theory
Asymptotic and Probabilistic Problems in Group Theory
Lattice problems in Group Theory
p-local analysis in finite simple groups
Representation Theory
Lie Theory
Module Theory
Ring Theory
Commutative Rings
Noncommutative Rings
Analysis and PDE
Algebraic and Complex Analysis
Algebraic Analysis
Microlocal Analysis
Several Complex Variables
Calculus of Variations
Existence, regularity, and necessary conditions
Geometric inequalities in the Calculus of Variations
Variational convergences and extremum problems
Control Theory and Hamilton-Jacobi PDE
Control of PDE
Differential inclusions and Nonsmooth analysis
Geometric and optimal control
Hamilton-Jacobi PDE and Viscosity solutions
Impulsive control
Quantum control
Subriemannian geodesics
Functional Analysis, Harmonic Analysis and PDE
Asymptotic Analysis of Elliptic and Parabolic PDE
Nonlinear Harmonic Analysis and Operator Theory
Spectral Theory of Differential Operators
Geometric Measure Theory and Geometric Analysis
Analysis in Carnot groups
Geometric Measure Theory
Minimal surfaces
Prescribed curvature problems and conformal geometry
Hyperbolic and Dispersive PDE
Dispersive equations
Hyperbolic conservation laws
Mean Field and Differential Games
Mean Field Games
Mean Field Control
Differential Games
Nonlinear Elliptic and Parabolic problems
Existence, uniqueness and regularity of solutions, quasilinear equations
Multiscale problems in PDE
Semilinear equations
Potential Theory
Theory of function spaces
Didactics of Mathematics
Mathematical modelling, problem posing, and teacher training at all levels of schooling
Geometry and Number Theory
Algebraic and Complex Analysis
Algebraic Analysis
Microlocal Analysis
Several Complex Variables
Algebraic and Complex Geometry
Algebraic Groups
Algebraic Varieties
Cohomological Theories
Moduli Problems
Arithmetic Geometry
Differential Geometry
Number Theory
Algebraic Number Theory
Analytic Number Theory
Mathematics for Economics and Finance
Differential games and applications
Quantitative finance
Stochastic Methods for Finance
Mathematical Logic
Categorical Logic
Constructive Mathematics and its Foundations
Type Theory
Mathematical Physics and Dynamical Systems
Celestial Mechanics
Continuum Mechanics
Hamiltonian Systems
Quantum Mechanics
Statistical Mechanics
Topological and Geometric Aspects of Mechanics and Dynamics
Numerical Analysis
Approximation theory
Extrapolation methods and convergence acceleration
Kernel-based approximation and meshless methods
Multivariate polynomial approximation, optimization and cubature
Multivariate polynomial inequalities
Numerical integration
Rational interpolation and approximation
Mathematical imaging and pattern recognition
Medical imaging, pattern recognition and MPI
Numerical linear and nonlinear algebra
Ill-posedness regularization
Matrix functions
Numerical methods for signals and systems
Numerical solution of linear and nonlinear systems
Parallel computing
Numerical methods for Data Science
Acceleration methods for higher-order data analysis
Imaging for Earth Observation
Machine learning
Mathematical systems modelling from data
Near-optimal regression designs
Numerical solution of PDEs
Computational fluid-dynamics, mechanics and geomechanics
Coupled problems in science and engineering
Finite elements and volumes
Special functions
Biorthogonality and formal orthogonal polynomials
Operations Research
Applications of Operations Research
Airport optimization and air traffic flow management
Computational biology
Industrial applications (scheduling, bin packing, optimal design)
Telecommunication network design
Vehicle routing and logistics
Combinatorial and network optimization
Graph theory and graph optimization algorithms
Matheuristics and meta-heuristics methods
Polyhedral combinatorics
Integer and mixed integer linear programming
Cutting plane methods
Decomposition methods for large scale (mixed) integer programs
Reformulations and extended formulations
Theory of (mixed) integer linear programming
Nonlinear optimization
Methods for constrained optimization
Methods for derivative-free optimization
Methods for mixed integer nonlinear programming
Methods for sparse optimization
Optimization and Data Science
Data-driven approaches to real-world problems
Optimization methods for machine learning
Probability
Maximum entropy and optimal transport
Stochastic Control and Filtering
Stochastic Differential Equations and Applications
Stochastic Methods for Finance
Stochastic Models for Ecology and Biology
Systems with Many Degrees of Freedom; Statistical Mechanics
Computer Science
Analysis of the Social Impact of New Technologies and Digital Revolution
Artificial Intelligence
Algorithms
Analysis of biological data and bioinformatics
Computer vision, multimedia and signal processing
Machine learning, natural language processing and knowledge representation
Process Analytics and Mining
Formal Methods for Software Reliability
Models of concurrency and distribution
Program semantics and theory of computing
Static program analysis, abstract interpretation
Temporal and modal logic
Theory of programming languages, type systems
Systems and Cybersecurity
Cloud Platforms for parallel/distributed systems
Cybersecurity
Development and verification of embedded and cyber-physical systems
Mobile Computing and Networking
Software engineering, Operating Systems, Computer Languages
Web technologies, Social Networks and Semantic Web
Web-based and Information Systems
Doctoral courses
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