Academy of Europe: Areas of Activity

algebra

Algebra
Algebra (Leibniz algebras, quasi-Lie-algebras, representation theory, braid groups, infinite dimen-sional algebras and groups)
Algebra and geometry
Analysis and algebra
Arithmetic and Algebra of Polynomials
Combinatorics, symmetric groups, approximations in algebra
Combinatory algebra and foundations of computer science
Commutative algebra
Commutative and homological algebra
Lie Algebras
Linear algebra
Numerical linear algebra
Operator Algebras
Operator algebras (C*, von Neumann algebras), spectral theory
Pro-p- Iwahori Hecke algebra
Quantum groups, quantized enveloping algebras
Representation theory of finite dimensional algebras
Universal algebra

algebraic

Algebraic and analytic geometry
Algebraic and arithmetic geometry of moduli spaces
Algebraic and differential topology
Algebraic and probabilistic methods in combinatorics
Algebraic and projective geometry
Algebraic and symplectic geometry
Algebraic and symplectic geometry: Kaehler manifolds, holomorphic symplectic varieties, vector bundles, rationality
Algebraic arithmetic geometry
Algebraic cycles
Algebraic dynamics
Algebraic formulation of quantum field theory
Algebraic geometry
Algebraic geometry
Algebraic geometry, Jacobians
Algebraic geometry, in particular enumerative geometry and intersection theory
Algebraic groups
Algebraic methods in computer aided geometric design
Algebraic number theory
Algebraic numbers, polynomials and binary forms with given discriminant
Algebraic stacks
Algebraic surfaces
Algebraic surfaces and their classification
Algebraic topology
Algebraic topology
Applications of algebraic topology in discrete geomtry and combinatorics
Applications of motivic integration to the representation theory of algebraic groups
Applications to algebraic number theory, irreducible polynomials, Diophantine approximation and Diophantine geometry
Arithmetic Algebraic Geometry, in particular Arakelov Geometry
Arithmetic algebraic geometry
Computational complexity of algebraic functions
Differential & algebraic geometry
Diophantine Approximation, Heights of Algebraic Numbers
Dynamical Systems of Algebraic Origin
Enumerative, algebraic, analytic combinatorics
Geometry of algebraic of curves
History of algebraic geometry
Hodge theory, algebraic cycles, rational points, fundamental groups
Integral Points on Algebraic Varieties over Number Fields and Function Fields
Locally symmetric algebraic varieties
Non-commutative algebraic geometry
Rational points on algebraic varieties
Rational points on algebraic varieties
Real algebraic geometry
Representation theory of algebraic groups and arithmetic groups
Topology of algebraic varieties
Topology of algebraic varieties

algorithm

Adaptive algorithms for partial differential equations and a-posteriori error control
Algorithms
Combinatorial algorithms, streaming algorithms and circuit complexity
Lattice basis reduction algorithm.
Numerical algorithms
Theory of algorithms

analysis

Analysis
Analysis
Analysis (real and complex infinite dimensional, functional, non-standard, p-adic and non-Archimedean)
Analysis / automorphic forms
Analysis and algebra
Analysis of models for tumor growth
Analysis of partial differential equations
Asymptotic analysis
Asymptotic analysis
Asymptotic analysis, stabilization techniques for finite element discretizations
Complex analysis
Convex analysis, optimization, control theory, calculus of variations
Dynamical systems, ergodic theory, fractal analysis
Entropy analysis
Finite element analysis of plates and shells
Fourier analysis
Fourier analysis
Functional Analysis
Functional Analysis, Ergodic theory, Representation theory, Dynamical systems, Optimization, Stochastic processes
Geometric analysis
Geometric functional analysis
Geometry and analysis
Global analysis
Global analysis
Harmonic analysis on locally symmetric spaces
Isogeometric analysis, finite element techniques for Maxwell equations
Isoperimetric and functional inequalities in analysis and geometry
Mathematical Modelling, Numerical Analysis, Scientific Computing
Mathematical analysis
Mathematical analysis
Mathematical and numerical analysis of nonlinear partial differential equations
Mathematical and numerical analysis of wave propagation problems in complex structures
Measure-theoretical analysis
Non-commutative harmonic analysis
Nonlinear Functional Analysis
Nonlinear analysis
Nonlinear analysis
Nonlinear eigenvalue analysis
Numerical analysis
Numerical analysis
Numerical analysis and modelling
Numerical analysis, discretization of partial differential equations
Partial differential equations and nonlinear analysis
Probability theory, in particular stochastic analysis and applications to mathematical finance
Relations with complex analysis
Singular perturbation theory of differential operators (e. g. Schrödinger operators), asymptotic analysis
Spectral analysis of magnetic Schrodinger operators
Stochastic analysis
Stochastic analysis
Time-frequency analysis
p-adic analysis

application

Applications in aeronautics, hydraulics and electrical networks
Applications in medicine and biology
Applications of Combinatorics to Theory of Computer Science
Applications of algebraic topology in discrete geomtry and combinatorics
Applications of combinatorics to computer science
Applications of l-adic Cohomology
Applications of mathematics in physics, architecture, biology, earth sciences, economics, engineer-ing, social sciences, urbanism
Applications of motivic integration to the representation theory of algebraic groups
Applications of operator theory
Applications of the theory of automorphic forms to Shimura varieties and hyperbolic manifolds
Applications to algebraic number theory, irreducible polynomials, Diophantine approximation and Diophantine geometry
Applications to: fluid mechanics; aerospace engineering; geophysics; biomechanics; medical systems; wave propagation phenomena
Combinatorics, graph theory and their applications to theoretical computer science
Degeneration techniques and applications
Fast rotating fluids and applications to ocean circulation
Mathematical modeling for biomedical applications
Probability theory, in particular stochastic analysis and applications to mathematical finance
Representation theory and its applications, asymptotic representation theory, infinite-dimensional groups, C*-algebras

approximation

Applications to algebraic number theory, irreducible polynomials, Diophantine approximation and Diophantine geometry
Approximation of NP-hard problems
Approximation theory
Combinatorics, symmetric groups, approximations in algebra
Diophantine Approximation, Heights of Algebraic Numbers
Diophantine approximations(the use and study of logarithmic forms)
Numerical Approximation of Partial Differential Equations

arakelov

Arakelov geometry
Arakelov geometry
Arakelov theory
Arithmetic Algebraic Geometry, in particular Arakelov Geometry

arithmetic

Algebraic and arithmetic geometry of moduli spaces
Algebraic arithmetic geometry
Arithmetic Algebraic Geometry, in particular Arakelov Geometry
Arithmetic algebraic geometry
Arithmetic and Algebra of Polynomials
Arithmetic geometry
Arithmetic geometry
Arithmetic geometry: rationality points, K3 surfaces, elliptic curves
Arithmetic theory of differential equations and theory of arithmetic Gevrey series
Field Arithmetic
Power values of products of consecutive terms in arithmetic progressions
Representation theory of algebraic groups and arithmetic groups

asymptotic

Asymptotic analysis
Asymptotic analysis
Asymptotic analysis, stabilization techniques for finite element discretizations
Asymptotic behavior of random polytopes
Representation theory and its applications, asymptotic representation theory, infinite-dimensional groups, C*-algebras
Singular perturbation theory of differential operators (e. g. Schrödinger operators), asymptotic analysis

automorphic

Analysis / automorphic forms
Applications of the theory of automorphic forms to Shimura varieties and hyperbolic manifolds
Automorphic forms
Automorphic forms
Automorphic forms and L-functions
Automorphic forms and allied representations
Automorphic forms and representations
Automorphic representations
Interaction of representation theory with the modern theory of automorphic forms (through Langlands program)
Theory of Automorphic Forms, in particular Theory of Modular Forms

boundary

Absorbing boundary conditions
Boundary layer theory
Boundary layers
Boundary value problems for P.D.E. (existence, uniqueness, regularity, etc.)
Boundary value problems of linear and integrable nonlinear PDEs
Free boundary problems
Proof of Dwork's conjecture on logarithmic growth of solutions of p-adic differential equations at the boundary

calculus

Calculus of variations
Calculus of variations and the mathematical theory of nonlinear elasticity
Calculus of variations, variational methods
Convex analysis, optimization, control theory, calculus of variations
Nonlinear expectations and stochastic calculus
Stochastic calculus

cohomology

Applications of l-adic Cohomology
Cohomology of groups
Cohomology theories
Etale cohomology
Galois cohomology
Motivic cohomology

combinatorics

Additive combinatorics
Additive combinatorics
Algebraic and probabilistic methods in combinatorics
Applications of Combinatorics to Theory of Computer Science
Applications of algebraic topology in discrete geomtry and combinatorics
Applications of combinatorics to computer science
Combinatorics
Combinatorics
Combinatorics, graph theory and their applications to theoretical computer science
Combinatorics, symmetric groups, approximations in algebra
Combinatorics: geometric, probabilistic and topological
Domain at the crossroads of combinatorics and optimization
Enumerative, algebraic, analytic combinatorics
Extremal combinatorics
Measure theory, statistics and asymptotics in combinatorics
Probabilistic and Extremal Combinatorics
Probabilistic and extremal combinatorics
Probabilistic combinatorics

complex

Complex analysis
Complex differential geometry
Complex geometry
Complex geometry
Complex networks
Mathematical and numerical analysis of wave propagation problems in complex structures
Relations with complex analysis

computational

Computational Mathematics
Computational Mechanics
Computational complexity of algebraic functions
Computational complexity of analytic functions
Computational fluid dynamics
Computational high frequency wave propagations
Computational mathematics
Computational number theory
Computational statistics
Computational statistics
Computational uncertainty quantification
Computational wave problems
Discrete and computational geometry
Free-discontinuity problems, computational modelling of fracture, and quasi-continuum methods

conjecture

André-Oort conjecture
Goldbach conjecture
Polya conjecture
Proof of Crew's local monodromy conjecture
Proof of Dwork's conjecture on logarithmic growth of solutions of p-adic differential equations at the boundary
Proof of Malgrange's conjecture on the variation of irregularity of meromorphic differential systems
Twin prime conjecture

conservation

High-resolution methods for nonlinear conservation laws
Hyperbolic conservation laws
Hyperbolic conservation laws
Hyperbolic systems of conservation laws
Kinetic formulation and regularizing effects in nonlinear conservation laws
Numerical methods for conservation laws
Numerical methods for conservation laws

control

Adaptive algorithms for partial differential equations and a-posteriori error control
Control theory
Control theory
Control theory for finite dimensional systems
Control theory for partial differential equations
Convex analysis, optimization, control theory, calculus of variations
Filter theory, optimal control (deterministic and stochastic), optimization theory
Inventory control and finance
Optimal control
Optimal control and Hamilton-Jacobi equations
Stochastic control
Stochastic control systems
Stochastic realization theory, estimation and control

convex

Combinatorial properties of convex sets
Convex analysis, optimization, control theory, calculus of variations
Convex geometry
Convex geometry, discrete geometry, subriemannian geometry
Convex sets and convex polytopes
Fluid Setworks: Convex models and numerical schemes for designing the fluid networks
Optimal methods for convex programming
Polynomial time methods for convex programming
Random points and lattice points in convex bodies

curve

Arithmetic geometry: rationality points, K3 surfaces, elliptic curves
Elliptic curve factorization method
Elliptic curves
Families of singular curves
Geometry of algebraic of curves
Group actions on curves and higher dimensional varieties
Linear systems of plane curves
Moduli of curves
Moduli spaces of curves
Projective curves and their moduli spaces
Syzygies of curves

differential

Adaptive algorithms for partial differential equations and a-posteriori error control
Algebraic and differential topology
Analysis of partial differential equations
Applied partial differential equations
Arithmetic theory of differential equations and theory of arithmetic Gevrey series
Backward stochastic differential equations
Complex differential geometry
Control theory for partial differential equations
Differential & algebraic geometry
Differential equations
Differential geometry
Differential geometry
Differential geometry and Lie group techniques in geometric integration
Linear and nonlinear partial differential equations
Mathematical and numerical analysis of nonlinear partial differential equations
Non-linear differential equations of KdV type
Nonlinear Partial Differential Equations
Nonlinear ordinary and partial differential equations arising in the applied sciences
Nonlinear partial differential equations
Nonlinear partial differential equations of mixed type
Nonlinear partial differential equations of parabolic and elliptic types
Numerical Approximation of Partial Differential Equations
Numerical analysis, discretization of partial differential equations
Numerical methods for partial differential equations
Numerical methods for time-dependent partial differential equations
Partial differential equations
Partial differential equations
Partial differential equations and nonlinear analysis
Partial differential equations of nonequilibrium statistical mechanics, in particular Boltzmann-like equations
Probabilistic interpretation of nonlinear partial differential equations measure-valued processes
Proof of Dwork's conjecture on logarithmic growth of solutions of p-adic differential equations at the boundary
Proof of Malgrange's conjecture on the variation of irregularity of meromorphic differential systems
Singular perturbation theory of differential operators (e. g. Schrödinger operators), asymptotic analysis
Singularly perturbed stochastic differential equations
Spectral theory of partial differential equations
Theory of nonlinear partial differential equations
Theory of stochastic differential games
Variational methods for partial differential equations

diophantine

Algorithmic resolution of Diophantine equations
Applications to algebraic number theory, irreducible polynomials, Diophantine approximation and Diophantine geometry
Bounds for the integral solutions and for the number of integral solutions of Diophantine equations
Description of the structure of the set of integral solutions of Diophantine equations
Diophantine Approximation, Heights of Algebraic Numbers
Diophantine Geometry (elliptic curves, abelian varieties, multiplicative groups, additive groups, Carlitz modules)
Diophantine approximations(the use and study of logarithmic forms)
Diophantine equations
Diophantine geometry
Diophantine geometry
Effective results for integral solutions of Diophantine equations over number fields, function fields and finitely generated domains over Z

discrete

Actions of discrete groups on manifolds
Applications of algebraic topology in discrete geomtry and combinatorics
Convex geometry, discrete geometry, subriemannian geometry
Discrete and computational geometry
Discrete geometry
Discrete geometry, combinatorial properties of finite point sets in d-space
Discrete mathematics
Discrete optimization
High-dimensional and discrete geometry
Random discrete structures

dynamical

Differentiable and topological dynamical systems
Dynamical Systems of Algebraic Origin
Dynamical systems
Dynamical systems
Dynamical systems of geometric origin
Dynamical systems, ergodic theory, fractal analysis
Dynamical theory of Brownian motion
Ergodic theory and dynamical systems
Functional Analysis, Ergodic theory, Representation theory, Dynamical systems, Optimization, Stochastic processes
Smooth dynamical systems
Theory of dynamical systems

element

Asymptotic analysis, stabilization techniques for finite element discretizations
Basic properties of finite element methods (in particular, mixed, hybrid, etc.)
Discontinuous Galerkin finite elements
Discontinuous, stabilised, and multiscale finite element methods
Finite Element Method
Finite element analysis of plates and shells
Finite element methods
Isogeometric analysis, finite element techniques for Maxwell equations
Stabilization techniques for finite element formulations
Virtual element methods

elliptic

Arithmetic geometry: rationality points, K3 surfaces, elliptic curves
Elliptic curve factorization method
Elliptic curves
Nonlinear partial differential equations of parabolic and elliptic types
Numerical solution of linear elliptic problems with irregular data

equation

Adaptive algorithms for partial differential equations and a-posteriori error control
Algorithmic resolution of Diophantine equations
Analysis of partial differential equations
Applied partial differential equations
Arithmetic theory of differential equations and theory of arithmetic Gevrey series
Backward stochastic differential equations
Boltzmann equation
Bounds for the integral solutions and for the number of integral solutions of Diophantine equations
Compressible Euler equations
Control theory for partial differential equations
Description of the structure of the set of integral solutions of Diophantine equations
Differential equations
Differential-algebraic equations
Diophantine equations
Dispersive equations
Effective results for integral solutions of Diophantine equations over number fields, function fields and finitely generated domains over Z
Equations arising in liquid crystals, superconductors, Ginzberg-Landau
Geat equation proof
Geometric evolution equations, particularly the Ricci Flow
Gross-Pitaevskii equation for Bose-Einstein condensate
Isogeometric analysis, finite element techniques for Maxwell equations
Kinetic equations
Kinetic equations
Linear and nonlinear partial differential equations
Mathematical and numerical analysis of nonlinear partial differential equations
Non-linear differential equations of KdV type
Nonlinear Partial Differential Equations
Nonlinear diffusion processes and higher order model equations
Nonlinear ordinary and partial differential equations arising in the applied sciences
Nonlinear partial differential equations
Nonlinear partial differential equations of mixed type
Nonlinear partial differential equations of parabolic and elliptic types
Numerical Approximation of Partial Differential Equations
Numerical analysis, discretization of partial differential equations
Numerical methods for partial differential equations
Numerical methods for time-dependent partial differential equations
Optimal control and Hamilton-Jacobi equations
Painleve equations, orthogonal polynomials and random matrices
Parametric families of S-unit equations
Partial differential equations
Partial differential equations
Partial differential equations and nonlinear analysis
Partial differential equations of nonequilibrium statistical mechanics, in particular Boltzmann-like equations
Prandtl equation
Probabilistic interpretation of nonlinear partial differential equations measure-valued processes
Proof of Dwork's conjecture on logarithmic growth of solutions of p-adic differential equations at the boundary
Qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations
Qualitative properties of kinetic equations of granular media
Singularly perturbed stochastic differential equations
Spectral theory of partial differential equations
Structural properties of field equations
Swift-Hohenberg equation
Ternary equations, including generalized Fermat equations
Theory of nonlinear partial differential equations
Unit equations, decompodable form equations and discriminant equations
Variational methods for partial differential equations
Vlasov equations

ergodic

Dynamical systems, ergodic theory, fractal analysis
Ergodic and stochastic properties
Ergodic properties and perturbations of diffeomorphisms and flows.
Ergodic theory
Ergodic theory
Ergodic theory and dynamical systems
Ergodicity of hard ball systems: Boltzmann-Sinai ergodic hypothesis
Functional Analysis, Ergodic theory, Representation theory, Dynamical systems, Optimization, Stochastic processes

field

Algebraic formulation of quantum field theory
Effective results for integral solutions of Diophantine equations over number fields, function fields and finitely generated domains over Z
Field Arithmetic
Geometry of topological quantum field theories
Higher-dimensional class field theory
Integral Points on Algebraic Varieties over Number Fields and Function Fields
Mathematical physics and Gauge Field Theory
Mean field models for neural networks
Non-local field theories and micromorphic materials
Pseudodifferential operators, generalized processes, random fields, point processes
Quantum Field Theory
Representation theory of reductive groups over p-adic fields
Representation theory of reductive groups, in particular over p-adic fields
Representations of affine Kac-Moody groups and loop groups over local and global fields
Rigorous constructive Euclidean field theory
Structural properties of field equations
Symplectic field theory

finance

Inventory control and finance
Mathematical finance
Mathematical finance
Mathematical finance (Arbitrage theory)
Mathematical finance: nonlinear option pricing and risk measurement
Probability theory, in particular stochastic analysis and applications to mathematical finance

finite

Asymptotic analysis, stabilization techniques for finite element discretizations
Basic properties of finite element methods (in particular, mixed, hybrid, etc.)
Behavior of finite dimensional discretizations of bifurcation problems
Control theory for finite dimensional systems
Discontinuous Galerkin finite elements
Discontinuous, stabilised, and multiscale finite element methods
Discrete geometry, combinatorial properties of finite point sets in d-space
Finite Element Method
Finite element analysis of plates and shells
Finite element methods
Isogeometric analysis, finite element techniques for Maxwell equations
Mimetic finite differences
Representation theory of finite dimensional algebras
Stabilization techniques for finite element formulations

flow

Ergodic properties and perturbations of diffeomorphisms and flows.
Flow in porous media
Flows on homogeneous spaces
Geometric evolution equations, particularly the Ricci Flow
Geometric flows
Navier-Stokes-Fokker-Planck systems and non-Newtonian fluid flow models

fluid

Applications to: fluid mechanics; aerospace engineering; geophysics; biomechanics; medical systems; wave propagation phenomena
Computational fluid dynamics
Fast rotating fluids and applications to ocean circulation
Fluid Setworks: Convex models and numerical schemes for designing the fluid networks
Fluid dynamics
Fluid mechanics
Fluid mechanics and turbulence
Incompressible fluid dynamics
Mathematical fluid dynamics
Navier-Stokes-Fokker-Planck systems and non-Newtonian fluid flow models

form

Algebraic numbers, polynomials and binary forms with given discriminant
Analysis / automorphic forms
Analytic Number Theory of Modular Forms
Applications of the theory of automorphic forms to Shimura varieties and hyperbolic manifolds
Automorphic forms
Automorphic forms
Automorphic forms and L-functions
Automorphic forms and allied representations
Automorphic forms and representations
Interaction of representation theory with the modern theory of automorphic forms (through Langlands program)
Modular Forms
Theory of Automorphic Forms, in particular Theory of Modular Forms
Unit equations, decompodable form equations and discriminant equations

function

Analytic functions
Computational complexity of algebraic functions
Computational complexity of analytic functions
Differentiation techniques for nonsmooth functions
Effective results for integral solutions of Diophantine equations over number fields, function fields and finitely generated domains over Z
Hard inverse function theorems
Integral Points on Algebraic Varieties over Number Fields and Function Fields
Multiplicative functions
Special functions
Theta functions

galois

Galois cohomology
Galois groups
Galois representations
Galois representations

geometric

Algebraic methods in computer aided geometric design
Combinatorics: geometric, probabilistic and topological
Differential geometry and Lie group techniques in geometric integration
Dynamical systems of geometric origin
Geometric analysis
Geometric evolution equations, particularly the Ricci Flow
Geometric flows
Geometric functional analysis
Geometric graph theory
Geometric group theory
Geometric group theory
Geometric measure theory
Geometric measure theory
Geometric mechanics
Geometric representation theory

geometry

Algebra and geometry
Algebraic and analytic geometry
Algebraic and arithmetic geometry of moduli spaces
Algebraic and projective geometry
Algebraic and symplectic geometry
Algebraic and symplectic geometry: Kaehler manifolds, holomorphic symplectic varieties, vector bundles, rationality
Algebraic arithmetic geometry
Algebraic geometry
Algebraic geometry
Algebraic geometry, Jacobians
Algebraic geometry, in particular enumerative geometry and intersection theory
Applications to algebraic number theory, irreducible polynomials, Diophantine approximation and Diophantine geometry
Arakelov geometry
Arakelov geometry
Arithmetic Algebraic Geometry, in particular Arakelov Geometry
Arithmetic algebraic geometry
Arithmetic geometry
Arithmetic geometry
Arithmetic geometry: rationality points, K3 surfaces, elliptic curves
Birational geometry
Combinatorial geometry
Combinatorial geometry and combinatorial number theory
Complex differential geometry
Complex geometry
Complex geometry
Contact geometry
Convex geometry
Convex geometry, discrete geometry, subriemannian geometry
Differential & algebraic geometry
Differential geometry
Differential geometry
Differential geometry and Lie group techniques in geometric integration
Diophantine Geometry (elliptic curves, abelian varieties, multiplicative groups, additive groups, Carlitz modules)
Diophantine geometry
Diophantine geometry
Discrete and computational geometry
Discrete geometry
Discrete geometry, combinatorial properties of finite point sets in d-space
Enumerative geometry
Geometry
Geometry and analysis
Geometry and regularity of foliations
Geometry and topology
Geometry and topology
Geometry of algebraic of curves
Geometry of surfaces
Geometry of topological quantum field theories
Hamiltonian mechanics, symplectic geometry and topology
High-dimensional and discrete geometry
History of algebraic geometry
Isoperimetric and functional inequalities in analysis and geometry
Non archimedean geometry in the sense of Berkovich
Non-commutative algebraic geometry
Non-commutative geometry
Projective-differential geometry
Real algebraic geometry
Representation theory: l-adic representations, invariant theory, equivariant geometry
Riemannian geometry
Stochastic Geometry
Symplectic geometry
Symplectic geometry
Symplectic geometry and topology
Tempered fundamental group in p-adic geometry
Toric geometry

graph

Combinatorics, graph theory and their applications to theoretical computer science
Extremal graph theory
Geometric graph theory
Graph drawing
Graph theory
Graph theory
Polynomials of graphs and knots
Random graphs
Spectral graph theory

group

Abstract duality theory for compact groups
Actions of discrete groups on manifolds
Algebraic groups
Applications of motivic integration to the representation theory of algebraic groups
Cohomology of groups
Combinatorics, symmetric groups, approximations in algebra
Differential geometry and Lie group techniques in geometric integration
Galois groups
Geometric group theory
Geometric group theory
Group actions on curves and higher dimensional varieties
Group theory
Hodge theory, algebraic cycles, rational points, fundamental groups
Kleinian groups
Quantum groups, quantized enveloping algebras
Reductive p-adic groups
Renormalization group and its probabilistic aspects
Representation theory and its applications, asymptotic representation theory, infinite-dimensional groups, C*-algebras
Representation theory of algebraic groups and arithmetic groups
Representation theory of reductive groups over p-adic fields
Representation theory of reductive groups, in particular over p-adic fields
Representations of affine Kac-Moody groups and loop groups over local and global fields
Representations of p-adic Lie groups
Tempered fundamental group in p-adic geometry

high

Computational high frequency wave propagations
Group actions on curves and higher dimensional varieties
High Reynolds number limits
High frequency limits
Nonlinear diffusion processes and higher order model equations

hodge

Hodge theory
Hodge theory, algebraic cycles, rational points, fundamental groups
P-adic Hodge theory
p-adic Hodge theory

hyperbolic

Applications of the theory of automorphic forms to Shimura varieties and hyperbolic manifolds
Hyperbolic conservation laws
Hyperbolic conservation laws
Hyperbolic systems
Hyperbolic systems of conservation laws
Hyperbolic systems with singularities, billiards
Hyperbolic three-manifolds

imaging

Biomedical imaging and modeling of hybrid medical modalities
Functional medical imaging
Hierarchical decompositions (HD) for multi-scale representations in imaging and PDEs
Mathematical imaging and inverse problems
Mathematics for bio-inspired imaging
Super-resolution imaging

integrable

Boundary value problems of linear and integrable nonlinear PDEs
Completely integrable systems
Integrable stochastic systems
Integrable systems
Integrable systems
Integrable systems (both finite and infinite dimensional)

inverse

Hard inverse function theorems
Inverse and ill-posed problems
Inverse problems
Inverse problems
Mathematical imaging and inverse problems

kinetic

Kinetic equations
Kinetic equations
Kinetic formulation and regularizing effects in nonlinear conservation laws
Kinetic formultion and Kinetic schemes
Kinetic theory
Kinetic theory
Qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations
Qualitative properties of kinetic equations of granular media

law

Fourier law of heat conduction
High-resolution methods for nonlinear conservation laws
Hyperbolic conservation laws
Hyperbolic conservation laws
Hyperbolic systems of conservation laws
Kinetic formulation and regularizing effects in nonlinear conservation laws
Numerical methods for conservation laws
Numerical methods for conservation laws

learning

Machine learning
Machine learning
Mathematics for machine learning
Scientific machine learning
Statistical learning

limit

Fluctuations, scaling limits
High Reynolds number limits
High frequency limits
Hydrodynamic limit
Hydrodynamic limit
Method of semi-relaxed limits

linear

Boundary value problems of linear and integrable nonlinear PDEs
Linear algebra
Linear and non-linear waves
Linear and nonlinear partial differential equations
Linear and nonlinear programming, optimization
Linear programming and theoretical computer science
Linear systems of plane curves
Numerical linear algebra
Numerical solution of linear elliptic problems with irregular data

logic

Algorithmic logic
Infinitary logic
Logic
Logic
Mathematical logic
Mathematical logic
Mathematical logic, in particular theory of models

machine

Machine learning
Machine learning
Mathematics for machine learning
Scientific machine learning

manifold

Actions of discrete groups on manifolds
Algebraic and symplectic geometry: Kaehler manifolds, holomorphic symplectic varieties, vector bundles, rationality
Applications of the theory of automorphic forms to Shimura varieties and hyperbolic manifolds
Stein manifolds

mathematical

Calculus of variations and the mathematical theory of nonlinear elasticity
Information theory and mathematical statistics
Mathematical Elasticity
Mathematical Modeling
Mathematical Modelling, Numerical Analysis, Scientific Computing
Mathematical Statistics
Mathematical analysis
Mathematical analysis
Mathematical and numerical analysis of nonlinear partial differential equations
Mathematical and numerical analysis of wave propagation problems in complex structures
Mathematical and theoretical physics
Mathematical aspects of string theory
Mathematical biology
Mathematical chemistry
Mathematical economics
Mathematical finance
Mathematical finance
Mathematical finance (Arbitrage theory)
Mathematical finance: nonlinear option pricing and risk measurement
Mathematical fluid dynamics
Mathematical fundamentals for metamaterials and topological properties at subwavelength scales
Mathematical imaging and inverse problems
Mathematical logic
Mathematical logic
Mathematical logic, in particular theory of models
Mathematical methods in relativistic quantum chemistry
Mathematical modeling for biomedical applications
Mathematical modeling for ecology, biodiversity
Mathematical modeling for hematopoiesis and leukemogenesis
Mathematical modelling
Mathematical optimization
Mathematical physics
Mathematical physics
Mathematical physics (classical and quantum)
Mathematical physics and Gauge Field Theory
Mathematical population genetics
Mathematical relativity
Mathematical software
Mathematical statistical physics
Mathematical statistics
Mathematical statistics and probability theory
Mathematical systems theory
Mathematical theory of shock waves and other nonlinear waves
PDE models in mathematical biology
Probability theory, in particular stochastic analysis and applications to mathematical finance
Related theories in probability theory and mathematical physics

matrix

Matrix computations
Matrix theory
Painleve equations, orthogonal polynomials and random matrices
Random matrices
Random matrix theory
Wigner-Dyson-Mehta universality in random matrices

measure

Concentration of measure
Functional concentration of measure
Geometric measure theory
Geometric measure theory
Measure theory, statistics and asymptotics in combinatorics
Metric measure space

mechanic

Applications to: fluid mechanics; aerospace engineering; geophysics; biomechanics; medical systems; wave propagation phenomena
Celestial mechanics
Computational Mechanics
Continuum mechanics
Fluid mechanics
Fluid mechanics and turbulence
Geometric mechanics
Hamiltonian mechanics, symplectic geometry and topology
Non-equilibrium statistical mechanics
Partial differential equations of nonequilibrium statistical mechanics, in particular Boltzmann-like equations
Quantum mechanics
Quantum statistical mechanics
Statistical mechanics
Statistical mechanics
Statistical mechanics of equilibrium and non-equilibrium systems
Stochastic mechanics

method

Algebraic and probabilistic methods in combinatorics
Algebraic methods in computer aided geometric design
Basic properties of finite element methods (in particular, mixed, hybrid, etc.)
Calculus of variations, variational methods
Circle method
Discontinuous, stabilised, and multiscale finite element methods
Domain decomposition methods
Elliptic curve factorization method
Finite Element Method
Finite element methods
Free-discontinuity problems, computational modelling of fracture, and quasi-continuum methods
High-order accurate methods
High-resolution methods for nonlinear conservation laws
Interacting particle systems, stochastic particle methods
Interior-point methods
Mathematical methods in relativistic quantum chemistry
Method of semi-relaxed limits
Multi-scale methods
Multigrid methods
Neural methods
Numerical methods for conservation laws
Numerical methods for conservation laws
Numerical methods for partial differential equations
Numerical methods for time-dependent partial differential equations
Numerical methods in nonlinear programming
Optimal methods for convex programming
Polynomial time methods for convex programming
Semiclassical and multiscale methods in quantum dynamics
Sieve methods
Sieve methods
Smoothing methods
Spectral merhods: the spectral viscosity method
Spectral methods
Stability: scheme-independent stability criteria for initial-boundary methods
Variational methods for partial differential equations
Virtual element methods
Weak convergence methods

model

Analysis of models for tumor growth
Fluid Setworks: Convex models and numerical schemes for designing the fluid networks
Graphical Models
Implicitly constituted material models
Mathematical logic, in particular theory of models
Mean field models for neural networks
Minimal model program
Model Theory
Model order reduction
Modelling auxin transport in Arabidopsis plant stems
Models for evolution/selection
Navier-Stokes-Fokker-Planck systems and non-Newtonian fluid flow models
Nonlinear diffusion processes and higher order model equations
PDE models in mathematical biology
Random models for adaptive evolution

modulus

Algebraic and arithmetic geometry of moduli spaces
Foliations of moduli spaces.
Moduli of abelian varieties
Moduli of curves
Moduli problems
Moduli problems
Moduli spaces
Moduli spaces and Hilbert schemes
Projective curves and their moduli spaces
Stratifications of moduli spaces

motion

Bacterial cell motion (kinetic to macroscopic)
Derivation of quantum Brownian motion
Dynamical theory of Brownian motion
Interacting particle systems and Brownian motions
Interface motion

network

Applications in aeronautics, hydraulics and electrical networks
Complex networks
Deep neural networks
Fluid Setworks: Convex models and numerical schemes for designing the fluid networks
Mean field models for neural networks
Network science

nonlinear

Boundary value problems of linear and integrable nonlinear PDEs
Calculus of variations and the mathematical theory of nonlinear elasticity
High-resolution methods for nonlinear conservation laws
Kinetic formulation and regularizing effects in nonlinear conservation laws
Linear and nonlinear partial differential equations
Linear and nonlinear programming, optimization
Mathematical and numerical analysis of nonlinear partial differential equations
Mathematical finance: nonlinear option pricing and risk measurement
Mathematical theory of shock waves and other nonlinear waves
Nonlinear Functional Analysis
Nonlinear Partial Differential Equations
Nonlinear analysis
Nonlinear analysis
Nonlinear diffusion processes and higher order model equations
Nonlinear eigenvalue analysis
Nonlinear expectations and stochastic calculus
Nonlinear ordinary and partial differential equations arising in the applied sciences
Nonlinear partial differential equations
Nonlinear partial differential equations of mixed type
Nonlinear partial differential equations of parabolic and elliptic types
Numerical methods in nonlinear programming
Partial differential equations and nonlinear analysis
Probabilistic interpretation of nonlinear partial differential equations measure-valued processes
Qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations
Theory of nonlinear partial differential equations

number

Algebraic number theory
Algebraic numbers, polynomials and binary forms with given discriminant
Analytic Number Theory of Modular Forms
Analytic number theory
Analytic number theory
Applications to algebraic number theory, irreducible polynomials, Diophantine approximation and Diophantine geometry
Bounds for the integral solutions and for the number of integral solutions of Diophantine equations
Combinatorial geometry and combinatorial number theory
Combinatorial number theory
Computational number theory
Diophantine Approximation, Heights of Algebraic Numbers
Effective results for integral solutions of Diophantine equations over number fields, function fields and finitely generated domains over Z
High Reynolds number limits
Integral Points on Algebraic Varieties over Number Fields and Function Fields
Number Theory (transcendence, algebraic independence)
Number theory
Number theory
Number theory (mainly combinatorial and probabilistic)
Prime number theory
Prime numbers
Probabilistic number theory

numerical

Fluid Setworks: Convex models and numerical schemes for designing the fluid networks
Mathematical Modelling, Numerical Analysis, Scientific Computing
Mathematical and numerical analysis of nonlinear partial differential equations
Mathematical and numerical analysis of wave propagation problems in complex structures
Numerical Approximation of Partial Differential Equations
Numerical algorithms
Numerical analysis
Numerical analysis
Numerical analysis and modelling
Numerical analysis, discretization of partial differential equations
Numerical linear algebra
Numerical mathematics
Numerical methods for conservation laws
Numerical methods for conservation laws
Numerical methods for partial differential equations
Numerical methods for time-dependent partial differential equations
Numerical methods in nonlinear programming
Numerical solution of linear elliptic problems with irregular data
Qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations

operator

Applications of operator theory
Operator Algebras
Operator algebras (C*, von Neumann algebras), spectral theory
Operator theory
Pseudodifferential operators
Pseudodifferential operators, generalized processes, random fields, point processes
Random Schrodinger operators; Lifshitz tail and localization
Schrödinger operators
Singular perturbation theory of differential operators (e. g. Schrödinger operators), asymptotic analysis
Spectral analysis of magnetic Schrodinger operators

optimization

Combinatorial optimization
Combinatorial optimization
Convex analysis, optimization, control theory, calculus of variations
Discrete optimization
Domain at the crossroads of combinatorics and optimization
Filter theory, optimal control (deterministic and stochastic), optimization theory
Functional Analysis, Ergodic theory, Representation theory, Dynamical systems, Optimization, Stochastic processes
Linear and nonlinear programming, optimization
Mathematical optimization
Optimization theory

p-adic

P-adic Hodge theory
Proof of Dwork's conjecture on logarithmic growth of solutions of p-adic differential equations at the boundary
Reductive p-adic groups
Representation theory of reductive groups over p-adic fields
Representation theory of reductive groups, in particular over p-adic fields
Representations of p-adic Lie groups
Tempered fundamental group in p-adic geometry
p-adic Hodge theory
p-adic analysis

partial

Adaptive algorithms for partial differential equations and a-posteriori error control
Analysis of partial differential equations
Applied partial differential equations
Control theory for partial differential equations
Linear and nonlinear partial differential equations
Mathematical and numerical analysis of nonlinear partial differential equations
Nonlinear Partial Differential Equations
Nonlinear ordinary and partial differential equations arising in the applied sciences
Nonlinear partial differential equations
Nonlinear partial differential equations of mixed type
Nonlinear partial differential equations of parabolic and elliptic types
Numerical Approximation of Partial Differential Equations
Numerical analysis, discretization of partial differential equations
Numerical methods for partial differential equations
Numerical methods for time-dependent partial differential equations
Partial differential equations
Partial differential equations
Partial differential equations and nonlinear analysis
Partial differential equations of nonequilibrium statistical mechanics, in particular Boltzmann-like equations
Probabilistic interpretation of nonlinear partial differential equations measure-valued processes
Spectral theory of partial differential equations
Theory of nonlinear partial differential equations
Variational methods for partial differential equations

particle

Dynamics of stochastic particle systems
Interacting particle systems
Interacting particle systems and Brownian motions
Interacting particle systems, stochastic particle methods
Random walks, interacting particle systems
Theoretical elementary particle physics

particular

Algebraic geometry, in particular enumerative geometry and intersection theory
Arithmetic Algebraic Geometry, in particular Arakelov Geometry
Mathematical logic, in particular theory of models
Partial differential equations of nonequilibrium statistical mechanics, in particular Boltzmann-like equations
Probability theory, in particular stochastic analysis and applications to mathematical finance
Representation theory of reductive groups, in particular over p-adic fields
Theory of Automorphic Forms, in particular Theory of Modular Forms

physic

Applications of mathematics in physics, architecture, biology, earth sciences, economics, engineer-ing, social sciences, urbanism
Axiomatic foundations of the physics of continuous media
Condensed matter physics
Interface of mathematics and physics
Mathematical and theoretical physics
Mathematical physics
Mathematical physics
Mathematical physics (classical and quantum)
Mathematical physics and Gauge Field Theory
Mathematical statistical physics
Philosopy of physics
Probability theory, with a special focus on random media and problems connected with physics
Related theories in probability theory and mathematical physics
Statistical physics
Statistical physics
Statistical physics (classical and quantum)
Theoretical elementary particle physics
Vector bundles on Riemann surfaces and links to Math Physics

point

Arithmetic geometry: rationality points, K3 surfaces, elliptic curves
Discrete geometry, combinatorial properties of finite point sets in d-space
Hodge theory, algebraic cycles, rational points, fundamental groups
Integral Points on Algebraic Varieties over Number Fields and Function Fields
Optimal point configurations
Pseudodifferential operators, generalized processes, random fields, point processes
Random points and lattice points in convex bodies
Rational points on algebraic varieties
Rational points on algebraic varieties

polynomial

Algebraic numbers, polynomials and binary forms with given discriminant
Applications to algebraic number theory, irreducible polynomials, Diophantine approximation and Diophantine geometry
Arithmetic and Algebra of Polynomials
Kazhdan-Lusztig polynomials
Painleve equations, orthogonal polynomials and random matrices
Polynomial time methods for convex programming
Polynomials of graphs and knots

probability

Mathematical statistics and probability theory
Probability
Probability and Stochastic processes
Probability and stochastic processes
Probability in Banach spaces
Probability theory
Probability theory
Probability theory, in particular stochastic analysis and applications to mathematical finance
Probability theory, with a special focus on random media and problems connected with physics
Related theories in probability theory and mathematical physics

problem

Approximation of NP-hard problems
Behavior of finite dimensional discretizations of bifurcation problems
Boundary value problems for P.D.E. (existence, uniqueness, regularity, etc.)
Boundary value problems of linear and integrable nonlinear PDEs
Computational wave problems
Extendability problems
Free boundary problems
Free-discontinuity problems, computational modelling of fracture, and quasi-continuum methods
Generalized Szegö problems
Inverse and ill-posed problems
Inverse problems
Inverse problems
Mathematical and numerical analysis of wave propagation problems in complex structures
Mathematical imaging and inverse problems
Moduli problems
Moduli problems
Moment problems with complexity constraints
Numerical solution of linear elliptic problems with irregular data
Probability theory, with a special focus on random media and problems connected with physics
Sixth problem of Hilbert (from system of particles to Boltzmann equation and hydrodynamics)

process

Diffusion process
Empirical processes
Functional Analysis, Ergodic theory, Representation theory, Dynamical systems, Optimization, Stochastic processes
Markov processes
Nonlinear diffusion processes and higher order model equations
Probabilistic interpretation of nonlinear partial differential equations measure-valued processes
Probability and Stochastic processes
Probability and stochastic processes
Pseudodifferential operators, generalized processes, random fields, point processes
Quantitive modelling of pharmaceutical processes
Recurrence of Lorentz process
Stochastic processes
Subadditive random processes

program

Langlands program
Minimal model program

property

Basic properties of finite element methods (in particular, mixed, hybrid, etc.)
Combinatorial properties of convex sets
Discrete geometry, combinatorial properties of finite point sets in d-space
Ergodic and stochastic properties
Ergodic properties and perturbations of diffeomorphisms and flows.
Kazhdan's T property
Mathematical fundamentals for metamaterials and topological properties at subwavelength scales
Qualitative properties and numerical schemes for nonlinear diffusion, hydrodynamic, and kinetic equations
Qualitative properties of kinetic equations of granular media
Structural properties of field equations

quantum

Algebraic formulation of quantum field theory
Derivation of quantum Brownian motion
Geometry of topological quantum field theories
Many body quantum dynamics
Mathematical methods in relativistic quantum chemistry
Quantum Field Theory
Quantum chaos
Quantum chemistry
Quantum groups, quantized enveloping algebras
Quantum many-body systems
Quantum mechanics
Quantum space-time
Quantum statistical mechanics
Quantum theory
Quantum theory
Semiclassical and multiscale methods in quantum dynamics

random

Asymptotic behavior of random polytopes
Painleve equations, orthogonal polynomials and random matrices
Probability theory, with a special focus on random media and problems connected with physics
Pseudodifferential operators, generalized processes, random fields, point processes
Random Schrodinger operators; Lifshitz tail and localization
Random Structures
Random cellular automata
Random discrete structures
Random graphs
Random matrices
Random matrix theory
Random models for adaptive evolution
Random points and lattice points in convex bodies
Random structures
Random walks and percolation
Random walks, interacting particle systems
Subadditive random processes
Wigner-Dyson-Mehta universality in random matrices

representation

Applications of motivic integration to the representation theory of algebraic groups
Automorphic forms and allied representations
Automorphic forms and representations
Automorphic representations
Functional Analysis, Ergodic theory, Representation theory, Dynamical systems, Optimization, Stochastic processes
Galois representations
Galois representations
Geometric representation theory
Hierarchical decompositions (HD) for multi-scale representations in imaging and PDEs
Interaction of representation theory with the modern theory of automorphic forms (through Langlands program)
Representation theory
Representation theory and its applications, asymptotic representation theory, infinite-dimensional groups, C*-algebras
Representation theory of algebraic groups and arithmetic groups
Representation theory of finite dimensional algebras
Representation theory of reductive groups over p-adic fields
Representation theory of reductive groups, in particular over p-adic fields
Representation theory: l-adic representations, invariant theory, equivariant geometry
Representations of affine Kac-Moody groups and loop groups over local and global fields
Representations of p-adic Lie groups

science

Applications of Combinatorics to Theory of Computer Science
Applications of combinatorics to computer science
Applications of mathematics in physics, architecture, biology, earth sciences, economics, engineer-ing, social sciences, urbanism
Brain science
Combinatorics, graph theory and their applications to theoretical computer science
Combinatory algebra and foundations of computer science
Computer science, parallell computing
History of science
Linear programming and theoretical computer science
Matematical aspects of material science
Network science
Nonlinear ordinary and partial differential equations arising in the applied sciences
Theoretical computer science
Transportation sciences

solution

Bounds for the integral solutions and for the number of integral solutions of Diophantine equations
Description of the structure of the set of integral solutions of Diophantine equations
Effective results for integral solutions of Diophantine equations over number fields, function fields and finitely generated domains over Z
Numerical solution of linear elliptic problems with irregular data
Proof of Dwork's conjecture on logarithmic growth of solutions of p-adic differential equations at the boundary

space

Algebraic and arithmetic geometry of moduli spaces
Banach spaces
Configuration spaces (lemnisctaes, monodromy)
Flows on homogeneous spaces
Foliations of moduli spaces.
Harmonic analysis on locally symmetric spaces
Loop spaces and string topology
Metric measure space
Moduli spaces
Moduli spaces and Hilbert schemes
Moduli spaces of abelian varieties
Moduli spaces of curves
Moduli spaces of vectorbundles
Probability in Banach spaces
Projective curves and their moduli spaces
Randomness in space and time
Spaces of non-positive curvature
Stratifications of moduli spaces

spectral

Operator algebras (C*, von Neumann algebras), spectral theory
Spectral analysis of magnetic Schrodinger operators
Spectral estimation
Spectral graph theory
Spectral merhods: the spectral viscosity method
Spectral methods
Spectral theory
Spectral theory
Spectral theory of partial differential equations

statistical

Mathematical statistical physics
Non-equilibrium statistical mechanics
Partial differential equations of nonequilibrium statistical mechanics, in particular Boltzmann-like equations
Quantum statistical mechanics
Statistical Inference
Statistical genetics
Statistical learning
Statistical mechanics
Statistical mechanics
Statistical mechanics of equilibrium and non-equilibrium systems
Statistical physics
Statistical physics
Statistical physics (classical and quantum)
Statistical software

stochastic

Backward stochastic differential equations
Dynamics of stochastic particle systems
Ergodic and stochastic properties
Functional Analysis, Ergodic theory, Representation theory, Dynamical systems, Optimization, Stochastic processes
Integrable stochastic systems
Interacting particle systems, stochastic particle methods
Nonlinear expectations and stochastic calculus
Probability and Stochastic processes
Probability and stochastic processes
Probability theory, in particular stochastic analysis and applications to mathematical finance
Singularly perturbed stochastic differential equations
Stochastic Geometry
Stochastic analysis
Stochastic analysis
Stochastic calculus
Stochastic control
Stochastic control systems
Stochastic dynamic
Stochastic homogenization
Stochastic mechanics
Stochastic processes
Stochastic realization theory, estimation and control
Theory of stochastic differential games

string

"String theory"
Loop spaces and string topology
Mathematical aspects of string theory
Mathematics of string theory
String theory

structure

Description of the structure of the set of integral solutions of Diophantine equations
Mathematical and numerical analysis of wave propagation problems in complex structures
Micro structures
Protein structure and folding
Random Structures
Random discrete structures
Random structures

surface

Algebraic surfaces
Algebraic surfaces and their classification
Area-minimizing surfaces
Arithmetic geometry: rationality points, K3 surfaces, elliptic curves
Geometry of surfaces
K3 surfaces
Vector bundles on Riemann surfaces and links to Math Physics

symplectic

Algebraic and symplectic geometry
Algebraic and symplectic geometry: Kaehler manifolds, holomorphic symplectic varieties, vector bundles, rationality
Hamiltonian mechanics, symplectic geometry and topology
Symplectic field theory
Symplectic geometry
Symplectic geometry
Symplectic geometry and topology
Symplectic topology

technique

Asymptotic analysis, stabilization techniques for finite element discretizations
Degeneration techniques and applications
Differential geometry and Lie group techniques in geometric integration
Differentiation techniques for nonsmooth functions
Isogeometric analysis, finite element techniques for Maxwell equations
Stabilization techniques for finite element formulations

theoretical

Combinatorics, graph theory and their applications to theoretical computer science
Linear programming and theoretical computer science
Mathematical and theoretical physics
Theoretical computer science
Theoretical elementary particle physics
Theoretical neuroscience

topology

Algebraic and differential topology
Algebraic topology
Algebraic topology
Applications of algebraic topology in discrete geomtry and combinatorics
Geometry and topology
Geometry and topology
Hamiltonian mechanics, symplectic geometry and topology
Loop spaces and string topology
Low-dimensional topology
Symplectic geometry and topology
Symplectic topology
Topology
Topology (configuration spaces, knot theory, functional spaces, L²-Betti numbers)
Topology of algebraic varieties
Topology of algebraic varieties

transport

Modelling auxin transport in Arabidopsis plant stems
Operations research in transport and logistics
Optimal transport
Optimal transport
Transport theory

variety

Abelian varieties
Abelian varieties
Algebraic and symplectic geometry: Kaehler manifolds, holomorphic symplectic varieties, vector bundles, rationality
Applications of the theory of automorphic forms to Shimura varieties and hyperbolic manifolds
Classification of Fano varieties
Fano varieties
Group actions on curves and higher dimensional varieties
Integral Points on Algebraic Varieties over Number Fields and Function Fields
Locally symmetric algebraic varieties
Moduli of abelian varieties
Moduli spaces of abelian varieties
Rational points on algebraic varieties
Rational points on algebraic varieties
Secant defective varieties
Shimura varieties
Theory of modular varieties
Topology of algebraic varieties
Topology of algebraic varieties
Toric varieties

wave

Applications to: fluid mechanics; aerospace engineering; geophysics; biomechanics; medical systems; wave propagation phenomena
Computational high frequency wave propagations
Computational wave problems
Linear and non-linear waves
Mathematical and numerical analysis of wave propagation problems in complex structures
Mathematical theory of shock waves and other nonlinear waves

other

Adverse selection
Algorithmics
Applied mathematics
Applied mathematics
Applied statistics
Arrangements of hyperplanes
Artificial intelligence
Automatic differentiation
Averaging lemmas
Bifurcation theory
Biomathematics
Biostatistics
Brill-Noether theory
Category Theory
Causal inference
Climate Modelling
Cluster categories
Coarsening
Collective dynamics: alignment-based flocking/swarming
Combinatorial aspects of Index Theory
Complexity theory
Computer vision
Convexity
Cosmology
Cryptography
Cryptology
Deformation quantization
Diffusive behavior in Rayleigh gas
Digital humanities
Dimension theory
Disordered systems
Dispersion of environmental pollution
Distribution of primes
Dynamics
Ecological modelling
Econometrics
Electro-magneto-enchephalography
Electromagnetic ve thermal interactions
Electronic information
Entropy-stable schemes
Equidistribution
Exponential sums
Exponential sums
Extremal set systems
Fluid-structure interactions
Functional integration
Gauge theory
Gauss maps
Gcd computations
General relativity
Genomics
Growth theory, intergenerational equity, time inconsistency
Gynamical systems
HYP and HYPQ mathematica software
Hamiltonian dynamics
Hamiltonian dynamics
Hamiltonian systems and Arnold diffusion
Harmony in the music of Johann Sebastian Bach
Hedonic markets
Helly and Caratheodory type theorems
High-Dimensional statistics
History of mathematics:
Homogenization
Homological mirror symmetry
Improvement of sports performance and rehabilitation engineering
Industrial mathematics
Industrial mathematics
Information theory
Interactive software packages
Invariant theory
K-theory
L-functions
L-functions
Large deviations
Le Cam theory
Lie groupoids and Lie algebroids
Lieb-Thirring inequalities
Liquid crystals
Local-global principles
Logarithmic Sobolev inequalities
Long-Time asymptotics for evolutionary PDE
Magnetic Lieb-Thirring inequalities
Mathematics
Mathematics
Mathematics of social systems
Medical statistics
Micromagnetics
Mirror symmetry
Molecular dynamics
Motives
Motivic homotopy theory
Noether–Lefschetz theory
Non-linear geophysics
Nonparametric Bayesian statistics
Operations research in production planning
Operations research in telecommunications
Optimal design
Optimal transportation
PDE modelling of many-body systems
PDE theory
Packing and covering
Parallel computing
Percolation
Philosophy (epistemology), cultural and societal issues
Plate Theory
Popularization of Mathematics
Portfolio management
Potential theory
Pure Mathematics
Pure mathematics
Qualitative dynamics
Quasi-stationary distributions
Queueing Theory
Queueing theory
Ramsey theory
Rayleigh-Benard convection
Recursive utilities under risk and uncertainty
Reduced order modeling
Reduction theory
Regenerative phenomena
Relativity
Residual-free bubbles and subgrid-scale simulations
Resolution of singularities
Risk management
Sability theory
Schramm-Loewner evolution
Scientific computing
Semiparametric theory
Shell Theory
Simulation
Singularity theory
Sociophysics
Software for IBM-compatible personal computers
Spatial Statistics
Sphere packing
Statistics
Statistics
Statistics and financial mathematics
Super-diffusive behavior in Lorentz gas
Synthetic curvature bounds
Teaching of Mathematics
Teichmüller theory
Theory of cointegration
Theory of demand
Theory of invariants
Theory of motives
Theory of regulators
Theta correspondences
Time series
Topological dynamics
Topos theory
Trace formulae
Transcendance theory
Uncertainty quantification
Unconditional theory of pure motives
Urban economics
Variational integrators
Viscous thin films
Wavelets
o-minimality
weak KAM theory

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