Algebraic geometry and number theory
Areas of interest and activity include, but are not limited to: Clifford algebras, Arakelov geometry, additive number theory, combinatorial number theory, automorphic forms, L-functions, singularities, rational points on varieties, and algebraic surfaces.
Our researchers are working on different topics within AI, for example mathematical foundations, improved algorithms, new applications, and societal impacts.
Biomathematics and biostatistics
The members of the group are involved in research projects in the areas of systems biology, mathematical and statistical modeling of cancer, statistical genetics, bioinformatics, and metagenomics, quantitative evolutionary biology and ecology, population dynamics and genealogical models, medical statistics, clinical trials, and epidemiology.
Complex Analysis of Several Variables
The group currently conducts research in residue theory with connections to commutative algebra, and analysis on singular spaces, e.g., division problems, the dbar-equation, and integral representation. Another research theme in the group is Kähler geometry and its interplay with pluripotential theory. Connections to convex geometry and Okounkov bodies, as well as to point processes, are also explored.
In particular, we study adaptive finite element methods, stochastic partial differential equations, transport equations, geometric integration and applications in medical image registration, inverse problems, mathematical physics, design, architecture, construction and virtual/augmented reality (VR/AR).
Harmonic Analysis and Functional Analysis
We study a wide range of problems in classical and modern analysis, including spectral theory of differential operators on manifolds, real harmonic analysis and non-smooth partial differential equations, perturbation theory, non-linear partial differential equations, special functions and their applications in physics, operator theory and operator algebras.
Our research topics include partial differential equations arising in general relativity, kinetic theory, continuum mechanics and quantum physics, special functions in mathematical physics, quantum properties of black holes and connections with representation theory.
The topics of interest are theory for extremes in random processes and fields, reliability improvement, financial risk management, spatial and spatio-temporal statistics, stochastic geometry and imaging, statistical estimation and algorithms for non-stationary and non-Gaussian processes, computer intensive statistical methods and Big data statistics, environmental statistics, forensic statistics and bayesian statistics.
The research performed in the group focuses on two strongly connected areas: on the modelling and analysis of applied optimization problems arising in other sciences, industry, and society, and on the development and analysis of efficient algorithms for classes of large-scale optimization problems arising in these applications.
The probability group conducts research in theoretical probability. Some of the areas which are covered by the group are: interacting particle systems and percolation, statistical mechanics, stochastic partial differential equations, mixing rates for Markov chains, ergodic theory, stochastic optimization, stochastic geometry and point processes.
Teaching and Learning of Mathematics
The group conducts research in different aspects of the teaching and learning of mathematics and mathematics education. Some of the areas which are covered by the group are teacher education, history of mathematics and mathematical reasoning, problems solving strategies, assessment and gifted education.