At the Department of Mathematics there are several directions of research; either in pure mathematics, stochastics or science studies. These encompass theoretical aspects as well as investigations of interest in other fields of science, such as for example physics, coding theory, computer science, and mathematical finance. There are collaborations with other sciences and practical work in connection with medical and engineering problems, such as wind power.

The main research areas in Pure Mathematics are:

**Algebra and Discrete Mathematics**: Algebraic geometry and commutative algebra, algebraic groups and quantum groups, computer algebra, coding theory and cryptography, representation theory for Lie algebras, computational algebraic geometry.**Analysis**: Mathematical physics, spectral theory, spectral geometry, representation theory, analytic number theory, harmonic analysis, Lie groups, K-theory, C*-algebras, scattering theory, mathematical physics of fields and particles, magnetic fields and superconductivity.**Geometry and Topology**: Algebraic K-theory, homotopy theory, differential geometry, Kaehler geometry, gauge theory, quantum field theory, geometric quantization of symplectic varieties, quantization of moduli spaces, topology of smooth mapping germs, singularity theory.

At the Department of Mathematics, there are also several directions of research in stochastics; the most important ones are:

**Statistics**: Likelihood theory, statistical models, spatial statistics, stereology, asymptotic methods, geometry and statistics, inference for stochastic processes, time series analysis, simulation. Some important applications of statistics, particularly within biology, geology and economics are also studied: spatial biological structures, medical image processing, evolutionary development of DNA, turbulence and sand transport, insurance mathematics, financial markets and volatility.**Probability Theory**: Stochastic analysis, infinite dimensional probability theory, stationary processes, multiparameter processes, Levy theory, martingale theory, free probability and the connection to operator algebras.**Economics and Operational Research**: Optimization, production and financial theory. Stochastic programming, multicriteria optimization, combinatoric and discrete optimization and the application of Markov decision processes on inventory control and pricing.

At the Centre for Science Studies the main research areas are:

**History of science and technology**: Science and technology in Cold War Settings, scientific expeditions, natural resources and resource security, science diplomacy, popular science, science and the media, wind energy, science for children.**Philosophy of science**: Realism/anti-realism, virtues in science, Thomas S. Kuhn’s philosophy of science, experimental philosophy of science, scientific collaboration, retractions.**Science communication**: Science news, scientific controversies in public debate, online science communication, strategic science communication, science PR.**Ethics and science**: Bioethics, data ethics, research integrity, responsible research and innovation.

The employment of PhDs takes place in a wide range of positions, as for example statistical and medical companies, the wind turbine industry, financial institutions, research or teaching.

At the moment there are a total of 25 PhD students at the department.

Before you apply, please read the application guidelines, which specify required documentation, and note that your application must be completed via the online application system to be valid.

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