Interdisciplinary research units (IRUs)

The new interdisciplinary research units (IRUs) establish links to areas outside mathematics, addressing the ever-growing need in natural sciences, engineering, and the life sciences for increasingly advanced mathematics. This interdisciplinary research will be pursued in selected areas. In one IRU, we join forces with physicists to address mathematical challenges in field theory. In another IRU, we collaborate with the Fraunhofer Institute SCAI on data-driven material science. In three further IRUs, we work with UBonn's cluster ImmunoSensation on various challenges of mathematical modeling in life and medical sciences.

IRU D1: Data-driven materials science

Investigators: Sergio Conti, Michael Griebel, Werner Müller, Michael Ortiz, Marc Alexander Schweitzer

The IRU on data-driven materials science (DDMS) combines (big) data analysis of empirical and simulation data with multiscale modeling techniques to understand material behavior and design new materials and processes for their synthesis. The general aim is to build simulation strategies around large data sets, and not around specific empirical material models. In particular, we will focus on molecular dynamics with data-mined portentials from electronic structure calculations, and on relaxation and microstructure formation in a data-driven setting, with application to multiscale crystal plasticity. DDMS will require new analytical frameworks, new computational methods, and new multiscale concepts in order to first generate fundamental model-free material data and then to use them.

IRU D2: Mathematical challenges in field theory

Investigators: Gaetan Borot, Margherita Disertori, Massimiliano Gubinelli, Albrecht Klemm, Peter Teichner, Don Zagier, Martin Zirnbauer

Quantum field threory (QFT) is one of the most fundamental and successful frameworks of theoretical physics. However, its mathematical foundations are far from being understood and remain a great challenge. Bringing together leading experts from various areas of mathematics and physics, we plan to explore and apply rigorous approaches to QFT. We will pursue three complementary threads and their interactions: a geometrical approach based on duality relations between QFT and gravity, the anti-de Sitter/conformal field theory correspondence (AdS-CFT), a more algebraic approach based on cobordism (functional QFT), and a more analytical approach based on the connection between functional integrals and stochastic partial differential equations (stochastic PDEs).

IRU D3-5: Mathematics and life sciences

Investigators: Anton Bovier, Jochen Garcke, Barbara Niethammer, Martin Rumpf, Juan J. L. Velazquez

The enormous progress made in recent years in the experimental life sciences provides a wealth of data on the functioning of living organisms. This is especially true for the immune system. There is general consensus that in order to turn these data into knowledge about the functioning of this system, mathematical modeling as well as theoretical and numerical analysis in conjunction with experimental data is essential for future progress. The two existing clusters of excellence at UBonn, ImmunoSensation and HCM, provide the ideal environment to make substantial advances in this direction. Based on encouraging achievements in the previous funding period, the clusters have decided to particularly strengthen this cooperation institutionally by the creation of three internationally visible junior research groups in the field of mathematical modeling in life and medical sciences. The new research groups will be positioned at the interface of the two clusters. This provides a unique opportunity to develop new and challenging mathematical models with a significant impact on the understanding of the immune system and immune-mediated diseases. The range of research topics to be studied includes, but is not limited to, the analysis of information processing, the dynamics of the immune response, modeling and optimization of treatment protocols, sparse data problems in single cell approaches, predicting and modeling cell behavior from pertubation experiemnts, and the analysis of two to three-dimensional images including dynamic images in the context of immune responses.