GRK 3132:  Analysis of Nonlinear PDE: Conformal Energies, Optimal Shapes, and Continuum Mechanics

• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545046569

This international research training group (IRTG) is a center for mathematical research and qualification of doctoral researchers. It brings together researchers from the University of Freiburg, the University of Pisa, and Scuola Normale Superiore in Pisa. At the center of this IRTG is the study of nonlinear partial differential equations, from both an analytical as well as a numerical point of view. The individual research projects are situated in the areas of geometric analysis, shape optimization, and applications in continuum mechanics and their intersections. Furthermore, stochastic aspects provide a link to current topics like climate modeling and geometric data science, while being integrated with the geometric and continuum mechanics themes. The specific projects are selected to maximize the benefit of combining them under the roof of a research training group. To give some concrete examples, connections naturally arise in the study of the Willmore functional and the elastic properties of slender objects as well as phase field models, which in turn are useful as numerical tools in areas like shape optimization. Including noise in fluid mechanics equations may help in overcoming some of the difficulties in the deterministic theory, and statistics on the space of geometric shapes lead to advances in image analysis. The mutual benefit in combining pure and applied problems also becomes apparent when considering the employed mathematical methods, as for example monotonicity in geometric flows and a priori bounds are used to prove both geometric inequalities and stability of numerical schemes. The long history of effective cross-stimulation between pure and applied mathematics in nonlinear PDE underlines the advantage gained by the collaboration within this IRTG. In the same spirit as the research program, the joint qualification program is tailored such that all young researchers obtain both focused training in their respective specialization and a broader education in the field of nonlinear PDE, thus paving the way for new scientific connections and innovative modes of discovery via an expanded tool set. The IRTG will thus establish a comprehensive teaching program in addition to the regularly offered lectures at the respective sites. Each doctoral researcher in the IRTG will be supervised by two PI, one from Pisa and one from Freiburg, thus ensuring that the aforementioned complementarity is fully harnessed. To take full advantage of the IRTG, each young researcher will stay for an extended amount of time, up to eight months, at the respective partner site. This will ensure close collaboration with the co-supervisor and promote scientific independence from the primary supervisor. To summarize, this IRTG is thus a significant contribution to expeditiously provide researchers with the necessary qualification to succeed both in the academic and non-academic employment market.

• DFG Programme: International Research Training Groups
• International Connection: Italy
• Applicant Institution: Albert-Ludwigs-Universität Freiburg
• IRTG-Partner Institution: Scuola Normale Superiore (SNS); Università di Pisa
• Spokesperson: Professor Dr. Patrick Dondl
• Participating Researchers: Professor Dr. Sören Bartels; Professorin Dr. Nadine Große; Professor Dr. Ernst Kuwert; Professor Dr. Michael Ruzicka; Professorin Dr. Diyora Salimova; Professor Dr. Guofang Wang
• IRTG-Partner: Spokesperson: Professor Dr. Luigi Carlo Berselli