GRK 2491:  Fourier Analysis and Spectral Theory

• Subject Area: Mathematics
• Term: since 2019
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 398436923

The Research Training Group (RTG) 2491 is dedicated to modern Fourier analysis and spectral theory. We take an interdisciplinary and innovative approach to this classical and powerful machinery and focus on its development in the context of mathematical physics, topology and analytic number theory. Our qualification concept is thematically and methodologically concentrated in an important subarea of analysis, which is investigated from a variety of different view points, each based on the profound expertise of the participating PIs. A core theme of the RTG is analysis and spectral geometry on Riemannian manifolds, in particular, nilpotent Lie groups or more generally spaces acted on by groups. In the cases of interest, these are differential-topological objects with interesting arithmetic or combinatorial structure, and one of the key questions involves the fascinating interplay between the spectral properties of certain associated operators on the one hand, and their geometric or arithmetic properties on the other. Some prototypical examples of this interaction featured in this RTG are the spectral theory of sublaplacians on nilpotent Lie groups; analytic $L^2$-invariants, which link harmonic analysis to topology; and the resolvent and scattering theory of geometric differential operators on singular manifolds. Fourier and harmonic analysis also appear prominently in many applications of classical analytic number theory, in the representation theory of Lie groups and groupoids, and in the construction of quantum field theories with microlocal methods. Crucial analytic tools in our programme include microlocal analysis, symbolic calculi, Plancherel theory, Fourier analysis in numerous variations, spectral and scattering theory of operators, and C*-algebras and their K-theory. The RTG aims at establishing a school of excellent doctoral researchers with a broad horizon in areas of mathematics that are linked through the common theme of Fourier analysis and spectral theory. It fosters a flow of ideas within the triangle of analysis, topology and analytic number theory. Doctoral researchers more inclined towards number theory or geometry learn the full arsenal of powerful techniques in harmonic and microlocal analysis, whereas those more inclined towards analysis will learn about attractive applications of analysis in topology and number theory.

• DFG Programme: Research Training Groups
• Applicant Institution: Georg-August-Universität Göttingen
• Participating Institution: Gottfried Wilhelm Leibniz Universität Hannover
• Spokesperson: Professor Dr. Thomas Schick
• Participating Researchers: Professorin Dr. Dorothea Bahns; Professor Dr. Wolfram Bauer; Professor Dr. Jörg Brüdern; Professor Dr. Ralf Meyer; Professorin Dr. Damaris Schindler; Dr. Federico Vigolo; Professor Dr. Ingo Witt; Professorin Dr. Chenchang Zhu, Ph.D.