GRK 1463:  Analysis, Geometry and String Theory

• Subject Area: Mathematics
• Term: from 2008 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 43618843

The aim of this Research Training Group is to pursue research in the area where analysis, geometry and string theory interact and to offer a nationally and internationally attractive opportunity to work towards a PhD. If we imagine the three areas analysis, geometry and string theory as the vertices of a triangle, then it is the edges of this triangle, which gave rise to important developments in modern mathematics and theoretical physics.
The interplay between analysis and geometry has resulted in the creation of geometric analysis, which by now is a firmly established branch of mathematics in its own right and has produced important results. Research into mirror symmetry and Calabi-Yau varieties has led, during the last 15 years, to fruitful interactions between string theory and geometry. Topics such as deformation quantisation and solitons have brought with them exciting developments on the border between analysis and string theory.
Our research topics, which include analysis on singular manifolds and on manifolds with boundary, noncommutative geometry, complex and algebraic geometry, differential geometry, symplectic geometry, free boundary problems, geometric evolution equations, noncommutative field theory, topological string theories and integrable models, cover a wide area. While firmly rooted in one of the three areas, the proposed topics for PhD students all have a clear perspective pointing towards one of the neighbouring fields. In our teaching programme we strictly emphasise an interdisciplinary approach: All graduate students will be educated in all three areas and will receive in-depth training in at least two of the fields. In addition, the Research Training Group will offer
(1) a well structured and coordinated schedule of lecture courses,
(2) reading and research seminars on more specialised topics,
(3) regular workshops and internal meetings and
(4) a programme of international visitors and exchange opportunities.
Partners from various European and American Universities have agreed to cooperate with the Research Training Group and to help with the training of the graduate students. This will be achieved by hosting some of the graduate students, by advising them in their research or by giving guest lectures.

• DFG Programme: Research Training Groups
• Applicant Institution: Gottfried Wilhelm Leibniz Universität Hannover
• Participating Institution: Max-Planck-Institut für Gravitationsphysik; (Albert-Einstein-Institut)
• Spokesperson: Professor Dr. Elmar Schrohe
• Participating Researchers: Professor Dr. Wolfgang Ebeling; Professor Dr. Joachim Escher; Professor Dr. Holger Frahm; Professor Dr. Klaus Hulek; Professor Dr. Olaf Lechtenfeld; Professor Dr. Matthias Schütt; Professor Dr. Knut Smoczyk; Professor Dr. Christoph Walker