Riemann Center
  Fakultät für Mathematik und Physik - Universität Hannover
Department of Mathematics and Physics - Leibniz Universität Hannover - Welfengarten 1 - 30167 Hannover/Germany


It is the aim of this research training group to pursue research in the area where analysis, geometry and string theory interact and to offer to our graduate students a nationally and internationally attractive opportunity to work towards a Ph.D..

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 continue to give 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 linking string theory and geometry has led to fruitful interaction between these areas in the last 20 years. Solitons can be named as a research topic representing the many links between analysis and theoretical physics. Not only are these time-stable solutions to nonlinear wave equations analytically interesting objects, but they have also found numerous applications which extend even to string theory.

Our research fields cover a wide area, encompassing analysis on singular manifolds, noncommutative geometry, free boundary problems, geometric evolution equations, Kähler geometry, complex and algebraic geometry, in particular, moduli spaces, Calabi-Yau manifolds, and irreducible symplectic manifolds, singularities, noncommutative field theory, instantons in string compactification, and integrable models.

While firmly rooted in one of the three areas, the proposed topics for Ph.D. students all have a clear perspective pointing towards one of the neighboring fields. In our teaching programme we strictly emphasize 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 offers:
  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
  4. a programme of international visitors and exchange opportunities

Partners from various universities worldwide 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.