Event

Talk
The structure of GJMS-operators and Q-curvatures
Prof. Dr. Andreas Juhl
29 May 2012, 16:00 – 17:00

The significance of the Yamabe operator is widely known in conformal differential geometry. Moreover, some high-order conformally invariant generalizations of this operator are well-known since more than twenty years. In fact, such operators were constructed by Graham, Jenne,Mason and Sparling in a seminal paper by an application of the Fefferman-Graham ambient metric, and are now usually referred to as the GJMS-operators. In recent years, these operators played an increasingly important role in mathematics and theoretical physics. In particular, they gave rise to the notion of Branson's Q-curvature, and much recent work has been devoted to its understanding. Despite these developments, the insights into the structure of (and formulas for) these operators (and Q-curvatures) were poor.

In the lecture I will give an introduction to these questions and will describe some of the new tools which allowed to reveal a part of the hidden structures in the sequence of the GJMS-operators. In particular, we found how these operators can be described in terms of a sequence of remarkable geometric second-order operators and that the sequence of Q-curvatures have an intrinsic recursive structure. On a very basic level, the new techniques are inspired by representation theory and aspects of the AdS/CFT-duality.

Related to:

• Andreas Juhl