Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Sebastian Boldt
Affiliation:

Humboldt Universität zu Berlin
Date:

Thu, 2018-01-11 16:30 - 17:30 We consider nonsingular Heisenberg-like nilmanifolds. This class

strictly contains the well-known Heisenberg-type nilmanifolds. For any

compact nonsingular Heisenberg-like nilmanifold, we present a trace

formula. This formula enables us to access the height, i.e., the

derivative of the spectral zeta function at zero.

We then investigate the global behaviour of the height as a function on

the moduli space of volume-normalised Heisenberg-like metrics on a fixed

compact nonsingular nilmanifold. If the dimension of the underlying

manifold is 3 mod 4 then the height attains a global minimum. In

contrast, one can construct paths of metrics on which the height is not

bounded from below if the dimension is 0 or 1 mod 4. The existence of

global minima can be enforced in any dimension by bounding the sectional

curvature from above.

At last, we will construct the global minimiser of the height in

dimension 3 and consider certain local minima of Heisenberg-type metrics

in dimensions 5, 9 and 25.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/4652