Contact: Daniel Huybrechts
This talk is based on joint work with Luigi Lunardon. To every smooth and proper variety X with trivial canonical bundle over the field of complex Laurent series C((t)), one can attach its motivic zeta function, which measures how the variety degenerates as t goes to 0. We will show that this motivic zeta function is a birational invariant of X and deduce the birational invariance of the monodromy conjecture for X (the main open problem about these zeta functions). If time permits, we will also discuss a recent example by Cynk and van Straten of a Calabi-Yau threefold over C((t)) with trivial monodromy but no good reduction.
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/5285