Seminarium z Topologii Algebraicznej
Wtorki, 14:30-16:00, sala 4070
The computational aspects of property (T)
Marek Kaluba
11.10.2016
Abstract:
Kazhdan's Property (T) is a well known concept in the theory of group
actions. Its numerous applications include finite generation of
lattices, Fixed-point properties of isometric actions, constructions of
expanding graphs and product replacement algorithm.
However a complicated notion requires a serious fire-power to be
established. Indeed to prove that a group has property (T) requires a
non-trivial effort even in the case of most classical examples, such as
SL(3,Z).
We hope to ease the effort by drawing from the field of semi-definite
programming and cone-optimisation. Using the Positivestellensatz and
following the work of Ozawa and Netzer&Thom we will show how to
translate property (T) into a semi-definite optimisation problem. Given
an explicit generating set S of a finitely presented group G this
will (possibly) allow us to produce a "witness" for the property (T) and
simultaneously estimate the Kazhdan's constant for (G,S).