Data: piątek, 30.04.2021, godz. 12:30-14:00
Prelegent: dr Marek Kaluba (Karlsruhe Institute of Technology)
Abstrakt: Let G_n be either SL(n,Z) or Aut(F_n). I will show how the action of outer automorphism groups provides control over embeddings of group rings R[G_n]-->R[G_m], for m>n. By exercising this control one can derive sum of squares decompositions of specific elements in R[G_m] (for all m) from a single decomposition in R[G_n]. This reduces the proof of property (T) for G_m (for all m) to a single computation in G_n (n=3 in case of G=SL(n,Z), or n=5 in case of G=Aut(F_n)). By successfully performing the calculation in the preprint [arXiv:1812:03456], we provide a uniform argument, that G_n has property (T), obtaining additionally asymptotically optimal bounds on so called Kazhdan constants. This talk is based on joint work with Dawid Kielak (Oxford) and Piotr Nowak (IMPAN). This is the third and final lecture in a series by dr Kaluba.