Speaker
Mikhail Belolipetsky
(IMPA)
Description
We study growth of absolute and homological $k$-dimensional systoles of arithmetic $n$-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank $r>1$. We observe, in particular, that in some cases for $k=r$ the growth function tends to oscillate between a power of a logarithm and a power function of the degree of the covering which is a new phenomenon. We also prove the expected polylogarithmic and constant power bounds for small and large $k$, respectively. In the talk I will discuss the general picture and proofs of some results. It is based on joint work with S. Weinberger and work in progress with A. Erdnigor and S. Weinberger.
