First meeting, Ben Gurion University, 12.11.18, Building 58 room -101

Bounding the covolume of lattices in products.

The Kazhdan-Margulis theorem ensures that, in a semisimple Lie group without compact factors, the set of covolumes of all lattices is bounded away from 0. The goal of this talk, based on joint work with Adrien Le Boudec, is to discuss the validity of that theorem, and some of its relatives, in the broader context of lattices in products of compactly generated simple locally compact groups.

TBA

On algorithms in SL(n,Z)

I will introduce and analyze two algorithms in SLn(Z):

In 1983 D. carter and G.Keller proved that in SL(n,O) (where n>2 and O is the ring of integers of an algebraic number field) there exists an integer v_n(O)depending only on n and O such that every matrix in SL(n,O) is a product of at most v_n(O) elementary matrices. We ask the question: How does this decomposition behave? Based on the work of S.I.Adian and J.Mennicke for the case of SLn(Z), we can deduce an upper bound for the entries of those elementary matrices.

After the work of R.K. Dennis and L.N. Vaserstein, we can show that for n>>0, every matrix in SL(n,Z)is a product of six commutators, and again, get a bound for those matrices.

0.01 % improvement of the Liouville property for discrete harmonic functions on Z^2.

Let u be a harmonic function on the plane. The Liouville theorem claims that if |u| is bounded on the whole plane, then u is identically constant. It appears that if u is a harmonic function on the lattice Z^2, and |u| < 1 on 99,99% of Z^2, then u is a constant function. Based on a joint work (in progress) with A. Logunov, Eu. Malinnikova and M. Sodin.

Uri Bader Weizmann

What is the sum of angles of an n-gon?...

Wait, I meant an n-gon in the 3-dimensional space!

Jazz show

Tsachik Gelander

Elad Muskatel

Nimrod Talmon

You are cordially invited.

The support of BGU Center for advanced studies in mathematics is gratefully acknowledged.