Property (T)(T) for noncommutative universal lattices

We establish a new spectral criterion for Kazhdan's property $(T)$ which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property $(T)$ for the groups $EL_n(R)$, where $n\geq 3$ and $R$ is an arbitrary finitely generated associative ring. We also strengthen some of the results on property $(T)$ for Kac-Moody groups from a paper of Dymara and Januszkiewicz (Invent. Math 150 (2002)).Comment: 47 pages; final versio

Nucleosome mobilization by ISW2 requires the concerted action of the ATPase and SLIDE domains

The ISWI family of ATP-dependent chromatin remodelers represses transcription by changing nucleosome positioning. The interactions with extranucleosomal DNA and the requirement of a minimal length of extranucleosomal DNA by ISWI mediate the spacing of nucleosomes. ISW2 from Saccharomyces cerevisiae, a member of the ISWI family, has a conserved domain called SLIDE (SANT-like ISWI domain), whose binding to extranucleosomal DNA ~19 bp from the edge of nucleosomes is required for efficiently pushing DNA into nucleosomes and maintaining the unidirectional movement of nucleosomes, as reported here. Loss of SLIDE binding does not perturb ATPase domain binding to the SHL2 site of nucleosomes or its initial movement of DNA inside of nucleosomes. ISW2 has therefore two distinct roles in mobilizing nucleosomes, with the ATPase domain translocating and moving DNA inside nucleosomes, and the SLIDE domain facilitating the entry of linker DNA into nucleosomes

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc