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

Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report

This Report summarizes the proceedings of the 2015 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt with (I) new developments relevant for high precision Standard Model calculations, (II) the new PDF4LHC parton distributions, (III) issues in the theoretical description of the production of Standard Model Higgs bosons and how to relate experimental measurements, (IV) a host of phenomenological studies essential for comparing LHC data from Run I with theoretical predictions and projections for future measurements in Run II, and (V) new developments in Monte Carlo event generators.Comment: Proceedings of the Standard Model Working Group of the 2015 Les Houches Workshop, Physics at TeV Colliders, Les Houches 1-19 June 2015. 227 page

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

A polar barrier to transcription can be circumvented by remodeler-induced nucleosome translocation

Many eukaryotic genes are regulated at the level of transcript elongation. Nucleosomes are likely targets for this regulation. Previously, we have shown that nucleosomes formed on very strong positioning sequences (601 and 603), present a high, orientation-dependent barrier to transcription by RNA polymerase II in vitro. The existence of this polar barrier correlates with the interaction of a 16-bp polar barrier signal (PBS) with the promoter-distal histone H3–H4 dimer. Here, we show that the polar barrier is relieved by ISW2, an ATP-dependent chromatin remodeler, which translocates the nucleosome over a short distance, such that the PBS no longer interacts with the distal H3–H4 dimer, although it remains within the nucleosome. In vivo, insertion of the 603 positioning sequence into the yeast CUP1 gene results in a modest reduction in transcription, but this reduction is orientation-independent, indicating that the polar barrier can be circumvented. However, the 603-nucleosome is present at the expected position in only a small fraction of cells. Thus, the polar barrier is probably non-functional in vivo because the nucleosome is not positioned appropriately, presumably due to nucleosome sliding activities. We suggest that interactions between PBSs and chromatin remodelers might have significant regulatory potential

Model theory of finite and pseudofinite groups

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory

The docking domain of histone H2A is required for H1 binding and RSC-mediated nucleosome remodeling

Histone variants within the H2A family show high divergences in their C-terminal regions. In this work, we have studied how these divergences and in particular, how a part of the H2A COOH-terminus, the docking domain, is implicated in both structural and functional properties of the nucleosome. Using biochemical methods in combination with Atomic Force Microscopy and Electron Cryo-Microscopy, we show that the H2A-docking domain is a key structural feature within the nucleosome. Deletion of this domain or replacement with the incomplete docking domain from the variant H2A.Bbd results in significant structural alterations in the nucleosome, including an increase in overall accessibility to nucleases, un-wrapping of ∼10 bp of DNA from each end of the nucleosome and associated changes in the entry/exit angle of DNA ends. These structural alterations are associated with a reduced ability of the chromatin remodeler RSC to both remodel and mobilize the nucleosomes. Linker histone H1 binding is also abrogated in nucleosomes containing the incomplete docking domain of H2A.Bbd. Our data illustrate the unique role of the H2A-docking domain in coordinating the structural-functional aspects of the nucleosome properties. Moreover, our data suggest that incorporation of a ‘defective’ docking domain may be a primary structural role of H2A.Bbd in chromatin