Results of a higgs boson searches in the ATLAS and CMS experiments at the large hadron collider at energies 7 and 8 TeV

Recent achievements of the ATLAS and CMS experiments at the Large Hadron Collider searching for a Higgs boson are summarized. A new particle with the mass of 125 GeV and properties expected for the Standard Model Higgs boson was discovered three years ago in these experiments in proton-proton collisions when analyzing part of the data taken at the centre-of-mass energies 7 TeV and 8 TeV in 2011 and 2012 year exposures. Today all the data are processed and fully analyzed. Experimental results of studies of individual Higgs boson decay channels as well as their combination to extract such properties as mass, signal strength, coupling constants, spin and parity are reviewed. All experimental results are found to be compatible with the Standard Model predictions.     

Homotopy Gerstenhaber Structures and Vertex Algebras

We provide a simple construction of a G _∞-algebra structure on an important class of vertex algebras V, which lifts the Gerstenhaber algebra structure on BRST cohomology of V introduced by Lian and Zuckerman. We outline two applications to algebraic topology: the construction of a sheaf of G _∞ algebras on a Calabi–Yau manifold M, extending the operations of multiplication and bracket of functions and vector fields on M, and of a Lie_∞ structure related to the bracket of Courant (Trans Amer Math Soc 319:631–661, 1990).     

Mirror symmetry formulae for the elliptic genus of complete intersections

In this paper, we calculate the elliptic genus of certain completeintersections in products of projective spaces. We show thatit is equal to the elliptic genus of the Landau–Ginzburgmodels that are, according to Hori and Vafa, mirror partnersof these complete intersections. This provides additional evidenceof the validity of their construction. Received July 6, 2007.     

BRST Operator for Quantum Lie Algebras: Relation to the Bar Complex

Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super)algebras. Many notions from the theory of Lie (super)algebras admit quantum generalizations. In particular, there is a BRST operator Q (Q ²=0) that generates the differential in the Woronowicz theory and gives information about (co)homologies of quantum Lie algebras. In our previous papers, we gave and solved a recursive relation for the operator Q for quantum Lie algebras. Here, we consider the bar complex for q-Lie algebras and its subcomplex of q-antisymmetric chains. We establish a chain map (which is an isomorphism) of the standard complex for a q-Lie algebra to the subcomplex of the antisymmetric chains. The construction requires a set of nontrivial identities in the group algebra of the braid group. We also discuss a generalization of the standard complex to the case where a q-Lie algebra is equipped with a grading operator.     

The cohomology of the Morava stabilizer group at the prime 3

We compute the cohomology of the Morava stabilizer group at the prime by resolving it by a free product and analyzing the ``relation module.'