CMS results on multijet correlations

We present recent measurements of multijet correlations using forward and low-$p_{\mathrm{T}}$ jets performed by the CMS collaboration at the LHC collider. In pp collisions at $\sqrt{s} = 7$ TeV, azimuthal correlations in dijets separated in rapidity by up to 9.4 units were measured. The results are compared to BFKL- and DGLAP-based Monte Carlo generator and analytic predictions. In pp collisions at $\sqrt{s} = 8$ TeV, cross sections for jets with $p_{\mathrm{T}}$ > 21 GeV and |y| < 4.7, and for track-jets with $p_{\mathrm{T}}$ > 1 GeV (minijets) are presented. The minijet results are sensitive to the bound imposed by the total inelastic cross section, and are compared to various models for taming the growth of the $2 \rightarrow 2$ cross section at low $p_{\mathrm{T}}$.Comment: Talk at "Diffraction 2014" workshop, Primosten, Croatia, September 10-16, 201

Estimates for eigenvalues of the Schr\"odinger operator with a complex potential

We study the distribution of eigenvalues of the Schr\"odinger operator with a complex valued potential $V$. We prove that if $|V|$ decays faster than the Coulomb potential, then all eigenvalues are in a disc of a finite radius

A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes

Pantev, Toen, Vaqui\'e and Vezzosi arXiv:1111.3209 defined $k$-shifted symplectic derived schemes and stacks ${\bf X}$ for $k\in\mathbb Z$, and Lagrangians ${\bf f}:{\bf L}\to{\bf X}$ in them. They have important applications to Calabi-Yau geometry and quantization. Bussi, Brav and Joyce arXiv:1305.6302 proved a 'Darboux Theorem' giving explicit Zariski or \'etale local models for $k$-shifted symplectic derived schemes ${\bf X}$ for $k<0$ presenting them as twisted shifted cotangent bundles. We prove a 'Lagrangian Neighbourhood Theorem' giving explicit Zariski or etale local models for Lagrangians ${\bf f}:{\bf L}\to{\bf X}$ in $k$-shifted symplectic derived schemes ${\bf X}$ for $k<0$, relative to the Bussi-Brav-Joyce 'Darboux form' local models for ${\bf X}$. That is, locally such Lagrangians can be presented as twisted shifted conormal bundles. We also give a partial result when $k=0$. We expect our results will have future applications to $k$-shifted Poisson geometry (see arXiv:1506.03699), to defining 'Fukaya categories' of complex or algebraic symplectic manifolds, and to categorifying Donaldson-Thomas theory of Calabi-Yau 3-folds and 'Cohomological Hall algebras'.Comment: 68 page

Time scale for the formation of the earth and planets and its role in their geochemical evolution

The initial mass of the solar nebula is discussed. Models of a massive nebula (two solar masses and more) encounter serious difficulties: an effective mechanism of transfer of the momentum from the central part of the nebula outward, capable of leading to formation of the sun and removal of half the mass of the nebula from the solar system has not been found. As a consequence of the instability of these models, their evolution can end with the formation, not a planetary system, but of a binary star. The possibility is demonstrated of obtaining acceptable growth rates for Uranus and Neptune by prolonging the thickening of preplanetary dust in the region of large masses. The important role of large bodies in the process of formation of the planets is noted. The impacts of such bodies, moving in heliocentric orbits, could have imparted considerable additional energy to the forming Moon, which, together with the energy given off by the joining of a small number of large protomoons, could have led to a high initial temperature of the moon