The NA62 experiment at CERN: status and perspectives

The NA62 experiment at CERN will measure the branching ratio of the K+ -> pi+ nu nubar decay with a precision of 10%, collecting about 100 events in two years of run. This paper will review the design of the experiment, the strategy for the measurement and the actual status of the installation. Prospects for the data collection and for the measurement of other rare K+ channels will be presented.Comment: Presented at the 2014 Flavour Physics and CP Violation (FPCP2014), Marseille, France, May 26-30 2014, 10 pages, 4 figure

Riemann-Roch theorems and elliptic genus for virtually smooth Schemes

For a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves.Comment: 31 page