Pure & Applied MathematicsPure & Applied Mathematicshttp://hdl.handle.net/2262/592014-12-22T08:32:44Z2014-12-22T08:32:44ZQuillen homology for operads via Gröbner basesDOTSENKO, VLADIMIRhttp://hdl.handle.net/2262/727402014-12-20T03:05:23Z2013-01-01T00:00:00ZQuillen homology for operads via Gröbner bases
DOTSENKO, VLADIMIR
The main goal of this paper is to present a way to compute Quillen homology of operads. The key idea is to use the notion of a shuffle operad we introduced earlier; this allows to compute, for a symmetric operad, the homology classes and the shape of the differential in its minimal model, although does not give an insight on the symmetric groups action on the homology. Our approach goes in several steps. First, we regard our symmetric operad as a shuffle operad, which allows to compute its Grobner basis. Next, we define a combinatorial resolution for the "monomial replacement" of each shuffle operad (provided by the Grobner bases theory). Finally, we explain how to "deform" the differential to handle every operad with a Grobner basis, and find explicit representatives of Quillen homology classes for a large class of operads. We also present various applications, including a new proof of Hoffbeck's PBW criterion, a proof of Koszulness for a class of operads coming from commutative algebras, and a homology computation for the operads of Batalin-Vilkovisky algebras and of Rota-Baxter algebras.
PUBLISHED
2013-01-01T00:00:00ZS wave bottomonium states moving in a quark-gluon plasma from lattice NRQCDRYAN, SINEAD MARIEhttp://hdl.handle.net/2262/721882014-11-26T03:03:27Z2013-01-01T00:00:00ZS wave bottomonium states moving in a quark-gluon plasma from lattice NRQCD
RYAN, SINEAD MARIE
We extend our study of bottomonium spectral functions in the quark-gluon plasma to nonzero momentum. We use lattice QCD simulations with two flavours of light quark on highly anisotropic lattices and treat the bottom quark with nonrelativistic QCD (NRQCD). We focus on S wave (? and ? b ) channels and consider nonrelativistic velocities, v/c ? 0.2. A comparison with predictions from effective field theory is made
PUBLISHED
2013-01-01T00:00:00ZExcited and exotic charmonium spectroscopy from lattice QCDRYAN, SINEAD MARIEPEARDON, MICHAEL JAMEShttp://hdl.handle.net/2262/721852014-11-25T03:03:22Z2012-01-01T00:00:00ZExcited and exotic charmonium spectroscopy from lattice QCD
RYAN, SINEAD MARIE; PEARDON, MICHAEL JAMES
We present a spectrum of highly excited charmonium mesons up to around 4.5 GeV calculated using dynamical lattice QCD. Employing novel computational techniques and the variational method with a large basis of carefully constructed operators, we extract and reliably identify the continuum spin of an extensive set of excited states, states with exotic quantum numbers (0+-, 1-+, 2+-) and states with high spin. Calculations are performed on two lattice volumes with pion mass approximately 400 MeV and the mass determinations have high statistical precision even for excited states. We discuss the results in light of experimental observations, identify the lightest 'supermultiplet' of hybrid mesons and comment on the phenomenological implications of the spectrum of exotic mesons.
2012-01-01T00:00:00ZExcited spectroscopy of charmed mesons from lattice QCDRYAN, SINEAD MARIEPEARDON, MICHAEL JAMEShttp://hdl.handle.net/2262/721842014-11-25T03:03:19Z2013-01-01T00:00:00ZExcited spectroscopy of charmed mesons from lattice QCD
RYAN, SINEAD MARIE; PEARDON, MICHAEL JAMES
We present spectra of highly excited D and D s mesons up to around 3.8 GeV determined using dynamical lattice QCD. We employ novel computational techniques and the variational method with a large basis of carefully constructed operators in order to extract and reliably identify the continuum spin of an extensive set of excited states. These include states with high spin and states identified as having an explicit gluonic contribution. Calculations were performed on two volumes, both with a pion mass of approximately 400 MeV, achieving a high statistical precision for both ground and excited states. We discuss our results in light of experimental observations, comment on the phenomenological implications and identify the lightest ‘supermultiplet’ of hybrid mesons in each sector.
2013-01-01T00:00:00Z