Quantum gravity and Riemannian geometry on the fuzzy sphere

We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2\imath\lambda_p \epsilon_{ijk}x_k$ modulo setting $\sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant differential structure. Metrics are given by symmetric $3 \times 3$ matrices $g$ and we show that for each metric there is a unique quantum Levi-Civita connection with constant coefficients, with scalar curvature $\frac{1}{2}({\rm Tr}(g^2)-\frac{1}{2}{\rm Tr}(g)^2)/\det(g)$. As an application, we construct Euclidean quantum gravity on the fuzzy unit sphere. We also calculate the charge 1 monopole for the 3D differential structure.Comment: 15 pages latex, 1 figur

Geometric Dirac operator on noncommutative torus and M2(C)M_2(\Bbb C)

We solve for quantum-geometrically realised spectral triples or `Dirac operators' on the noncommutative torus $\Bbb C_\theta[T^2]$ and on the algebra $M_2(\Bbb C)$ of $2\times 2$ matrices with their standard quantum metrics and associated quantum Levi-Civita connections. For $\Bbb C_\theta[T^2]$, we obtain an even standard spectral triple but now uniquely determined by full geometric realisability. For $M_2(\Bbb C)$, we are forced to the flat quantum Levi-Civita connection and again obtain a natural fully geometrically realised even spectral triple. In both case there is also an odd spectral triple for a different choice of a sign parameter. We also consider an alternate quantum metric on $M_2(\Bbb C)$ with curved quantum Levi-Civita connection and find a natural 2-parameter of almost spectral triple in that $D$ fails to be antihermitian. In all cases, we split the construction into a local tensorial level related to the quantum geometry, where we classify the results more broadly, and the further requirements relating to the Hilbert space structure. We also illustrate the Lichnerowicz formula for $D^2$ which applies in the case of a full geometric realisation.Comment: 33 pages latex no figures. Moved the less interesting second quantum metric on M_2(C) into an appendix, corrected typos and added details of Lichnerowicz theorem related D^2 and Laplacian. This is a sequel to 2104.13212 (math.QA

Occurrence of Ophiocordyceps myrmicarum on a non-Formicidae insect in integrated crop-livestock farming systems.

Na publicação: Fabricia Z. V. Torres; Daniela A. Souza; Marcos Faria; Edison Sujii; Rogerio B. Lopes

Monitoramento de percevejo castanho em sistemas integrados de produção da Embrapa Gado de Corte.

Comissão organizadora: Grácia Maria Soares Rosinha, Alexandra Rocha de Oliveir, Rodrigo Carvalho Alva

Avaliação de genótipos de Brachiaria quanto à resistência às cigarrinhas-das-pastagens (Hemiptera: Cercopidae).

Comissão organizadora: Grácia Maria Soares Rosinha, Alexandra Rocha de Oliveir, Rodrigo Carvalho Alva