sotto trovate le informazioni sul seminario di Lorenzo dello Schiavo a Roma 1.
Dove: Sala di Consiglio, Dipartimento di Matematica, Università La Sapienza
Speaker: Lorenzo Dello Schiavo (IST Austria)
Title: Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension
Abstract: On large classes of closed even-dimensional Riemannian manifolds M, we construct and study the
Copolyharmonic Gaussian Field, i.e. a conformally invariant log-correlated Gaussian field of distributions on M. This random field is defined as the unique centered Gaussian field with covariance kernel given as the resolvent kernel of Graham—Jenne—Mason—Sparling (GJMS) operators of maximal order. The corresponding Gaussian Multiplicative Chaos is a generalization to the 2m-dimensional case of the celebrated Liouville Quantum Gravity measure in dimension two. We study the associated Liouville Brownian motion and random GJMS operator, the higher-dimensional analogues of the 2d Liouville Brownian Motion and of the random Laplacian. Finally, we study the Polyakov–Liouville on the space of distributions on M induced by the copolyharmonic Gaussian field, providing explicit conditions for its finiteness and computing the conformal anomaly.
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Prof. Alessandra Faggionato
Department of Mathematics
University "La Sapienza"
Piazzale Aldo Moro, 5
00185 - Rome
Office 5, Phone (0039) 06 49913252
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