BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Guido Carlet (Institut de Mathématiques de Bourgogne) DTSTART:20250326T150000Z DTEND:20250326T170000Z DTSTAMP:20260506T093213Z UID:SISSAmath-ph/5 DESCRIPTION:Title: Structure\, cohomology and deformations of local homogeneous Poisson brackets of arbitrary degree\nby Guido Carlet (Institut de Mathématiq ues de Bourgogne) as part of SISSA Mathematical Physics seminar\n\n\nAbstr act\nDubrovin and Novikov initiated the study of local homogeneous differe ntial-geometric Poisson brackets of arbitrary degree k in their seminal 19 84 paper. Despite many efforts\, and several results in low degree\, very little is known about their structure for arbitrary k. After an introducti on to the topic\, we first report on our recent results on the structure o f DN brackets of degree k. By applying homological algebra methods to the computation of their Poisson cohomology (or rather of an associated differ ential complex) we show that certain linear combinations of the coefficien ts of a degree k DN bracket define k flat connections. Moreover the Poisso n cohomology of such brackets is related with the Chevalley-Eilenberg coho mology of an associate finite-dimensional Lie algebra. In collaboration wi th M. Casati.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/5/ END:VEVENT END:VCALENDAR