BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Luca Rizzi DTSTART:20200626T150000Z DTEND:20200626T160000Z DTSTAMP:20260423T021650Z UID:ISRS/6 DESCRIPTION:Title: Hea t content asymptotics for sub-Riemannian manifolds\nby Luca Rizzi as p art of International sub-Riemannian seminar\n\n\nAbstract\nWe study the sm all-time asymptotics of the heat content of smooth non-characteristic doma ins of a general rank-varying sub-Riemannian structure\, equipped with an arbitrary smooth measure. By adapting to the sub-Riemannian case a techniq ue due to Savo\, we establish the existence of the full asymptotic series for small times\, at arbitrary order. We compute explicitly the coefficien ts up to order k = 5\, in terms of sub-Riemannian invariants of the domain . Furthermore\, as an independent result\, we prove that every coefficient can be obtained as the limit of the corresponding one for a suitable Riem annian extension. As a particular case we recover\, using non-probabilisti c techniques\, the order 2 formula recently obtained by Tyson and Wang in the Heisenberg group [Comm. PDE\, 2018]. A consequence of our fifth-order analysis is the evidence for new phenomena in presence of characteristic p oints. In particular\, we prove that the higher order coefficients in the asymptotics can blow-up in their presence.\n\nThis is a joint work with T. Rossi (Institut Fourier & SISSA)\n LOCATION:https://researchseminars.org/talk/ISRS/6/ END:VEVENT END:VCALENDAR