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11/11/2026 - Francesca Tripaldi - 5:30 p. m.
11/11/2026 - Francesca Tripaldi - 5:30 p. m.
(University of Leeds)
(University of Leeds)
Possible div-curl estimates on the 5-dimensional Cartan group
Possible div-curl estimates on the 5-dimensional Cartan group
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Abstract. On arbitrary Carnot groups, the only hypoelliptic Hodge-Laplacians on forms that have been introduced are 0-order pseudodifferential operators constructed using the Rumin complex. However, to address questions where one needs sharp estimates, this 0-order operator is not suitable. This is a rather difficult problem to tackle in full generality, the main issue being that the Rumin exterior differential is not homogeneous on arbitrary Carnot groups. In this talk, I will focus on the specific example of the free Carnot group of step 3 with 2 generators, where it is possible to introduce different hypoelliptic Hodge-Laplacians on forms. Such Laplacians can be used to obtain sharp div-curl type inequalities akin to those considered by Bourgain & Brezis and Lanzani & Stein for the de Rham complex, or their subelliptic counterparts obtained by Baldi, Franchi & Pansu for the Rumin complex on Heisenberg groups.
This series of seminars is addressed to an audience interested in Harmonic Analysis in the broadest possible sense. The seminars will not necessarily concern the latest research results; the speaker may also give a talk about open problems or a survey colloquium.
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Organizers:
Tommaso Bruno (Università di Genova)
Valentina Casarino (Università degli Studi di Padova)
Bianca Gariboldi (Università Unipegaso)
Alessio Martini (Politecnico di Torino)
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