BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Enrico Le Donne (University of Pisa & University of Jyväskylä) DTSTART:20200417T150000Z DTEND:20200417T160000Z DTSTAMP:20260422T212606Z UID:ISRS/1 DESCRIPTION:Title: Mat hematical appearances of sub-Riemannian geometries\nby Enrico Le Donne (University of Pisa & University of Jyväskylä) as part of International sub-Riemannian seminar\n\n\nAbstract\nSub-Riemannian geometries are a gen eralization of Riemannian\ngeometries. Roughly speaking\, in order to meas ure distances in a\nsub-Riemannian manifold\, one is allowed to only measu re distances\nalong curves that are tangent to some subspace of the tangen t space.\n\nThese geometries arise in many areas of pure and applied mat hematics\n(such as algebra\, geometry\, analysis\, mechanics\, control the ory\,\nmathematical\nphysics\, theoretical computer science)\, as well as in applications\n(e.g.\, robotics\, vision).\n This talk introduces sub-Ri emannian geometry from the metric\nviewpoint and focus on a few classical situations in pure mathematics\nwhere sub-Riemannian geometries appear. Fo r example\, we shall discuss\nboundaries of rank-one symmetric spaces and asymptotic cones of\nnilpotent groups.\nThe goal is to present several met ric characterizations of\nsub-Riemannian geometries so to give an explanat ion of their natural\nmanifestation.\n We first give a characterization of Carnot groups\, which are very\nspecial sub-Riemannian geometries.\n We e xtend the result to self-similar metric Lie groups (in\ncollaboration with Cowling\, Kivioja\, Nicolussi Golo\, and Ottazzi).\n We then present some recent results characterizing boundaries of\nrank-one symmetric spaces (i n collaboration with Freeman).\n LOCATION:https://researchseminars.org/talk/ISRS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Montgomery (UC Santa Cruz) DTSTART:20200430T150000Z DTEND:20200430T160000Z DTSTAMP:20260422T212606Z UID:ISRS/2 DESCRIPTION:Title: Mag netic playground fields for understanding subRiemannian geodesics\nby Richard Montgomery (UC Santa Cruz) as part of International sub-Riemannian seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ISRS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Karmanova DTSTART:20200515T150000Z DTEND:20200515T160000Z DTSTAMP:20260422T212606Z UID:ISRS/3 DESCRIPTION:Title: A n ew look at Carnot-Caratheodory spaces theory and related topics\nby Ma ria Karmanova as part of International sub-Riemannian seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/ISRS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Ritoré (Universidad de Granada) DTSTART:20200529T150000Z DTEND:20200529T160000Z DTSTAMP:20260422T212606Z UID:ISRS/4 DESCRIPTION:Title: Wul ff shapes in the Heisenberg group\nby Manuel Ritoré (Universidad de G ranada) as part of International sub-Riemannian seminar\n\n\nAbstract\nGiv en a not necessarily symmetric left-invariant norm $||\\cdot ||_K$ in\nthe first Heisenberg group $\\mathbb{H}^1$ induced by a convex body\n$K\\subs et\\mathbb{R}^2$ containing the origin in its interior\, we\nconsider the associated perimeter functional\, that coincides with the\nclassical sub-R iemannian perimeter in case $K$ is the closed unit disk\ncentered at the o rigin of $\\rr^2$. Under the assumption that $K$ has\nstrictly convex smoo th boundary we compute the first variation formula\nof perimeter for sets with $C^2$ boundary. The localization of the\nvariational formula in the n on-singular part of the boundary\, composed\nof the points where the tange nt plane is not horizontal\, allows us to\ndefine a mean curvature functio n $H_K$ out of the singular set. In the\ncase of non-vanishing mean curvat ure\, the condition that $H_K$ be\nconstant implies that the non-singular portion of the boundary is\nfoliated by horizontal liftings of translation s of $\\ptl K$ dilated by a\nfactor of $1/H_K$. Based on this we can defin ed a sphere $\\mathbb{B}_K$\nwith constant mean curvature $1$ by consideri ng the union of all\nhorizontal liftings of $\\partial K$ starting from $( 0\,0\,0)$ until they\nmeet again. We give some geometric properties of thi s sphere and\,\nmoreover\, we prove that\, up to non-homogenoeus dilations and\nleft-translations\, they are the only solutions of the sub-Finsler\n isoperimetric problem in a restricted class of sets. This is joint work\nw ith Julián Pozuelo.\n LOCATION:https://researchseminars.org/talk/ISRS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Tuomas Orponen DTSTART:20200612T150000Z DTEND:20200612T160000Z DTSTAMP:20260422T212606Z UID:ISRS/5 DESCRIPTION:Title: Sub -elliptic boundary value problems in flag domains\nby Tuomas Orponen a s part of International sub-Riemannian seminar\n\n\nAbstract\nI will talk about solving the sub-Laplacian Dirichlet and Neumann problems with $L^2$ boundary data in “flag domains” of the first Heisenberg group. These a re domains bounded by a vertically ruled Lipschitz graph. The solutions ar e obtained via the method of layer potentials. This is joint work with Mic hele Villa.\n LOCATION:https://researchseminars.org/talk/ISRS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Rizzi DTSTART:20200626T150000Z DTEND:20200626T160000Z DTSTAMP:20260422T212606Z 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