BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Robert Young (New York University) DTSTART:20201030T150000Z DTEND:20201030T160000Z DTSTAMP:20260404T111103Z UID:SRS/1 DESCRIPTION:Title: Metric differentiation and embeddings of the Heisenberg group\nby R obert Young (New York University) as part of Sub-Riemannian Seminars\n\n\n Abstract\nPansu and Semmes used a version of Rademacher's differentiation theorem to show that there is no bilipschitz embedding from the Heisenberg groups into Euclidean space. More generally\, the non-commutativity of th e Heisenberg group makes it impossible to embed into any $L_p$ space for $ p\\in (1\,\\infty)$. Recently\, with Assaf Naor\, we proved sharp quantit ative bounds on embeddings of the Heisenberg groups into $L_1$ and constru cted a metric space based on the Heisenberg group which embeds into $L_1$ and $L_4$ but not in $L_2$\; our construction is based on constructing a s urface in $\\mathbb{H}$ which is as bumpy as possible. In this talk\, we w ill describe what are the best ways to embed the Heisenberg group into Ban ach spaces\, why good embeddings of the Heisenberg group must be "bumpy" a t many scales\, and how to study embeddings into $L_1$ by studying surface s in $\\mathbb{H}$\n\nVIRTUAL SESSION\n LOCATION:https://stable.researchseminars.org/talk/SRS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Clotilde Fermanian Kammerer (Université Paris Est) DTSTART:20201120T150000Z DTEND:20201120T160000Z DTSTAMP:20260404T111103Z UID:SRS/2 DESCRIPTION:Title: Semi-classical analysis on H-type groups\nby Clotilde Fermanian Kam merer (Université Paris Est) as part of Sub-Riemannian Seminars\n\n\nAbst ract\nWe present in this talk recent results obtained in collaboration wit h Véronique Fischer (University of Bath\, UK) aiming at developing a semi -classical approach in sub-Laplacian geometry. In the context of H-type gr oups\, we describe how to construct a semi-classical pseudodifferential ca lculus compatible with the Lie group structure and we discuss the associat ed notion of semi-classical measures\, together with some of their propert ies. We will discuss an application to control developed with Cyril Letrou it (ENS Paris).\n\nPhysical session in Paris --> moved to virtual session due to new lockdown in France\n LOCATION:https://stable.researchseminars.org/talk/SRS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Vittone (Padova) DTSTART:20201211T150000Z DTEND:20201211T160000Z DTSTAMP:20260404T111103Z UID:SRS/3 DESCRIPTION:Title: Differentiability of intrinsic Lipschitz graphs in Carnot groups\nb y Davide Vittone (Padova) as part of Sub-Riemannian Seminars\n\n\nAbstract \nSubmanifolds with intrinsic Lipschitz regularity in sub-Riemannian\nCarn ot groups can be introduced using the theory of intrinsic\nLipschitz graph s started by B. Franchi\, R. Serapioni and F. Serra\nCassano almost 15 yea rs ago. One of the main related questions\nconcerns a Rademacher-type theo rem (i.e.\, existence of a tangent\nplane) for such graphs: in this talk I will discuss a recent positive\nsolution to the problem in Heisenberg gro ups. The proof uses currents\nin Heisenberg groups (in particular\, a vers ion of the celebrated\nConstancy Theorem) and a number of complementary re sults such as\nextension and smooth approximation theorems for intrinsic L ipschitz\ngraphs. I will also show a recent example (joint with A. Julia a nd S.\nNicolussi Golo) of an intrinsic Lipschitz graph in a Carnot group t hat\nis nowhere intrinsically differentiable.\n LOCATION:https://stable.researchseminars.org/talk/SRS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Dario Prandi (CentraleSupelec) DTSTART:20210108T150000Z DTEND:20210108T160000Z DTSTAMP:20260404T111103Z UID:SRS/8 DESCRIPTION:Title: Point interactions for 3D sub-Laplacians\nby Dario Prandi (Centrale Supelec) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThe aim of this seminar is to present some recent results on the essential self-adjointne ss of pointed sub-Laplacians in three dimensions. These are the natural (n on-negative) hypoelliptic operators $H$ associated with a sub-Riemannian s tructure on a 3D manifold $M$\, with domain $\\operatorname{Dom}(H)=C^\\in fty_c(M\\setminus \\{p\\})$\, for $p\\in M$.\n\nIf $M=\\mathbb{R}^n$ and t he geometry is Euclidean\, $H$ is the standard Laplacian. It is then well- known that $H$ is essentially self-adjoint with $\\operatorname{Dom}(H) =C ^\\infty_c(\\mathbb{R}^n\\setminus\\{p\\})$ if and only if $n\\ge 4$. This follows\, for instance\, by the Euclidean Hardy inequality.\n\nIn this se minar we show that\, unlike the Euclidean case\, pointed sub-Laplacians (a s-sociated with smooth measures) are essentially self-adjoint already for contact sub-Riemannian manifolds of\n(topological) dimension $3$. Although this is not surprising\, since the Hausdorff dimension of these structure s is $4$\, we will sow that this result cannot be deduced via Hardy inequa lities as in the Euclidean case but requires a much finer machinery. Indee d\, our strategy of proof is based on a localicazion argument which allows to reduce to the study of the 3D Heisenberg pointed sub-Laplacian. The es sential self-adjoitness of the latter is then obtained by exploiting non-c ommutative Fourier transform techniques.\n\nThis is a joint work with R. A dami (Politecnico di Torino\, Italy)\, U. Boscain (CNRS &UPMC\, Sorbonne Université\, France)\, and V. Franceschi (Università di Padova\, Italy). \n LOCATION:https://stable.researchseminars.org/talk/SRS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Sachkov and Andrei Ardentov (Pereslavl) DTSTART:20210129T150000Z DTEND:20210129T160000Z DTSTAMP:20260404T111103Z UID:SRS/9 DESCRIPTION:Title: Sub-Riemannian geometry on the group of motions of the plane\nby Yu ri Sachkov and Andrei Ardentov (Pereslavl) as part of Sub-Riemannian Semin ars\n\n\nAbstract\nWe will discuss the unique\, up to local isometries\, c ontact sub-Riemannian structure on the group SE(2) of proper motions of th e plane (aka group of rototranslations).\nThe following questions will be addressed:\n- geodesics\,\n- their local and global optimality\,\n- cut ti me\, cut locus\, and spheres\,\n- infinite geodesics\,\n- bicycle transfor m and relation of geodesics with Euler elasticae\, \n- group of isometries and homogeneous geodesics\,\n- applications to imaging and robotics.\n LOCATION:https://stable.researchseminars.org/talk/SRS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuel Milman (Techion) DTSTART:20210312T150000Z DTEND:20210312T160000Z DTSTAMP:20260404T111103Z UID:SRS/10 DESCRIPTION:Title: Functional Inequalities on sub-Riemannian manifolds via QCD\nby Em anuel Milman (Techion) as part of Sub-Riemannian Seminars\n\n\nAbstract\nW e are interested in obtaining Poincarè and log-Sobolev inequalities on do mains in sub-Riemannian manifolds (equipped with their natural sub-Riemann ian metric and volume measure).\n\nIt is well-known that strictly sub-Riem annian manifolds do not satisfy any type of Curvature-Dimension condition CD(K\,N)\, introduced by Lott-Sturm-Villani some 15 years ago\, so we must follow a different path. Motivated by recent work of Barilari-Rizzi and B alogh-Kristàly-Sipos\, we show that in the ideal setting or for general c orank 1 Carnot groups\, these spaces nevertheless do satisfy a quasi-conve x relaxation of the CD condition\, which we name QCD(Q\,K\,N). As a conseq uence\, these spaces satisfy numerous functional inequalities with exactly the same quantitative dependence (up to the slack parameter Q>1) as their CD counterparts. We achieve this by extending the localization paradigm t o completely general interpolation inequalities\, and a one-dimensional co mparison of QCD densities with their "CD upper envelope". We thus obtain the best known quantitative estimates for (say) the $L^p$-Poincare and log -Sobolev inequalities on domains in ideal sub-Riemannian manifolds and in general corank 1 Carnot groups\, which in particular are independent of th e topological dimension. For instance\, the classical Li-Yau / Zhong-Yang spectral-gap estimate holds on all Heisenberg groups of arbitrary dimensio n up to a factor of 4.\n LOCATION:https://stable.researchseminars.org/talk/SRS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Shanbrom (Sacramento State University) DTSTART:20210219T150000Z DTEND:20210219T160000Z DTSTAMP:20260404T111103Z UID:SRS/11 DESCRIPTION:Title: Self-similarity in the Kepler-Heisenberg problem\nby Corey Shanbro m (Sacramento State University) as part of Sub-Riemannian Seminars\n\n\nAb stract\nThe Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the Heisenberg group\, thought of as a three-dim ensional sub-Riemannian manifold. The sub-Riemannian Hamiltonian provides the kinetic energy\, and the gravitational potential is given by the funda mental solution to the sub-Laplacian. The dynamics are at least partially integrable\, possessing two first integrals as well as a dilational moment um which is conserved by orbits with zero energy. The system is known to a dmit closed orbits of any rational rotation number\, which all lie within the fundamental zero energy integrable subsystem. Here\, we demonstrate th at all zero energy orbits are self-similar.\n LOCATION:https://stable.researchseminars.org/talk/SRS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Flynn (University of Bath) DTSTART:20210402T140000Z DTEND:20210402T150000Z DTSTAMP:20260404T111103Z UID:SRS/12 DESCRIPTION:Title: Unraveling X-ray Transforms on the Heisenberg group\nby Steven Fly nn (University of Bath) as part of Sub-Riemannian Seminars\n\n\nAbstract\n The classical X-ray Transform maps a function on Euclidean space to a fun ction on the space of lines on this Euclidean space by integrating the fun ction over the given line. Inverting the X-ray transform has wide-ranging applications\, including to medical imaging and seismology. Much work has been done to understand this inverse problem in Euclidean space\, Euclidea n domains\, and more generally\, for symmetric spaces and Riemannian manif olds with boundary where the lines become geodesics. We formulate a sub-Ri emannian version of the X-ray transform on the simplest sub-Riemannnian ma nifold\, the Heisenberg group. Here serious geometric obstructions to clas sical inverse problems\, such as existence of conjugate points\, appear ge nerically. With tools adapted to the geometry\, such as an operator-valued Fourier Slice Theorem\, we prove nonetheless that an integrable function on the Heisenberg group is indeed determined by its line integrals over su b-Riemannian (as well as over its compatible Riemannian and Lorentzian) ge odesics.\n\nWe also pose an abundance of accessible follow-up questions\, standard in the inverse problems community\, concerning the sub-Riemannian case\, and report progress answering some of them.\n LOCATION:https://stable.researchseminars.org/talk/SRS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphael Ponge (Sichuan University) DTSTART:20210423T140000Z DTEND:20210423T150000Z DTSTAMP:20260404T111103Z UID:SRS/13 DESCRIPTION:Title: The tangent groupoid of a Carnot manifold\nby Raphael Ponge (Sichu an University) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThis talk will deal with the infinitesimal structure of Carnot manifolds. By a Carn ot manifold we mean a manifold together with a subbundle filtration of its tangent bundle which is compatible with the Lie bracket of vector fields. We introduce a notion of differential\, called Carnot differential\, for Carnot manifolds maps (i.e.\, maps that are compatible with the Carnot man ifold structure). This differential is obtained as a group map between th e corresponding tangent groups. We prove that\, at every point\, a Carnot manifold map is osculated in a very precise way by its Carnot differential at the point. We also show that\, in the case of maps between nilpotent g raded groups\, the Carnot differential is given by the Pansu derivative. T herefore\, the Carnot differential is the natural generalization of the Pa nsu derivative to maps between general Carnot manifolds. Another main resu lt is a construction of an analogue for Carnot manifolds of Connes' tangen t groupoid. Given any Carnot manifold $(M\,H)$ we get a smooth groupoid th at encodes the smooth deformation of the pair $M\\times M$ to the tangent group bundle $GM$. This shows that\, at every point\, the tangent group i s the tangent space in a true differential-geometric fashion. Moreover\, t he very fact that we have a groupoid accounts for the group structure of t he tangent group. Incidentally\, this answers a well-known question of Bel laiche. This is joint work with Woocheol Choi.\n LOCATION:https://stable.researchseminars.org/talk/SRS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Yves Colin de Verdière (Institut Fourier) DTSTART:20210604T140000Z DTEND:20210604T150000Z DTSTAMP:20260404T111103Z UID:SRS/14 DESCRIPTION:Title: Geodesics and Laplace spectrum on 3D contact sub-Riemannian manifolds: the Reeb flow\nby Yves Colin de Verdière (Institut Fourier) as part of Sub-Riemannian Seminars\n\n\nAbstract\nJoint work with Luc Hillairet (O rléans) and Emmanuel Trélat (Paris).\nA 3D closed manifold with a conta ct distribution and a metric on it carries a canonical contact form. The associated Reeb flow plays a central role for the asymptotics of the geo desics and for the spectral asymptotics of the Laplace operator. I plan to describe it using some Birkhoff normal forms.\n LOCATION:https://stable.researchseminars.org/talk/SRS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Federica Dragoni (Cardiff University) DTSTART:20210521T140000Z DTEND:20210521T150000Z DTSTAMP:20260404T111103Z UID:SRS/15 DESCRIPTION:Title: Asymptotics for optimal controls for horizontal mean curvature flow\nby Federica Dragoni (Cardiff University) as part of Sub-Riemannian Semi nars\n\n\nAbstract\nThe solutions to surface evolution problems like mean curvature flow can be expressed as value functions of suitable stochastic control problems\, obtained as limit of a family of regularised control pr oblems. The control-theoretical approach is particularly suited for such p roblems for degenerate geometries like the Heisenberg group. In this situa tion a new type of singularities absent for the Euclidean mean curvature f low occurs\, the so-called characteristic points. In this talk I will inve stigate the asymptotic behaviour of the regularised optimal controls in th e vicinity of such characteristic points.\n\nJoin work with Nicolas Dirr a nd Raffaele Grande.\n LOCATION:https://stable.researchseminars.org/talk/SRS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Beschastnyi (Universidade de Aveiro) DTSTART:20210625T140000Z DTEND:20210625T150000Z DTSTAMP:20260404T111103Z UID:SRS/16 DESCRIPTION:Title: Lie groupoids and the minimal domain of the Laplace operator on almost -Riemannian manifolds\nby Ivan Beschastnyi (Universidade de Aveiro) as part of Sub-Riemannian Seminars\n\n\nAbstract\nLie groupoids are objects that are used in various branches of mathematics as desingularisations of singular objects. They come with an array of useful analytic tools\, such as an associated pseudo-differential calculus\, convolution and C*-algebra s. One can use those tools to answer purely analytic questions about compa tible differential operators. In the talk I will explain how one can use t hem to find minimal domains of singular differential operators and\, in pa rticular\, how to find minimal domains of perturbations of the Laplace-Bel trami operator on 2D almost-Riemannian manifolds even in the presence of t he tangency points.\n LOCATION:https://stable.researchseminars.org/talk/SRS/16/ END:VEVENT END:VCALENDAR