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:20260422T225759Z UID:SRS/1 DESCRIPTION:Title: Metr ic differentiation and embeddings of the Heisenberg group\nby Robert Y oung (New York University) as part of Sub-Riemannian Seminars\n\n\nAbstrac t\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 the Heise nberg group makes it impossible to embed into any $L_p$ space for $p\\in ( 1\,\\infty)$. Recently\, with Assaf Naor\, we proved sharp quantitative b ounds on embeddings of the Heisenberg groups into $L_1$ and constructed 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 surface in $\\mathbb{H}$ which is as bumpy as possible. In this talk\, we will des cribe what are the best ways to embed the Heisenberg group into Banach spa ces\, why good embeddings of the Heisenberg group must be "bumpy" at many scales\, and how to study embeddings into $L_1$ by studying surfaces in $\ \mathbb{H}$\n\nVIRTUAL SESSION\n LOCATION:https://researchseminars.org/talk/SRS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Clotilde Fermanian Kammerer (Université Paris Est) DTSTART:20201120T150000Z DTEND:20201120T160000Z DTSTAMP:20260422T225759Z UID:SRS/2 DESCRIPTION:Title: Semi -classical analysis on H-type groups\nby Clotilde Fermanian Kammerer ( Université Paris Est) as part of Sub-Riemannian Seminars\n\n\nAbstract\nW e present in this talk recent results obtained in collaboration with Véro nique Fischer (University of Bath\, UK) aiming at developing a semi-classi cal approach in sub-Laplacian geometry. In the context of H-type groups\, we describe how to construct a semi-classical pseudodifferential calculus compatible with the Lie group structure and we discuss the associated noti on of semi-classical measures\, together with some of their properties. We will discuss an application to control developed with Cyril Letrouit (ENS Paris).\n\nPhysical session in Paris --> moved to virtual session due to new lockdown in France\n LOCATION:https://researchseminars.org/talk/SRS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Vittone (Padova) DTSTART:20201211T150000Z DTEND:20201211T160000Z DTSTAMP:20260422T225759Z UID:SRS/3 DESCRIPTION:Title: Diff erentiability of intrinsic Lipschitz graphs in Carnot groups\nby David e Vittone (Padova) as part of Sub-Riemannian Seminars\n\n\nAbstract\nSubma nifolds with intrinsic Lipschitz regularity in sub-Riemannian\nCarnot grou ps can be introduced using the theory of intrinsic\nLipschitz graphs start ed by B. Franchi\, R. Serapioni and F. Serra\nCassano almost 15 years ago. One of the main related questions\nconcerns a Rademacher-type theorem (i. e.\, existence of a tangent\nplane) for such graphs: in this talk I will d iscuss a recent positive\nsolution to the problem in Heisenberg groups. Th e proof uses currents\nin Heisenberg groups (in particular\, a version of the celebrated\nConstancy Theorem) and a number of complementary results s uch as\nextension and smooth approximation theorems for intrinsic Lipschit z\ngraphs. I will also show a recent example (joint with A. Julia and S.\n Nicolussi Golo) of an intrinsic Lipschitz graph in a Carnot group that\nis nowhere intrinsically differentiable.\n LOCATION:https://researchseminars.org/talk/SRS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Dario Prandi (CentraleSupelec) DTSTART:20210108T150000Z DTEND:20210108T160000Z DTSTAMP:20260422T225759Z UID:SRS/8 DESCRIPTION:Title: Poin t interactions for 3D sub-Laplacians\nby Dario Prandi (CentraleSupelec ) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThe aim of this semina r is to present some recent results on the essential self-adjointness of p ointed sub-Laplacians in three dimensions. These are the natural (non-nega tive) hypoelliptic operators $H$ associated with a sub-Riemannian structur e on a 3D manifold $M$\, with domain $\\operatorname{Dom}(H)=C^\\infty_c(M \\setminus \\{p\\})$\, for $p\\in M$.\n\nIf $M=\\mathbb{R}^n$ and the geom etry is Euclidean\, $H$ is the standard Laplacian. It is then well-known t hat $H$ is essentially self-adjoint with $\\operatorname{Dom}(H) =C^\\inft y_c(\\mathbb{R}^n\\setminus\\{p\\})$ if and only if $n\\ge 4$. This follow s\, for instance\, by the Euclidean Hardy inequality.\n\nIn this seminar w e show that\, unlike the Euclidean case\, pointed sub-Laplacians (as-socia ted with smooth measures) are essentially self-adjoint already for contact sub-Riemannian manifolds of\n(topological) dimension $3$. Although this i s not surprising\, since the Hausdorff dimension of these structures is $4 $\, we will sow that this result cannot be deduced via Hardy inequalities as in the Euclidean case but requires a much finer machinery. Indeed\, our strategy of proof is based on a localicazion argument which allows to red uce to the study of the 3D Heisenberg pointed sub-Laplacian. The essential self-adjoitness of the latter is then obtained by exploiting non-commutat ive Fourier transform techniques.\n\nThis is a joint work with R. Adami (P olitecnico di Torino\, Italy)\, U. Boscain (CNRS &UPMC\, Sorbonne Univers ité\, France)\, and V. Franceschi (Università di Padova\, Italy).\n LOCATION:https://researchseminars.org/talk/SRS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Sachkov and Andrei Ardentov (Pereslavl) DTSTART:20210129T150000Z DTEND:20210129T160000Z DTSTAMP:20260422T225759Z UID:SRS/9 DESCRIPTION:Title: Sub- Riemannian geometry on the group of motions of the plane\nby Yuri Sach kov and Andrei Ardentov (Pereslavl) as part of Sub-Riemannian Seminars\n\n \nAbstract\nWe will discuss the unique\, up to local isometries\, contact sub-Riemannian structure on the group SE(2) of proper motions of the plane (aka group of rototranslations).\nThe following questions will be address ed:\n- geodesics\,\n- their local and global optimality\,\n- cut time\, cu t locus\, and spheres\,\n- infinite geodesics\,\n- bicycle transform and r elation of geodesics with Euler elasticae\, \n- group of isometries and ho mogeneous geodesics\,\n- applications to imaging and robotics.\n LOCATION:https://researchseminars.org/talk/SRS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuel Milman (Techion) DTSTART:20210312T150000Z DTEND:20210312T160000Z DTSTAMP:20260422T225759Z UID:SRS/10 DESCRIPTION:Title: Fun ctional Inequalities on sub-Riemannian manifolds via QCD\nby Emanuel M ilman (Techion) as part of Sub-Riemannian Seminars\n\n\nAbstract\nWe are i nterested in obtaining Poincarè and log-Sobolev inequalities on domains i n sub-Riemannian manifolds (equipped with their natural sub-Riemannian met ric and volume measure).\n\nIt is well-known that strictly sub-Riemannian 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 Balogh-K ristàly-Sipos\, we show that in the ideal setting or for general corank 1 Carnot groups\, these spaces nevertheless do satisfy a quasi-convex relax ation of the CD condition\, which we name QCD(Q\,K\,N). As a consequence\, these spaces satisfy numerous functional inequalities with exactly the sa me quantitative dependence (up to the slack parameter Q>1) as their CD cou nterparts. We achieve this by extending the localization paradigm to compl etely general interpolation inequalities\, and a one-dimensional compariso n of QCD densities with their "CD upper envelope". We thus obtain the bes t known quantitative estimates for (say) the $L^p$-Poincare and log-Sobole v inequalities on domains in ideal sub-Riemannian manifolds and in general corank 1 Carnot groups\, which in particular are independent of the topol ogical dimension. For instance\, the classical Li-Yau / Zhong-Yang spectra l-gap estimate holds on all Heisenberg groups of arbitrary dimension up to a factor of 4.\n LOCATION:https://researchseminars.org/talk/SRS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Shanbrom (Sacramento State University) DTSTART:20210219T150000Z DTEND:20210219T160000Z DTSTAMP:20260422T225759Z UID:SRS/11 DESCRIPTION:Title: Sel f-similarity in the Kepler-Heisenberg problem\nby Corey Shanbrom (Sacr amento State University) as part of Sub-Riemannian Seminars\n\n\nAbstract\ nThe Kepler-Heisenberg problem is that of determining the motion of a plan et around a sun in the Heisenberg group\, thought of as a three-dimensiona l sub-Riemannian manifold. The sub-Riemannian Hamiltonian provides the kin etic energy\, and the gravitational potential is given by the fundamental solution to the sub-Laplacian. The dynamics are at least partially integra ble\, possessing two first integrals as well as a dilational momentum whic h is conserved by orbits with zero energy. The system is known to admit cl osed orbits of any rational rotation number\, which all lie within the fun damental zero energy integrable subsystem. Here\, we demonstrate that all zero energy orbits are self-similar.\n LOCATION:https://researchseminars.org/talk/SRS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Flynn (University of Bath) DTSTART:20210402T140000Z DTEND:20210402T150000Z DTSTAMP:20260422T225759Z UID:SRS/12 DESCRIPTION:Title: Unr aveling X-ray Transforms on the Heisenberg group\nby Steven Flynn (Uni versity of Bath) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThe cla ssical X-ray Transform maps a function on Euclidean space to a function o n the space of lines on this Euclidean space by integrating the function o ver the given line. Inverting the X-ray transform has wide-ranging applica tions\, including to medical imaging and seismology. Much work has been do ne to understand this inverse problem in Euclidean space\, Euclidean domai ns\, and more generally\, for symmetric spaces and Riemannian manifolds wi th boundary where the lines become geodesics. We formulate a sub-Riemannia n version of the X-ray transform on the simplest sub-Riemannnian manifold\ , the Heisenberg group. Here serious geometric obstructions to classical i nverse problems\, such as existence of conjugate points\, appear generical ly. With tools adapted to the geometry\, such as an operator-valued Fourie r Slice Theorem\, we prove nonetheless that an integrable function on the Heisenberg group is indeed determined by its line integrals over sub-Riema nnian (as well as over its compatible Riemannian and Lorentzian) geodesics .\n\nWe also pose an abundance of accessible follow-up questions\, standar d in the inverse problems community\, concerning the sub-Riemannian case\, and report progress answering some of them.\n LOCATION:https://researchseminars.org/talk/SRS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphael Ponge (Sichuan University) DTSTART:20210423T140000Z DTEND:20210423T150000Z DTSTAMP:20260422T225759Z UID:SRS/13 DESCRIPTION:Title: The tangent groupoid of a Carnot manifold\nby Raphael Ponge (Sichuan Univ ersity) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThis talk will d eal with the infinitesimal structure of Carnot manifolds. By a Carnot mani fold we mean a manifold together with a subbundle filtration of its tangen t bundle which is compatible with the Lie bracket of vector fields. We int roduce a notion of differential\, called Carnot differential\, for Carnot manifolds maps (i.e.\, maps that are compatible with the Carnot manifold s tructure). This differential is obtained as a group map between the corre sponding tangent groups. We prove that\, at every point\, a Carnot manifol d 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 graded g roups\, the Carnot differential is given by the Pansu derivative. Therefor e\, the Carnot differential is the natural generalization of the Pansu der ivative to maps between general Carnot manifolds. Another main result is a construction of an analogue for Carnot manifolds of Connes' tangent group oid. Given any Carnot manifold $(M\,H)$ we get a smooth groupoid that enco des the smooth deformation of the pair $M\\times M$ to the tangent group b undle $GM$. This shows that\, at every point\, the tangent group is the t angent space in a true differential-geometric fashion. Moreover\, the very fact that we have a groupoid accounts for the group structure of the tang ent group. Incidentally\, this answers a well-known question of Bellaiche. This is joint work with Woocheol Choi.\n LOCATION:https://researchseminars.org/talk/SRS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Yves Colin de Verdière (Institut Fourier) DTSTART:20210604T140000Z DTEND:20210604T150000Z DTSTAMP:20260422T225759Z UID:SRS/14 DESCRIPTION:Title: Geo desics and Laplace spectrum on 3D contact sub-Riemannian manifolds: the Re eb flow\nby Yves Colin de Verdière (Institut Fourier) as part of Sub- Riemannian Seminars\n\n\nAbstract\nJoint work with Luc Hillairet (Orléans ) and Emmanuel Trélat (Paris).\nA 3D closed manifold with a contact dist ribution and a metric on it carries a canonical contact form. The associ ated Reeb flow plays a central role for the asymptotics of the geodesics and for the spectral asymptotics of the Laplace operator. I plan to descri be it using some Birkhoff normal forms.\n LOCATION:https://researchseminars.org/talk/SRS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Federica Dragoni (Cardiff University) DTSTART:20210521T140000Z DTEND:20210521T150000Z DTSTAMP:20260422T225759Z UID:SRS/15 DESCRIPTION:Title: Asy mptotics for optimal controls for horizontal mean curvature flow\nby F ederica Dragoni (Cardiff University) as part of Sub-Riemannian Seminars\n\ n\nAbstract\nThe solutions to surface evolution problems like mean curvatu re flow can be expressed as value functions of suitable stochastic control problems\, obtained as limit of a family of regularised control problems. The control-theoretical approach is particularly suited for such problems for degenerate geometries like the Heisenberg group. In this situation a new type of singularities absent for the Euclidean mean curvature flow occ urs\, the so-called characteristic points. In this talk I will investigate the asymptotic behaviour of the regularised optimal controls in the vicin ity of such characteristic points.\n\nJoin work with Nicolas Dirr and Raff aele Grande.\n LOCATION:https://researchseminars.org/talk/SRS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Beschastnyi (Universidade de Aveiro) DTSTART:20210625T140000Z DTEND:20210625T150000Z DTSTAMP:20260422T225759Z UID:SRS/16 DESCRIPTION:Title: Lie groupoids and the minimal domain of the Laplace operator on almost-Rieman nian manifolds\nby Ivan Beschastnyi (Universidade de Aveiro) as part o f Sub-Riemannian Seminars\n\n\nAbstract\nLie groupoids are objects that ar e used in various branches of mathematics as desingularisations of singula r objects. They come with an array of useful analytic tools\, such as an a ssociated pseudo-differential calculus\, convolution and C*-algebras. One can use those tools to answer purely analytic questions about compatible d ifferential operators. In the talk I will explain how one can use them to find minimal domains of singular differential operators and\, in particula r\, how to find minimal domains of perturbations of the Laplace-Beltrami o perator on 2D almost-Riemannian manifolds even in the presence of the tang ency points.\n LOCATION:https://researchseminars.org/talk/SRS/16/ END:VEVENT END:VCALENDAR