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BEGIN:VEVENT
SUMMARY:Robert Young (New York University)
DTSTART;VALUE=DATE-TIME:20201030T150000Z
DTEND;VALUE=DATE-TIME:20201030T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20201120T150000Z
DTEND;VALUE=DATE-TIME:20201120T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20201211T150000Z
DTEND;VALUE=DATE-TIME:20201211T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210108T150000Z
DTEND;VALUE=DATE-TIME:20210108T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210129T150000Z
DTEND;VALUE=DATE-TIME:20210129T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210312T150000Z
DTEND;VALUE=DATE-TIME:20210312T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210219T150000Z
DTEND;VALUE=DATE-TIME:20210219T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210402T140000Z
DTEND;VALUE=DATE-TIME:20210402T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210423T140000Z
DTEND;VALUE=DATE-TIME:20210423T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210604T140000Z
DTEND;VALUE=DATE-TIME:20210604T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210521T140000Z
DTEND;VALUE=DATE-TIME:20210521T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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;VALUE=DATE-TIME:20210625T140000Z
DTEND;VALUE=DATE-TIME:20210625T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T114400Z
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
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