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SUMMARY:Enrico Le Donne (University of Pisa & University of Jyväskylä)
DTSTART;VALUE=DATE-TIME:20200417T150000Z
DTEND;VALUE=DATE-TIME:20200417T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T013219Z
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/
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BEGIN:VEVENT
SUMMARY:Richard Montgomery (UC Santa Cruz)
DTSTART;VALUE=DATE-TIME:20200430T150000Z
DTEND;VALUE=DATE-TIME:20200430T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T013219Z
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;VALUE=DATE-TIME:20200515T150000Z
DTEND;VALUE=DATE-TIME:20200515T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T013219Z
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;VALUE=DATE-TIME:20200529T150000Z
DTEND;VALUE=DATE-TIME:20200529T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T013219Z
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;VALUE=DATE-TIME:20200612T150000Z
DTEND;VALUE=DATE-TIME:20200612T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T013219Z
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;VALUE=DATE-TIME:20200626T150000Z
DTEND;VALUE=DATE-TIME:20200626T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T013219Z
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/
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