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BEGIN:VEVENT
SUMMARY:Enrico Le Donne (University of Pisa & University of Jyväskylä)
DTSTART:20200417T150000Z
DTEND:20200417T160000Z
DTSTAMP:20260404T095546Z
UID:ISRS/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ISRS/
 1/">Mathematical appearances of sub-Riemannian geometries</a>\nby Enrico L
 e Donne (University of Pisa & University of Jyväskylä) as part of Intern
 ational sub-Riemannian seminar\n\n\nAbstract\nSub-Riemannian geometries ar
 e a generalization of Riemannian\ngeometries. Roughly speaking\, in order 
 to measure distances in a\nsub-Riemannian manifold\, one is allowed to onl
 y measure distances\nalong curves that are tangent to some subspace of the
  tangent space.\n\nThese geometries arise in many areas of pure  and appli
 ed  mathematics\n(such as algebra\, geometry\, analysis\, mechanics\, cont
 rol theory\,\nmathematical\nphysics\, theoretical computer science)\, as w
 ell as in applications\n(e.g.\, robotics\, vision).\n This talk introduces
  sub-Riemannian geometry from the metric\nviewpoint and focus on a few cla
 ssical situations in pure mathematics\nwhere sub-Riemannian geometries app
 ear. For example\, we shall discuss\nboundaries of rank-one symmetric spac
 es and asymptotic cones of\nnilpotent groups.\nThe goal is to present seve
 ral metric characterizations of\nsub-Riemannian geometries so to give an e
 xplanation of their natural\nmanifestation.\n We first give a characteriza
 tion of Carnot groups\, which are very\nspecial sub-Riemannian geometries.
 \n We extend the result to self-similar metric Lie groups (in\ncollaborati
 on with Cowling\, Kivioja\, Nicolussi Golo\, and Ottazzi).\n We then prese
 nt some recent results characterizing boundaries of\nrank-one symmetric sp
 aces (in collaboration with Freeman).\n
LOCATION:https://stable.researchseminars.org/talk/ISRS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Montgomery (UC Santa Cruz)
DTSTART:20200430T150000Z
DTEND:20200430T160000Z
DTSTAMP:20260404T095546Z
UID:ISRS/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ISRS/
 2/">Magnetic playground fields for understanding subRiemannian geodesics</
 a>\nby Richard Montgomery (UC Santa Cruz) as part of International sub-Rie
 mannian seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ISRS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Karmanova
DTSTART:20200515T150000Z
DTEND:20200515T160000Z
DTSTAMP:20260404T095546Z
UID:ISRS/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ISRS/
 3/">A new look at Carnot-Caratheodory spaces theory and related topics</a>
 \nby Maria Karmanova as part of International sub-Riemannian seminar\n\nAb
 stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ISRS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Ritoré (Universidad de Granada)
DTSTART:20200529T150000Z
DTEND:20200529T160000Z
DTSTAMP:20260404T095546Z
UID:ISRS/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ISRS/
 4/">Wulff shapes in the Heisenberg group</a>\nby Manuel Ritoré (Universid
 ad de Granada) as part of International sub-Riemannian seminar\n\n\nAbstra
 ct\nGiven a not necessarily symmetric left-invariant norm $||\\cdot ||_K$ 
 in\nthe first Heisenberg group $\\mathbb{H}^1$ induced by a convex body\n$
 K\\subset\\mathbb{R}^2$ containing the origin in its interior\, we\nconsid
 er the associated perimeter functional\, that coincides with the\nclassica
 l sub-Riemannian perimeter in case $K$ is the closed unit disk\ncentered a
 t the origin of $\\rr^2$. Under the assumption that $K$ has\nstrictly conv
 ex smooth boundary we compute the first variation formula\nof perimeter fo
 r sets with $C^2$ boundary. The localization of the\nvariational formula i
 n the non-singular part of the boundary\, composed\nof the points where th
 e tangent plane is not horizontal\, allows us to\ndefine a mean curvature 
 function $H_K$ out of the singular set. In the\ncase of non-vanishing mean
  curvature\, the condition that $H_K$ be\nconstant implies that the non-si
 ngular portion of the boundary is\nfoliated by horizontal liftings of tran
 slations of $\\ptl K$ dilated by a\nfactor of $1/H_K$. Based on this we ca
 n defined a sphere $\\mathbb{B}_K$\nwith constant mean curvature $1$ by co
 nsidering the union of all\nhorizontal liftings of $\\partial K$ starting 
 from $(0\,0\,0)$ until they\nmeet again. We give some geometric properties
  of this sphere and\,\nmoreover\, we prove that\, up to non-homogenoeus di
 lations and\nleft-translations\, they are the only solutions of the sub-Fi
 nsler\nisoperimetric problem in a restricted class of sets. This is joint 
 work\nwith Julián Pozuelo.\n
LOCATION:https://stable.researchseminars.org/talk/ISRS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Orponen
DTSTART:20200612T150000Z
DTEND:20200612T160000Z
DTSTAMP:20260404T095546Z
UID:ISRS/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ISRS/
 5/">Sub-elliptic boundary value problems in flag domains</a>\nby Tuomas Or
 ponen as part of International sub-Riemannian seminar\n\n\nAbstract\nI wil
 l talk about solving the sub-Laplacian Dirichlet and Neumann problems with
  $L^2$ boundary data in “flag domains” of the first Heisenberg group. 
 These are domains bounded by a vertically ruled Lipschitz graph. The solut
 ions are obtained via the method of layer potentials. This is joint work w
 ith Michele Villa.\n
LOCATION:https://stable.researchseminars.org/talk/ISRS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Rizzi
DTSTART:20200626T150000Z
DTEND:20200626T160000Z
DTSTAMP:20260404T095546Z
UID:ISRS/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/ISRS/
 6/">Heat content asymptotics for sub-Riemannian manifolds</a>\nby Luca Riz
 zi as part of International sub-Riemannian seminar\n\n\nAbstract\nWe study
  the small-time asymptotics of the heat content of smooth non-characterist
 ic domains of a general rank-varying sub-Riemannian structure\, equipped w
 ith an arbitrary smooth measure. By adapting to the sub-Riemannian case a 
 technique due to Savo\, we establish the existence of the full asymptotic 
 series for small times\, at arbitrary order. We compute explicitly the coe
 fficients up to order k = 5\, in terms of sub-Riemannian invariants of the
  domain. Furthermore\, as an independent result\, we prove that every coef
 ficient can be obtained as the limit of the corresponding one for a suitab
 le Riemannian extension. As a particular case we recover\, using non-proba
 bilistic techniques\, the order 2 formula recently obtained by Tyson and W
 ang in the Heisenberg group [Comm. PDE\, 2018]. A consequence of our fifth
 -order analysis is the evidence for new phenomena in presence of character
 istic points. 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://stable.researchseminars.org/talk/ISRS/6/
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