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BEGIN:VEVENT
SUMMARY:François Gay-Balmaz (CNRS-LMD\, ENS)
DTSTART;VALUE=DATE-TIME:20200616T144500Z
DTEND;VALUE=DATE-TIME:20200616T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/1
DESCRIPTION:Title: Geometric variational finite element discretization of compressible flu
ids\nby François Gay-Balmaz (CNRS-LMD\, ENS) as part of Geometry\, Dy
namics and Mechanics Seminar\n\n\nAbstract\nWe review recent progress made
in the development of structure preserving finite element integrators for
compressible fluids. This approach combines the geometric formulation of
fluid dynamics on groups of diffeomorphisms with finite element discretiza
tion techniques. A specific feature of the discrete geometric formulation
is the occurrence of a nonholonomic right-invariant distribution on the di
screte group of diffeomorphisms\, that is shown to be isomorphic to a Ravi
art-Thomas finite element space. The resulting finite element discretizati
ons correspond to weak forms of the compressible fluid equations that don'
t seem to have been used in the finite element literature. It extends prev
ious work done on incompressible flows and at the lowest order on compress
ible fluids. We illustrate the benefits of this geometric approach and pre
sent potential future directions. This is a joint work with E. Gawlik.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Khesin (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200519T144500Z
DTEND;VALUE=DATE-TIME:20200519T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/2
DESCRIPTION:Title: Pentagram maps and integrable hierarchies\nby Boris Khesin (Univers
ity of Toronto) as part of Geometry\, Dynamics and Mechanics Seminar\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Montgomery (UCSC)
DTSTART;VALUE=DATE-TIME:20200602T144500Z
DTEND;VALUE=DATE-TIME:20200602T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/3
DESCRIPTION:Title: Scattering and Metric Lines\nby Richard Montgomery (UCSC) as part o
f Geometry\, Dynamics and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Haller (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20200630T144500Z
DTEND;VALUE=DATE-TIME:20200630T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/4
DESCRIPTION:Title: Objective material barriers to the transport of momentum and vorticity<
/a>\nby George Haller (ETH Zurich) as part of Geometry\, Dynamics and Mech
anics Seminar\n\n\nAbstract\nI discuss a recent theory for material surfac
es that maximally inhibit the diffusive transport of a dynamically active
(i.e.\, velocity-dependent) vector field\, such as the linear momentum\, t
he angular momentum or the vorticity\, in three-dimensional unsteady flows
. These diffusion barriers provide physics-based\, observer-independent bo
undaries of dynamically active coherent structures. Instantaneous limits o
f these Lagrangian diffusion barriers mark objective Eulerian barriers to
short-term active transport. I show how active diffusion barriers can be
identified with active versions of Lagrangian coherent structure (LCS) dia
gnostics. In comparison to their passive counterparts\, however\, active L
CS diagnostics require no significant fluid particle separation and hence
provide substantially higher-resolved Lagrangian and Eulerian coherent str
ucture boundaries from shorter velocity data sets. I illustrate these resu
lts on two-dimensional turbulence and three-dimensional wall-bounded turbu
lence.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darryl Holm (Imperial College\, London)
DTSTART;VALUE=DATE-TIME:20200714T144500Z
DTEND;VALUE=DATE-TIME:20200714T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/5
DESCRIPTION:Title: What can Geometric Mechanics do for Climate Science?\nby Darryl Hol
m (Imperial College\, London) as part of Geometry\, Dynamics and Mechanics
Seminar\n\n\nAbstract\nThe prediction of climate change and its impact on
extreme \nweather events is one of the great societal and intellectual \n
challenges of our time. The first part of the problem is to make the \ndis
tinction between weather and climate. The second part is to \nunderstand t
he dynamics of the fluctuations of the physical variables. \nThe third par
t is to predict how the variances of the fluctuations are \naffected by st
atistical correlations in their fluctuating dynamics. \nThis GDM Seminar i
nvestigates a stochastic geometric mechanics \nframework called LA SALT wh
ich can at least formally meet all three \nparts of the challenge for the
problem of climate change\, given a \ndeterministic fluid theory derived f
rom the variational principles of \ngeometric mechanics.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yvette Kosmann-Schwarzbach (Ecole Polytechnique)
DTSTART;VALUE=DATE-TIME:20200728T144500Z
DTEND;VALUE=DATE-TIME:20200728T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/6
DESCRIPTION:Title: The Noether theorems a century later\nby Yvette Kosmann-Schwarzbach
(Ecole Polytechnique) as part of Geometry\, Dynamics and Mechanics Semina
r\n\n\nAbstract\nFor this mostly historical talk\, I wish to present the c
ontents of the now famous article of Emmy Noether\, "Invariante Variations
probleme"\, published in the Gőttingen Nachrichten in 1918\, an article t
hat is often cited but rarely cited faithfully. As background\, I shall sk
etch the work of her predecessors and I shall stress the motivation for he
r only contribution to mathematical physics\, namely the question of wheth
er energy was conserved in the general theory of relativity which had been
discussed by Einstein and Hilbert since 1915. How original\, how modern\,
how influential were her results? I shall comment on the curious transmis
sion and later recognition of the wide applicability of the Noether theore
ms.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Tomei (PUC-Rio)
DTSTART;VALUE=DATE-TIME:20200825T144500Z
DTEND;VALUE=DATE-TIME:20200825T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/7
DESCRIPTION:Title: Basic Todaism\nby Carlos Tomei (PUC-Rio) as part of Geometry\, Dyna
mics and Mechanics Seminar\n\n\nAbstract\nThe Toda flows are at the crossr
oads of a surprising amount \nof pure and applied mathematics. This talk s
tarts from zero and \npresents a very incomplete view of the subject\, cho
osing some high \npoints of more than fifty years of very active research.
\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Treschev (Steklov Mathematical Institute of Russian Academy
of Sciences)
DTSTART;VALUE=DATE-TIME:20200908T144500Z
DTEND;VALUE=DATE-TIME:20200908T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/8
DESCRIPTION:Title: Billiard systems with locally linear dynamics\nby Dmitry Treschev (
Steklov Mathematical Institute of Russian Academy of Sciences) as part of
Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nCan a billiard ma
p be locally conjugated to a rigid rotation?\nWe prove that the answer to
this question is positive in the\ncategory of formal series that determine
the boundary.\nWe also present numerical evidence\nthat for ``good'' rota
tion angles the answer is also positive\nin analytic category.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annalisa Calini (Charleston University)
DTSTART;VALUE=DATE-TIME:20200922T144500Z
DTEND;VALUE=DATE-TIME:20200922T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/9
DESCRIPTION:Title: Geometric flows in centro-affine space\nby Annalisa Calini (Charles
ton University) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\n
Abstract\nMany classical objects in differential geometry are described by
integrable systems: nonlinear PDE with infinitely many conserved quantit
ies that are (in some sense) solvable. Beginning in the 1980s\, studies of
curve evolutions that are invariant under the action of a geometric group
of transformations have unveiled more connections between geometric curve
flows and well-known integrable PDE (among them are the KdV\, mKdV\, sin
e-Gordon\, and NLS equations). More recently\, efforts have been directed
towards understanding geometric discretizations of surfaces and curves an
d associated evolutions.\nThis talk will describe some natural geometric
flows for curves and polygons in centro-affine geometry\, and their relat
ions with the KdV and Boussinesq equations and discretizations of Adler-Ge
l’fand-Dikii (AGD) flows for curves in projective space. The AGD discre
tizations (previously introduced in work by Marí-Beffa and Wang) will be
discussed in more detail\, as their lifts to the moduli space of centro-a
ffine arc length parametrized polygons promptly reveal their bihamiltonian
structures in terms of a pair of simple pre-symplectic forms.\n\nSome ref
erences:\n\nU. Pinkall\, Hamiltonian flows on the space of star-shaped cur
ves\, Result. Math. 27 (1995)\, 328–332.\n\nA. Calini\, T. Ivey\, and G.
Marí-Beffa\, Remarks on KdV-type Flows on Star-Shaped Curves\, Physica D
Vol. 238\, no. 8 (2009)\, 788–797\n\nG. Marí-Beffa and J.P. Wang\, Ham
iltonian structures and integrable evolutions of twisted gons in RPn\, Non
linearity 26 (2013) 2515-2551\n\nA. Calini\, T. Ivey\, and G. Marí-Beffa\
, An integrable flow for starlike curves in centroaffine space\, SIGMA 9
\, (2013)\, 022\, 21 pp.\n\nA. Calini and G. Marí-Beffa\, Integrable evol
utions of twisted polygons in centroaffine Rm\, IMRN\, rnaa161 (2020)\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (UPC Barcelona)
DTSTART;VALUE=DATE-TIME:20201020T144500Z
DTEND;VALUE=DATE-TIME:20201020T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/10
DESCRIPTION:by Eva Miranda (UPC Barcelona) as part of Geometry\, Dynamics
and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (ICMAT-CSIC)
DTSTART;VALUE=DATE-TIME:20201006T144500Z
DTEND;VALUE=DATE-TIME:20201006T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/11
DESCRIPTION:Title: Flexibility and rigidity aspects of the dynamics of the steady Euler f
lows\nby Daniel Peralta-Salas (ICMAT-CSIC) as part of Geometry\, Dynam
ics and Mechanics Seminar\n\n\nAbstract\nAn inviscid and incompressible fl
uid in equilibrium on a Riemannian manifold is described by (an autonomous
) vector field X that satisfies the\nstationary Euler equations. In this t
alk I will focus on the dynamics of steady Euler flows on compact manifold
s\, emphasizing the geometric aspects. The topics I\nwill cover include a
characterization of the volume-preserving vector fields that are Eulerizab
le and some rigidity results for steady Euler flows on the round sphere.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Veselov (Loughborough\, UK and Moscow\, Russia)
DTSTART;VALUE=DATE-TIME:20201103T154500Z
DTEND;VALUE=DATE-TIME:20201103T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/12
DESCRIPTION:Title: Geometrization\, integrability and knots\nby Alexander Veselov (Lo
ughborough\, UK and Moscow\, Russia) as part of Geometry\, Dynamics and Me
chanics Seminar\n\n\nAbstract\nAfter Arnold the classical integrability is
usually understood\nin the Liouville sense as the existence of sufficient
ly many Poisson\ncommuting integrals. About 20 years ago it was discovered
that this does\nnot exclude the chaotic behaviour of the system\, which m
ay even have\npositive topological entropy.\nI will review the current sit
uation with Liouville integrability in\nrelation with Thurston’s geometr
ization programme\, using as the main\nexample the geodesic flows on the 3
-folds with SL(2\,R)-geometry. A\nparticular case of such manifold SL(2\,R
)/SL(2\,Z) is known (after Milnor\nand Quillen) to be topologically equiva
lent to the complement of the\ntrefoil knot in 3-sphere. I will explain th
at the remarkable results of\nGhys about modular and Lorenz knots can be n
aturally extended to the\nintegrable region\, where these knots are replac
ed by the cable knots of\ntrefoil.\nThe talk is partly based on a joint wo
rk with Alexey Bolsinov and Yiru\nYe and will not require any specific kno
wledge.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:San Vu Ngoc (Rennes - France)
DTSTART;VALUE=DATE-TIME:20201117T154500Z
DTEND;VALUE=DATE-TIME:20201117T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/13
DESCRIPTION:Title: One can hear semi-toric systems\nby San Vu Ngoc (Rennes - France)
as part of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nI will
report on an ongoing work with Yohann Le Floch about inverse\nspectral th
eory for quantum integrable systems.\nThe question\, adapted from the famo
us "Can one hear the shape of a\ndrum?"\, is to fully reconstruct a semi-t
oric system from the joint\nspectrum of its quantum counterpart.\nSemi-tor
ic systems form a large class of 2D integrable systems that has\nbeen exte
nsively studied in the last 15 years.\nThe inverse spectral problem for th
ese systems was proposed as a\nconjecture about 10 years ago.\nWe show tha
t the conjecture is true\, by analyzing the quantum versions\nof all "symp
lectic invariants" of semi-toric systems.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Carlos Marrero (ULL)
DTSTART;VALUE=DATE-TIME:20201201T154500Z
DTEND;VALUE=DATE-TIME:20201201T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/14
DESCRIPTION:by Juan Carlos Marrero (ULL) as part of Geometry\, Dynamics an
d Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donald Saari (UC Irvine)
DTSTART;VALUE=DATE-TIME:20201215T154500Z
DTEND;VALUE=DATE-TIME:20201215T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/15
DESCRIPTION:Title: From dynamics and celestial mechanics to dark matter\nby Donald Sa
ari (UC Irvine) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\n
Abstract\nAlmost everyone has heard of dark matter\, but what is it?\nWher
e did it come from? In this expository talk\, which outlines some\nbasic i
deas of celestial mechanics\, not only is the dark matter issue\nintroduce
d\, but it is shown how elementary dynamics raises doubts about\nits exist
ence.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Cabrera (UFRJ - Brazil)
DTSTART;VALUE=DATE-TIME:20210202T154500Z
DTEND;VALUE=DATE-TIME:20210202T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/16
DESCRIPTION:Title: Dirac structures for infinite dimensional geometries and applications<
/a>\nby Alejandro Cabrera (UFRJ - Brazil) as part of Geometry\, Dynamics a
nd Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Salomão (USP - Brazil)
DTSTART;VALUE=DATE-TIME:20210216T154500Z
DTEND;VALUE=DATE-TIME:20210216T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/17
DESCRIPTION:Title: Transverse foliations in the Euler problem of two fixed centers\nb
y Pedro Salomão (USP - Brazil) as part of Geometry\, Dynamics and Mechani
cs Seminar\n\n\nAbstract\nThe Euler problem of two fixed centers describes
a particle's motion in the plane attracted by two fixed Newtonian centers
. Being Liouville integrable\, this mechanical system is a starting point
to the more involving circular planar restricted three-body problem. In th
is talk\, I will explain the use of pseudo-holomorphic curves to obtain gl
obal surfaces of sections\, and transverse foliations in the Euler problem
of two fixed centers\, for energies above the critical value. I will also
discuss generalizations of these constructions to other models in Celesti
al Mechanics. This work is joint with N. de Paulo\, U. Hryniewicz\, and S.
Kim.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tere M-Seara (UPC Barcelona)
DTSTART;VALUE=DATE-TIME:20210302T154500Z
DTEND;VALUE=DATE-TIME:20210302T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/18
DESCRIPTION:Title: Non existence of small amplitude breathers for Klein-Gordon equations
\nby Tere M-Seara (UPC Barcelona) as part of Geometry\, Dynamics and M
echanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Calleja (UNAM\, Mexico City)
DTSTART;VALUE=DATE-TIME:20210316T154500Z
DTEND;VALUE=DATE-TIME:20210316T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/19
DESCRIPTION:Title: Choreographies in the n-body problem and a conjecture of Marchal\n
by Renato Calleja (UNAM\, Mexico City) as part of Geometry\, Dynamics and
Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Rechtman (Strasburg)
DTSTART;VALUE=DATE-TIME:20210413T144500Z
DTEND;VALUE=DATE-TIME:20210413T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/20
DESCRIPTION:Title: Broken books and Reeb dynamics in dimension 3\nby Ana Rechtman (St
rasburg) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstrac
t\nGiven a contact structure on a closed 3-manifold\, Giroux’s correspon
dance gives an adapted open book decomposition. This implies that there ex
ists a Reeb vector that is tangent to the binding and transverse to the in
terior of the pages. For this vector field\, each page is a Birkhoff secti
on and the dynamics of the flow can be studied from the first return map.
This correspondance is unsatisfactory when one wants to study all the Reeb
vector fields associated to a contact structure.\n\nIn collaboration with
V. Colin and P. Dehornoy\, we proved that every non-degenerate Reeb vecto
r field on a closed 3-manifold is adapted to a broken book decomposition (
a generalisation of open book). This construction gives a system of transv
erse surfaces with boundary and allows to establish results on the dynamic
s of the vector field. We proved\, for example\, that any non-degenerate R
eeb vector field has either two or infinitely many periodic orbits.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bolsinov (Loughborough\, UK)
DTSTART;VALUE=DATE-TIME:20210330T144500Z
DTEND;VALUE=DATE-TIME:20210330T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/21
DESCRIPTION:Title: Nijenhuis Geometry\nby Alexey Bolsinov (Loughborough\, UK) as part
of Geometry\, Dynamics and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Bloch (University of Michigan)
DTSTART;VALUE=DATE-TIME:20210427T144500Z
DTEND;VALUE=DATE-TIME:20210427T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/22
DESCRIPTION:Title: Dynamics of Circulant Systems\nby Anthony Bloch (University of Mic
higan) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\
nIn this talk we analyze the dynamics and geometry of a class of so-called
\ncirculant systems of ODE's. Such equations are invariant under the actio
n\nof a cyclic group and are inspired by equations\nstudied in the synthet
ic biology literature. Examples include\nthe repressilator and the Sprott
system. We analyze\ninvariant sets\, global bifurcation behavior\,\nlong
time asymptotics and the existence of periodic orbits. We develop the\nthe
ory and present simulations. \n\nThis is joint work with Matthew Kvalheim.
\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain Chenciner (Observatoire de Paris)
DTSTART;VALUE=DATE-TIME:20210511T144500Z
DTEND;VALUE=DATE-TIME:20210511T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/23
DESCRIPTION:Title: ABC\nby Alain Chenciner (Observatoire de Paris) as part of Geometr
y\, Dynamics and Mechanics Seminar\n\n\nAbstract\nA as forces\, B as shape
\, C as angular momentum. In this ABC I’ll consider n-body relative equi
libria in dimensions greater than 3. The family of n-body configurations w
hich\, when submitted to Newtonian or similar attraction\, admit a relativ
e equilibrium motion (the “balanced” configurations) then becomes much
richer. Also\, a given balanced configuration admits a variety of relativ
e equilibria\, namely one for each choice of a hermitian structure on the
space where the motion really takes place\; in general\, if the configurat
ion is not central\, such relative equilibria are quasi-periodic.\n\nI sha
ll discuss several problems\, like the one of deciding what is the smalles
t dimension in which a given configuration admits a relative equilibrium m
otion\, or when bifurcations from the periodic relative equilibrium of a c
entral configuration may bifurcate into a family of quasi-periodic relativ
e equilibria of balanced configurations.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klas Modin (Chalmers University of Technology\, Sweden)
DTSTART;VALUE=DATE-TIME:20210525T144500Z
DTEND;VALUE=DATE-TIME:20210525T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/24
DESCRIPTION:Title: What makes nonholonomic integrators work?\nby Klas Modin (Chalmers
University of Technology\, Sweden) as part of Geometry\, Dynamics and Mec
hanics Seminar\n\n\nAbstract\nA "nonholonomic integrator" is a numerical m
ethod specifically designed for nonholonomic systems. But what does that m
ean? In this talk I show that KAM theory can be used to rigorously explain
the observed superior behaviour of such methods (in terms of near conserv
ation of integrals for integrable systems). I also give examples of integr
able nonholonomic systems for which nonholonomic integrators fail to nearl
y conserve the integrals.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Montaldi (University of Manchester)
DTSTART;VALUE=DATE-TIME:20210622T144500Z
DTEND;VALUE=DATE-TIME:20210622T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/25
DESCRIPTION:Title: Point vortices on non-orientable surfaces\nby James Montaldi (Univ
ersity of Manchester) as part of Geometry\, Dynamics and Mechanics Seminar
\n\n\nAbstract\nThe standard Hamiltonian approach to the dynamics of point
vortices on a surface involves the symplectic form on the surface togethe
r with the vorticity of the point vortices. However\, both these ingredie
nts involve a choice of orientation of the surface\, which is of course no
t available for non-orientable surfaces. In this talk I will discuss how o
ne can set up a Hamiltonian approach in the non-orientable setting\, with
particular reference to the Möbius band. This is joint work with Nataliy
a Balabanova.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Bela Cruzeiro (IST\, Lisboa)
DTSTART;VALUE=DATE-TIME:20210720T144500Z
DTEND;VALUE=DATE-TIME:20210720T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/26
DESCRIPTION:Title: A stochastic view on the deterministic Navier-Stokes equation\nby
Ana Bela Cruzeiro (IST\, Lisboa) as part of Geometry\, Dynamics and Mechan
ics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jair Koiller (Universidade Federal de Juiz de Fora\, Brazil)
DTSTART;VALUE=DATE-TIME:20210608T144500Z
DTEND;VALUE=DATE-TIME:20210608T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/27
DESCRIPTION:Title: Vortex pairs on surfaces: can it be a tool for topology in the large?<
/a>\nby Jair Koiller (Universidade Federal de Juiz de Fora\, Brazil) as pa
rt of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nIn 1999 Yo
shifumi Kimura mentioned in his paper 'Vortex motion on surfaces with con
stant curvature'(//doi.org/10.1098/rspa.1999.0311) that a vortex dipole
(two infinitesimally close opposite vortices) on a curved surface should
move along a geodesic: "curvature checker"\, as he interestingly defined
. \n\n \n A proof outline was given in 2008 by Stefanella Boatto and JK
(arXiv:0802.4313\, //link.springer.com/book/10.1007/978-1-4939-2441-7).
In this talk I present some results of ongoing work with Umberto Hryniewic
z\, Alejandro Cabrera and Anilatmaja Aryasomayajula. Regarding vortex pai
rs at a small finite distance\, we show that close-by pairs can actually
be called "topology checkers". \n \nIn fact we suggest the idea that\,
very much like geodesics (perhaps only more so)\, the study of vortex pa
ir dynamics could be a good way to probe the topology in the large. This i
s because the Hamiltonian for vortex dynamics on surfaces involves the Lap
lace Beltrami operator Green's function and its regularizations (Robin's
function and its partner\, Batman). \n \nTime permitting I will briefly
review joint work with Adriano R. Rodrigues and Cesar Castilho (//doi.org
/10.1063/1.3146241\, doi: 10.3934/jgm.2018007\, http://mi.mathnet.ru/eng/r
cd389) on far-away vortices on a surface with antipodal symmetry. I will
also advertise work by Clodoaldo Ragazzo and Humberto Viglioni (//doi.org
/10.1098/rspa.2017.0447\, //link.springer.com/article/10.1007/s00332-017-9
380-7) on a the motion of a single vortex. \nDuring the talk we will make
some queries for the audience\, and research suggestions will be present
ed in the end.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcel Guardia (UPC\, Barcelona)
DTSTART;VALUE=DATE-TIME:20210706T144500Z
DTEND;VALUE=DATE-TIME:20210706T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/28
DESCRIPTION:Title: Oscillatory motions and symbolic dynamics in the three body problem\nby Marcel Guardia (UPC\, Barcelona) as part of Geometry\, Dynamics and
Mechanics Seminar\n\n\nAbstract\nConsider the three body problem with posi
tive masses $m_0$\, $m_1$ and $m_2$. In 1922 Chazy classified the possible
final motions the three bodies may possess\, that is the behaviors the bo
dies may have when time tends to infinity. One of them are what is known a
s oscillatory motions\, that is\, solutions of the three body problem such
that the liminf (as time tends to infinity) of the relative positions bet
ween bodies is finite whereas the limsup is infinite. That is\, solutions
for which the bodies keep oscillating between an increasingly large separa
tion and getting closer together. The first result of existence of oscilla
tory motions was provided by Sitnikov for a Restricted Three Body Problem\
, called nowadays Sitnkikov model. His result has been extended to several
Celestial Mechanics models but always with rather strong assumptions on t
he values of the masses.\nIn this talk I will explain how to construct osc
illatory motions for the three body problems for any values $m_0$\, $m_1$
and $m_2$ (except for the case of three equal masses). The proof relies on
the construction of a hyperbolic invariant sets whose dynamics is conjuga
ted to that of the shift of infinite symbols (i.e. symbolic dynamics). Tha
t is\, we construct invariant sets for the three body problem with chaotic
dynamics and positive topological entropy\, which moreover contain oscill
atory motions.\nThis is a joint work with Pau Martin and Tere M. Seara.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Martin de Diego (ICMAT)
DTSTART;VALUE=DATE-TIME:20210831T144500Z
DTEND;VALUE=DATE-TIME:20210831T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/29
DESCRIPTION:Title: Geometric integration and discrete variational calculus: some new deve
lopments\nby David Martin de Diego (ICMAT) as part of Geometry\, Dynam
ics and Mechanics Seminar\n\n\nAbstract\nThis talk will have two different
parts. The first one will give a motivation to the importance of geometri
c integration and\, in particular\, to the discrete variational calculus
for the numerical integration of continuous systems of differential equati
ons with some preservation properties. In the second part\, two recent re
sults of the author and his collaborators will be reviewed. One on the use
of retraction maps for the geometric derivation of symplectic integrator
s and how classical techniques of symplectic geometry are useful in their
derivation. The last result to be discussed will be a recent derivation o
f an iterative method for discrete variational methods appropriate for bou
ndary value problems. More concretely\, we explore a parallelization strat
egy that leverages the power of multicore CPUs and GPUs (graphics cards).
We study this parallel method for first-order and second-order Lagrangians
and we illustrate its excellent behavior in some interesting applications
\, namely Zermelo’s navigation problem\, a fuel-optimal navigation probl
em\, and an interpolation problem... all this if time allows\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sonja Hohloch (Antwerpen)
DTSTART;VALUE=DATE-TIME:20210914T144500Z
DTEND;VALUE=DATE-TIME:20210914T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/30
DESCRIPTION:Title: Hamiltonian S1-actions and integrable systems\nby Sonja Hohloch (A
ntwerpen) as part of Geometry\, Dynamics and Mechanics Seminar\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clodoaldo Grotta-Ragazzo (Sao Paulo)
DTSTART;VALUE=DATE-TIME:20210928T144500Z
DTEND;VALUE=DATE-TIME:20210928T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/31
DESCRIPTION:Title: Hydrodynamic Vortex on a Compact Surface: the “Steady Vortex Metric
” and possible generalizations to higher dimensions\nby Clodoaldo Gr
otta-Ragazzo (Sao Paulo) as part of Geometry\, Dynamics and Mechanics Semi
nar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Philippe Lessard (McGill\, Montreal)
DTSTART;VALUE=DATE-TIME:20211012T144500Z
DTEND;VALUE=DATE-TIME:20211012T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/32
DESCRIPTION:Title: Recent developments of computer-assisted proofs in the Navier-Stokes e
quations\nby Jean-Philippe Lessard (McGill\, Montreal) as part of Geom
etry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nIn the study of infin
ite dimensional dynamical systems exploring the dynamics in the entire pha
se space is impossible. One strategy to tackle this problem is to focus on
a set of special solutions that act as organizing centers. To single out
these solutions computer-assisted proofs are being developed to find\, for
example\, fixed points\, periodic orbits and connecting orbits between th
ose. Computer-assisted proofs in dynamics combine the strength of scientif
ic computing\, nonlinear analysis\, numerical analysis\, applied topology\
, functional analysis and approximation theory. While in the past decade\,
these techniques have primarily been applied to ODEs\, we are starting to
witness their applicability for infinite dimensional nonlinear dynamics g
enerated by partial differential equations (PDEs)\, integral equations\, d
elay differential equations (DDEs)\, and infinite dimensional maps. In thi
s talk we will present recent advances in this direction\, with a special
emphasize on the dynamics in the Navier-Stokes equations.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Chierchia (Roma Tre)
DTSTART;VALUE=DATE-TIME:20211026T144500Z
DTEND;VALUE=DATE-TIME:20211026T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/33
DESCRIPTION:Title: The ultimate frontier of KAM Theory (in finite dimensions)\nby Lui
gi Chierchia (Roma Tre) as part of Geometry\, Dynamics and Mechanics Semin
ar\n\n\nAbstract\nA fundamental question in KAM theory (which actually mot
ivated Arnold's 1963 paper "Proof of a Theorem by A.N. Kolmogorov...")\, i
s: what is the measure in phase space spanned by regular (quasi-periodic)
motions? I will discuss recent results (joint with Luca Biasco)\, which sh
ow that\, in the case of nearly-integrable generical mechanical systems\,
away from a "non perturbative set" around double resonances (i.e. a set in
phase space where the motion is essentially described by a parameter-free
Hamiltonian) of measure ~ O(ε)\, the phase space is filled by quasi-peri
odic motions up to a set exponentially small in 1/ε.\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Suris (TU Berlin)
DTSTART;VALUE=DATE-TIME:20211109T154500Z
DTEND;VALUE=DATE-TIME:20211109T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/34
DESCRIPTION:by Yuri Suris (TU Berlin) as part of Geometry\, Dynamics and M
echanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Mamaev
DTSTART;VALUE=DATE-TIME:20211207T154500Z
DTEND;VALUE=DATE-TIME:20211207T170000Z
DTSTAMP;VALUE=DATE-TIME:20240329T095701Z
UID:GDMSeminar/35
DESCRIPTION:Title: Special lecture in honour of Alexey Borisov\nby Ivan Mamaev as par
t of Geometry\, Dynamics and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDMSeminar/35/
END:VEVENT
END:VCALENDAR