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BEGIN:VEVENT
SUMMARY:François Gay-Balmaz (CNRS-LMD\, ENS)
DTSTART:20200616T144500Z
DTEND:20200616T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/1
DESCRIPTION:Title: Geometric variational finite element discretization of compressi
ble fluids\nby François Gay-Balmaz (CNRS-LMD\, ENS) as part of Geomet
ry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nWe review recent progre
ss made in the development of structure preserving finite element integrat
ors for compressible fluids. This approach combines the geometric formulat
ion of fluid dynamics on groups of diffeomorphisms with finite element dis
cretization techniques. A specific feature of the discrete geometric formu
lation is the occurrence of a nonholonomic right-invariant distribution on
the discrete group of diffeomorphisms\, that is shown to be isomorphic to
a Raviart-Thomas finite element space. The resulting finite element discr
etizations correspond to weak forms of the compressible fluid equations th
at don't seem to have been used in the finite element literature. It exten
ds previous work done on incompressible flows and at the lowest order on c
ompressible fluids. We illustrate the benefits of this geometric approach
and present potential future directions. This is a joint work with E. Gawl
ik.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Khesin (University of Toronto)
DTSTART:20200519T144500Z
DTEND:20200519T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/2
DESCRIPTION:Title: Pentagram maps and integrable hierarchies\nby Boris Khesin (
University of Toronto) as part of Geometry\, Dynamics and Mechanics Semina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Montgomery (UCSC)
DTSTART:20200602T144500Z
DTEND:20200602T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/3
DESCRIPTION:Title: Scattering and Metric Lines\nby Richard Montgomery (UCSC) as
part of Geometry\, Dynamics and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Haller (ETH Zurich)
DTSTART:20200630T144500Z
DTEND:20200630T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/4
DESCRIPTION:Title: Objective material barriers to the transport of momentum and vor
ticity\nby George Haller (ETH Zurich) as part of Geometry\, Dynamics a
nd Mechanics Seminar\n\n\nAbstract\nI discuss a recent theory for material
surfaces that maximally inhibit the diffusive transport of a dynamically
active (i.e.\, velocity-dependent) vector field\, such as the linear momen
tum\, the angular momentum or the vorticity\, in three-dimensional unstead
y flows. These diffusion barriers provide physics-based\, observer-indepen
dent boundaries of dynamically active coherent structures. Instantaneous l
imits of these Lagrangian diffusion barriers mark objective Eulerian barri
ers to short-term active transport. I show how active diffusion barriers
can be identified with active versions of Lagrangian coherent structure (L
CS) diagnostics. In comparison to their passive counterparts\, however\, a
ctive LCS diagnostics require no significant fluid particle separation and
hence provide substantially higher-resolved Lagrangian and Eulerian coher
ent structure boundaries from shorter velocity data sets. I illustrate the
se results on two-dimensional turbulence and three-dimensional wall-bounde
d turbulence.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darryl Holm (Imperial College\, London)
DTSTART:20200714T144500Z
DTEND:20200714T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/5
DESCRIPTION:Title: What can Geometric Mechanics do for Climate Science?\nby Dar
ryl Holm (Imperial College\, London) as part of Geometry\, Dynamics and Me
chanics Seminar\n\n\nAbstract\nThe prediction of climate change and its im
pact on extreme \nweather events is one of the great societal and intellec
tual \nchallenges of our time. The first part of the problem is to make th
e \ndistinction between weather and climate. The second part is to \nunder
stand the dynamics of the fluctuations of the physical variables. \nThe th
ird part is to predict how the variances of the fluctuations are \naffecte
d by statistical correlations in their fluctuating dynamics. \nThis GDM Se
minar investigates a stochastic geometric mechanics \nframework called LA
SALT which can at least formally meet all three \nparts of the challenge f
or the problem of climate change\, given a \ndeterministic fluid theory de
rived from the variational principles of \ngeometric mechanics.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yvette Kosmann-Schwarzbach (Ecole Polytechnique)
DTSTART:20200728T144500Z
DTEND:20200728T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/6
DESCRIPTION:Title: The Noether theorems a century later\nby Yvette Kosmann-Schw
arzbach (Ecole Polytechnique) as part of Geometry\, Dynamics and Mechanics
Seminar\n\n\nAbstract\nFor this mostly historical talk\, I wish to presen
t the contents of the now famous article of Emmy Noether\, "Invariante Var
iationsprobleme"\, published in the Gőttingen Nachrichten in 1918\, an ar
ticle that is often cited but rarely cited faithfully. As background\, I s
hall sketch the work of her predecessors and I shall stress the motivation
for her only contribution to mathematical physics\, namely the question o
f whether energy was conserved in the general theory of relativity which h
ad been discussed by Einstein and Hilbert since 1915. How original\, how m
odern\, how influential were her results? I shall comment on the curious t
ransmission and later recognition of the wide applicability of the Noether
theorems.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Tomei (PUC-Rio)
DTSTART:20200825T144500Z
DTEND:20200825T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/7
DESCRIPTION:Title: Basic Todaism\nby Carlos Tomei (PUC-Rio) as part of Geometry
\, Dynamics and Mechanics Seminar\n\n\nAbstract\nThe Toda flows are at the
crossroads of a surprising amount \nof pure and applied mathematics. This
talk starts from zero and \npresents a very incomplete view of the subjec
t\, choosing some high \npoints of more than fifty years of very active re
search.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Treschev (Steklov Mathematical Institute of Russian Academy
of Sciences)
DTSTART:20200908T144500Z
DTEND:20200908T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/8
DESCRIPTION:Title: Billiard systems with locally linear dynamics\nby Dmitry Tre
schev (Steklov Mathematical Institute of Russian Academy of Sciences) as p
art of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nCan a bill
iard map be locally conjugated to a rigid rotation?\nWe prove that the ans
wer to this question is positive in the\ncategory of formal series that de
termine the boundary.\nWe also present numerical evidence\nthat for ``good
'' rotation angles the answer is also positive\nin analytic category.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annalisa Calini (Charleston University)
DTSTART:20200922T144500Z
DTEND:20200922T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/9
DESCRIPTION:Title: Geometric flows in centro-affine space\nby Annalisa Calini (
Charleston University) as part of Geometry\, Dynamics and Mechanics Semina
r\n\n\nAbstract\nMany classical objects in differential geometry are descr
ibed by integrable systems: nonlinear PDE with infinitely many conserved
quantities that are (in some sense) solvable. Beginning in the 1980s\, stu
dies of curve evolutions that are invariant under the action of a geometri
c group of transformations have unveiled more connections between geometri
c curve flows and well-known integrable PDE (among them are the KdV\, mKd
V\, sine-Gordon\, and NLS equations). More recently\, efforts have been d
irected towards understanding geometric discretizations of surfaces and cu
rves and associated evolutions.\nThis talk will describe some natural geom
etric flows for curves and polygons in centro-affine geometry\, and their
relations with the KdV and Boussinesq equations and discretizations of Ad
ler-Gel’fand-Dikii (AGD) flows for curves in projective space. The AGD
discretizations (previously introduced in work by Marí-Beffa and Wang) wi
ll be discussed in more detail\, as their lifts to the moduli space of cen
tro-affine arc length parametrized polygons promptly reveal their bihamilt
onian structures in terms of a pair of simple pre-symplectic forms.\n\nSom
e references:\n\nU. Pinkall\, Hamiltonian flows on the space of star-shape
d curves\, Result. Math. 27 (1995)\, 328–332.\n\nA. Calini\, T. Ivey\, a
nd G. Marí-Beffa\, Remarks on KdV-type Flows on Star-Shaped Curves\, Phys
ica D Vol. 238\, no. 8 (2009)\, 788–797\n\nG. Marí-Beffa and J.P. Wang\
, Hamiltonian structures and integrable evolutions of twisted gons in RPn\
, Nonlinearity 26 (2013) 2515-2551\n\nA. Calini\, T. Ivey\, and G. Marí-B
effa\, An integrable flow for starlike curves in centroaffine space\, SI
GMA 9\, (2013)\, 022\, 21 pp.\n\nA. Calini and G. Marí-Beffa\, Integrable
evolutions of twisted polygons in centroaffine Rm\, IMRN\, rnaa161 (2020
)\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (UPC Barcelona)
DTSTART:20201020T144500Z
DTEND:20201020T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/10
DESCRIPTION:by Eva Miranda (UPC Barcelona) as part of Geometry\, Dynamics
and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (ICMAT-CSIC)
DTSTART:20201006T144500Z
DTEND:20201006T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/11
DESCRIPTION:Title: Flexibility and rigidity aspects of the dynamics of the steady
Euler flows\nby Daniel Peralta-Salas (ICMAT-CSIC) as part of Geometry\
, Dynamics and Mechanics Seminar\n\n\nAbstract\nAn inviscid and incompress
ible fluid in equilibrium on a Riemannian manifold is described by (an aut
onomous) vector field X that satisfies the\nstationary Euler equations. In
this talk I will focus on the dynamics of steady Euler flows on compact m
anifolds\, emphasizing the geometric aspects. The topics I\nwill cover inc
lude a characterization of the volume-preserving vector fields that are Eu
lerizable and some rigidity results for steady Euler flows on the round sp
here.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Veselov (Loughborough\, UK and Moscow\, Russia)
DTSTART:20201103T154500Z
DTEND:20201103T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/12
DESCRIPTION:Title: Geometrization\, integrability and knots\nby Alexander Vese
lov (Loughborough\, UK and Moscow\, Russia) as part of Geometry\, Dynamics
and Mechanics Seminar\n\n\nAbstract\nAfter Arnold the classical integrabi
lity is usually understood\nin the Liouville sense as the existence of suf
ficiently many Poisson\ncommuting integrals. About 20 years ago it was dis
covered that this does\nnot exclude the chaotic behaviour of the system\,
which may even have\npositive topological entropy.\nI will review the curr
ent situation with Liouville integrability in\nrelation with Thurston’s
geometrization programme\, using as the main\nexample the geodesic flows o
n 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
equivalent to the complement of the\ntrefoil knot in 3-sphere. I will exp
lain that the remarkable results of\nGhys about modular and Lorenz knots c
an be naturally extended to the\nintegrable region\, where these knots are
replaced by the cable knots of\ntrefoil.\nThe talk is partly based on a j
oint work with Alexey Bolsinov and Yiru\nYe and will not require any speci
fic knowledge.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:San Vu Ngoc (Rennes - France)
DTSTART:20201117T154500Z
DTEND:20201117T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/13
DESCRIPTION:Title: One can hear semi-toric systems\nby San Vu Ngoc (Rennes - F
rance) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\
nI will report on an ongoing work with Yohann Le Floch about inverse\nspec
tral theory for quantum integrable systems.\nThe question\, adapted from t
he famous "Can one hear the shape of a\ndrum?"\, is to fully reconstruct a
semi-toric system from the joint\nspectrum of its quantum counterpart.\nS
emi-toric systems form a large class of 2D integrable systems that has\nbe
en extensively studied in the last 15 years.\nThe inverse spectral problem
for these systems was proposed as a\nconjecture about 10 years ago.\nWe s
how that the conjecture is true\, by analyzing the quantum versions\nof al
l "symplectic invariants" of semi-toric systems.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Carlos Marrero (ULL)
DTSTART:20201201T154500Z
DTEND:20201201T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/14
DESCRIPTION:by Juan Carlos Marrero (ULL) as part of Geometry\, Dynamics an
d Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donald Saari (UC Irvine)
DTSTART:20201215T154500Z
DTEND:20201215T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/15
DESCRIPTION:Title: From dynamics and celestial mechanics to dark matter\nby Do
nald Saari (UC Irvine) as part of Geometry\, Dynamics and Mechanics Semina
r\n\n\nAbstract\nAlmost everyone has heard of dark matter\, but what is it
?\nWhere did it come from? In this expository talk\, which outlines some\n
basic ideas of celestial mechanics\, not only is the dark matter issue\nin
troduced\, but it is shown how elementary dynamics raises doubts about\nit
s existence.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Cabrera (UFRJ - Brazil)
DTSTART:20210202T154500Z
DTEND:20210202T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/16
DESCRIPTION:Title: Dirac structures for infinite dimensional geometries and applic
ations\nby Alejandro Cabrera (UFRJ - Brazil) as part of Geometry\, Dyn
amics and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Salomão (USP - Brazil)
DTSTART:20210216T154500Z
DTEND:20210216T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/17
DESCRIPTION:Title: Transverse foliations in the Euler problem of two fixed centers
\nby Pedro Salomão (USP - Brazil) as part of Geometry\, Dynamics and
Mechanics Seminar\n\n\nAbstract\nThe Euler problem of two fixed centers de
scribes 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 this talk\, I will explain the use of pseudo-holomorphic curves to ob
tain global surfaces of sections\, and transverse foliations in the Euler
problem of two fixed centers\, for energies above the critical value. I wi
ll also discuss generalizations of these constructions to other models in
Celestial Mechanics. This work is joint with N. de Paulo\, U. Hryniewicz\,
and S. Kim.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tere M-Seara (UPC Barcelona)
DTSTART:20210302T154500Z
DTEND:20210302T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/18
DESCRIPTION:Title: Non existence of small amplitude breathers for Klein-Gordon eq
uations\nby Tere M-Seara (UPC Barcelona) as part of Geometry\, Dynamic
s and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Calleja (UNAM\, Mexico City)
DTSTART:20210316T154500Z
DTEND:20210316T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/19
DESCRIPTION:Title: Choreographies in the n-body problem and a conjecture of Marcha
l\nby Renato Calleja (UNAM\, Mexico City) as part of Geometry\, Dynami
cs and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Rechtman (Strasburg)
DTSTART:20210413T144500Z
DTEND:20210413T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/20
DESCRIPTION:Title: Broken books and Reeb dynamics in dimension 3\nby Ana Recht
man (Strasburg) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\n
Abstract\nGiven a contact structure on a closed 3-manifold\, Giroux’s co
rrespondance gives an adapted open book decomposition. This implies that t
here exists a Reeb vector that is tangent to the binding and transverse to
the interior of the pages. For this vector field\, each page is a Birkhof
f section and the dynamics of the flow can be studied from the first retur
n map. This correspondance is unsatisfactory when one wants to study all t
he Reeb vector fields associated to a contact structure.\n\nIn collaborati
on with V. Colin and P. Dehornoy\, we proved that every non-degenerate Ree
b vector field on a closed 3-manifold is adapted to a broken book decompos
ition (a generalisation of open book). This construction gives a system of
transverse surfaces with boundary and allows to establish results on the
dynamics of the vector field. We proved\, for example\, that any non-degen
erate Reeb vector field has either two or infinitely many periodic orbits.
\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bolsinov (Loughborough\, UK)
DTSTART:20210330T144500Z
DTEND:20210330T160000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/GDMSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Bloch (University of Michigan)
DTSTART:20210427T144500Z
DTEND:20210427T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/22
DESCRIPTION:Title: Dynamics of Circulant Systems\nby Anthony Bloch (University
of Michigan) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\nAb
stract\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 th
e action\nof a cyclic group and are inspired by equations\nstudied in the
synthetic 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 t
he\ntheory and present simulations. \n\nThis is joint work with Matthew Kv
alheim.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain Chenciner (Observatoire de Paris)
DTSTART:20210511T144500Z
DTEND:20210511T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/23
DESCRIPTION:Title: ABC\nby Alain Chenciner (Observatoire de Paris) as part of
Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nA as forces\, B a
s shape\, C as angular momentum. In this ABC I’ll consider n-body relati
ve equilibria in dimensions greater than 3. The family of n-body configura
tions which\, when submitted to Newtonian or similar attraction\, admit a
relative equilibrium motion (the “balanced” configurations) then becom
es much richer. Also\, a given balanced configuration admits a variety of
relative equilibria\, namely one for each choice of a hermitian structure
on the space where the motion really takes place\; in general\, if the con
figuration is not central\, such relative equilibria are quasi-periodic.\n
\nI shall discuss several problems\, like the one of deciding what is the
smallest dimension in which a given configuration admits a relative equili
brium motion\, or when bifurcations from the periodic relative equilibrium
of a central configuration may bifurcate into a family of quasi-periodic
relative equilibria of balanced configurations.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klas Modin (Chalmers University of Technology\, Sweden)
DTSTART:20210525T144500Z
DTEND:20210525T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/24
DESCRIPTION:Title: What makes nonholonomic integrators work?\nby Klas Modin (C
halmers University of Technology\, Sweden) as part of Geometry\, Dynamics
and Mechanics Seminar\n\n\nAbstract\nA "nonholonomic integrator" is a nume
rical method specifically designed for nonholonomic systems. But what does
that mean? 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
conservation of integrals for integrable systems). I also give examples of
integrable nonholonomic systems for which nonholonomic integrators fail t
o nearly conserve the integrals.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Montaldi (University of Manchester)
DTSTART:20210622T144500Z
DTEND:20210622T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/25
DESCRIPTION:Title: Point vortices on non-orientable surfaces\nby James Montald
i (University of Manchester) as part of Geometry\, Dynamics and Mechanics
Seminar\n\n\nAbstract\nThe standard Hamiltonian approach to the dynamics o
f point vortices on a surface involves the symplectic form on the surface
together with the vorticity of the point vortices. However\, both these i
ngredients involve a choice of orientation of the surface\, which is of co
urse not available for non-orientable surfaces. In this talk I will discus
s how one can set up a Hamiltonian approach in the non-orientable setting\
, with particular reference to the Möbius band. This is joint work with
Nataliya Balabanova.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Bela Cruzeiro (IST\, Lisboa)
DTSTART:20210720T144500Z
DTEND:20210720T160000Z
DTSTAMP:20260404T110958Z
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
Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jair Koiller (Universidade Federal de Juiz de Fora\, Brazil)
DTSTART:20210608T144500Z
DTEND:20210608T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/27
DESCRIPTION:Title: Vortex pairs on surfaces: can it be a tool for topology in the
large?\nby Jair Koiller (Universidade Federal de Juiz de Fora\, Brazil
) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nIn 1
999 Yoshifumi Kimura mentioned in his paper 'Vortex motion on surfaces w
ith constant 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/10.1007/978-1-4939-244
1-7). In this talk I present some results of ongoing work with Umberto Hr
yniewicz\, Alejandro Cabrera and Anilatmaja Aryasomayajula. Regarding vor
tex pairs at a small finite distance\, we show that close-by pairs can ac
tually be called "topology checkers". \n \nIn fact we suggest the idea
that\, very much like geodesics (perhaps only more so)\, the study of vo
rtex pair dynamics could be a good way to probe the topology in the large.
This is because the Hamiltonian for vortex dynamics on surfaces involves
the Laplace Beltrami operator Green's function and its regularizations (Ro
bin's function and its partner\, Batman). \n \nTime permitting I will b
riefly review joint work with Adriano R. Rodrigues and Cesar Castilho (//
doi.org/10.1063/1.3146241\, doi: 10.3934/jgm.2018007\, http://mi.mathnet.r
u/eng/rcd389) 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/s0033
2-017-9380-7) on a the motion of a single vortex. \nDuring the talk we wi
ll make some queries for the audience\, and research suggestions will be
presented in the end.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcel Guardia (UPC\, Barcelona)
DTSTART:20210706T144500Z
DTEND:20210706T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/28
DESCRIPTION:Title: Oscillatory motions and symbolic dynamics in the three body pro
blem\nby Marcel Guardia (UPC\, Barcelona) as part of Geometry\, Dynami
cs and Mechanics Seminar\n\n\nAbstract\nConsider the three body problem wi
th positive masses $m_0$\, $m_1$ and $m_2$. In 1922 Chazy classified the p
ossible final motions the three bodies may possess\, that is the behaviors
the bodies may have when time tends to infinity. One of them are what is
known as oscillatory motions\, that is\, solutions of the three body probl
em such that the liminf (as time tends to infinity) of the relative positi
ons between bodies is finite whereas the limsup is infinite. That is\, sol
utions for which the bodies keep oscillating between an increasingly large
separation and getting closer together. The first result of existence of
oscillatory motions was provided by Sitnikov for a Restricted Three Body P
roblem\, called nowadays Sitnkikov model. His result has been extended to
several Celestial Mechanics models but always with rather strong assumptio
ns on the values of the masses.\nIn this talk I will explain how to constr
uct oscillatory 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 re
lies on the construction of a hyperbolic invariant sets whose dynamics is
conjugated to that of the shift of infinite symbols (i.e. symbolic dynamic
s). That is\, we construct invariant sets for the three body problem with
chaotic dynamics and positive topological entropy\, which moreover contain
oscillatory motions.\nThis is a joint work with Pau Martin and Tere M. Se
ara.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Martin de Diego (ICMAT)
DTSTART:20210831T144500Z
DTEND:20210831T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/29
DESCRIPTION:Title: Geometric integration and discrete variational calculus: some n
ew developments\nby David Martin de Diego (ICMAT) as part of Geometry\
, Dynamics and Mechanics Seminar\n\n\nAbstract\nThis talk will have two di
fferent parts. The first one will give a motivation to the importance of g
eometric integration and\, in particular\, to the discrete variational ca
lculus for the numerical integration of continuous systems of differential
equations with some preservation properties. In the second part\, two re
cent results of the author and his collaborators will be reviewed. One on
the use of retraction maps for the geometric derivation of symplectic int
egrators and how classical techniques of symplectic geometry are useful i
n their derivation. The last result to be discussed will be a recent deriv
ation of an iterative method for discrete variational methods appropriate
for boundary value problems. More concretely\, we explore a parallelizatio
n strategy that leverages the power of multicore CPUs and GPUs (graphics c
ards). We study this parallel method for first-order and second-order Lagr
angians and we illustrate its excellent behavior in some interesting appli
cations\, namely Zermelo’s navigation problem\, a fuel-optimal navigatio
n problem\, and an interpolation problem... all this if time allows\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sonja Hohloch (Antwerpen)
DTSTART:20210914T144500Z
DTEND:20210914T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/30
DESCRIPTION:Title: Hamiltonian S1-actions and integrable systems\nby Sonja Hoh
loch (Antwerpen) as part of Geometry\, Dynamics and Mechanics Seminar\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clodoaldo Grotta-Ragazzo (Sao Paulo)
DTSTART:20210928T144500Z
DTEND:20210928T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/31
DESCRIPTION:Title: Hydrodynamic Vortex on a Compact Surface: the “Steady Vortex
Metric” and possible generalizations to higher dimensions\nby Clodoa
ldo Grotta-Ragazzo (Sao Paulo) as part of Geometry\, Dynamics and Mechanic
s Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Philippe Lessard (McGill\, Montreal)
DTSTART:20211012T144500Z
DTEND:20211012T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/32
DESCRIPTION:Title: Recent developments of computer-assisted proofs in the Navier-S
tokes equations\nby Jean-Philippe Lessard (McGill\, Montreal) as part
of Geometry\, Dynamics and Mechanics Seminar\n\n\nAbstract\nIn the study o
f infinite dimensional dynamical systems exploring the dynamics in the ent
ire phase space is impossible. One strategy to tackle this problem is to f
ocus on a set of special solutions that act as organizing centers. To sing
le out these solutions computer-assisted proofs are being developed to fin
d\, for example\, fixed points\, periodic orbits and connecting orbits bet
ween those. Computer-assisted proofs in dynamics combine the strength of s
cientific computing\, nonlinear analysis\, numerical analysis\, applied to
pology\, functional analysis and approximation theory. While in the past d
ecade\, these techniques have primarily been applied to ODEs\, we are star
ting to witness their applicability for infinite dimensional nonlinear dyn
amics generated by partial differential equations (PDEs)\, integral equati
ons\, delay differential equations (DDEs)\, and infinite dimensional maps.
In this talk we will present recent advances in this direction\, with a s
pecial emphasize on the dynamics in the Navier-Stokes equations.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Chierchia (Roma Tre)
DTSTART:20211026T144500Z
DTEND:20211026T160000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/33
DESCRIPTION:Title: The ultimate frontier of KAM Theory (in finite dimensions)\
nby Luigi Chierchia (Roma Tre) as part of Geometry\, Dynamics and Mechanic
s Seminar\n\n\nAbstract\nA fundamental question in KAM theory (which actua
lly motivated Arnold's 1963 paper "Proof of a Theorem by A.N. Kolmogorov..
.")\, is: what is the measure in phase space spanned by regular (quasi-per
iodic) motions? I will discuss recent results (joint with Luca Biasco)\, w
hich show that\, in the case of nearly-integrable generical mechanical sys
tems\, away from a "non perturbative set" around double resonances (i.e. a
set in phase space where the motion is essentially described by a paramet
er-free Hamiltonian) of measure ~ O(ε)\, the phase space is filled by qua
si-periodic motions up to a set exponentially small in 1/ε.\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Suris (TU Berlin)
DTSTART:20211109T154500Z
DTEND:20211109T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/34
DESCRIPTION:by Yuri Suris (TU Berlin) as part of Geometry\, Dynamics and M
echanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Mamaev
DTSTART:20211207T154500Z
DTEND:20211207T170000Z
DTSTAMP:20260404T110958Z
UID:GDMSeminar/35
DESCRIPTION:Title: Special lecture in honour of Alexey Borisov\nby Ivan Mamaev
as part of Geometry\, Dynamics and Mechanics Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GDMSeminar/35/
END:VEVENT
END:VCALENDAR