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BEGIN:VEVENT
SUMMARY:A hybrid WKB-based method for Schrödinger scattering problems in
the semi-classical limit
DTSTART;VALUE=DATE-TIME:20190903T094500Z
DTEND;VALUE=DATE-TIME:20190903T103000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3964@indico.math.cnrs.fr
DESCRIPTION:Speakers: Anton Arnold (Vienna University of Technology)\nWe c
onsider 1D scattering problems related to quantum transport in diodes. We
discuss the efficient numerical integration of ODEs like $\\epsilon^2*u"+a
(x)*u=0$ for $00$) and evanescent regimes (for $a(x)<0$)\, partly includi
ng turning points. In the oscillatory case we use a marching method that i
s based on an analytic WKB-preprocessing of the equation. And in the evane
scent case we use a FEM with WKB-ansatz functions.\n\n(co-authors: Claudia
Negulescu\; Kirian Döpfner\; Christian Klein\, Bernhard Ujvari)\n\nhttps
://indico.math.cnrs.fr/event/4493/contributions/3964/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3964/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The stability of periodic solutions of the focusing NLS equation
DTSTART;VALUE=DATE-TIME:20190903T123000Z
DTEND;VALUE=DATE-TIME:20190903T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3965@indico.math.cnrs.fr
DESCRIPTION:Speakers: Bernard Deconinck (University of Washington)\nA surp
risingly large number of physically relevant dispersive partial differenti
al equations are integrable. Using the connection between the spectrum and
the eigenfunctions of the associated Lax pair and the linear stability pr
oblem\, we investigate the stability of the spatially periodic traveling w
ave solutions of such equations\, extending the results to orbital stabili
ty in those case where solutions are linearly stable. The talk will emphas
ize recent results for the focusing NLS equation\, as this situation is mo
re complicated than that of other equations previously studied\, for which
the Lax pair is self adjoint.\n\nhttps://indico.math.cnrs.fr/event/4493/c
ontributions/3965/
LOCATION: Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3965/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inverse Scattering for the Intermediate Long Wave Equation
DTSTART;VALUE=DATE-TIME:20190905T070000Z
DTEND;VALUE=DATE-TIME:20190905T074500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3977@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Perry (University of Kentucky)\nThis talk rep
orts on joint work with Joel Klipfel (University of Kentucky) and Yilun Wu
(University of Oklahoma). The intermediate long wave equation (ILW) is a
model of weakly nonlinear wave propagation in a fluid of finite depth. It
interpolates between the Benjamin-Ono equation (infinite depth) and the Ko
rteweg-de Vries equation (shallow water). Ablowitz and Kodama showed that
ILW is completely integrable and\, subsequently\, an inverse scattering ap
proach to solving ILW was developed by Ablowitz-Kodama-Satsuma and Santini
-Ablowitz-Fokas. Our work is\, to our knowledge\, the first rigorous analy
sis of direct and inverse scattering maps for ILW. Both the direct and in
verse problems are Riemann-Hilbert problems (respectively local and non-lo
cal)\; their proper formulation involves several interesting technical cha
llenges.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3977/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3977/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edge vectors on planar networks and tropical limit of real finite
gap solutions of KP hierarchy
DTSTART;VALUE=DATE-TIME:20190903T130000Z
DTEND;VALUE=DATE-TIME:20190903T133000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3966@indico.math.cnrs.fr
DESCRIPTION:Speakers: Simonetta Abenda (University of Bologna)\nIn this ta
lk\, I shall report on some recent results obtained in collaboration with
P.G. Grinevich (LITP\,RAS). We construct edge vectors on planar networks o
btained by gluing the positive part of copies of Gr(1\,3) and Gr(2\,3) and
apply such construction to associate real regular KP divisors on rational
degenerations of M-curves.\n\nhttps://indico.math.cnrs.fr/event/4493/cont
ributions/3966/
LOCATION: Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3966/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a $\\partial\, \\overline{\\partial }$ system with a large para
meter.
DTSTART;VALUE=DATE-TIME:20190905T074500Z
DTEND;VALUE=DATE-TIME:20190905T083000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3978@indico.math.cnrs.fr
DESCRIPTION:Speakers: Johannes Sjöstrand (Université de Bourgogne)\nThis
is part of a joint work with\nChristian Klein and Nikola Stoilov. We cons
ider a $2\\times 2$ system of $\\partial \,\\overline{\\partial }$ type in
the large parameter limit\, appearing in the study of the Davey-Stuartson
II equation.\n\nWhen a certain potential is smooth\, we show that the sol
ution is given by a convergent perturbation series.\n\nWhen it is the char
acteristic function of a strictly convex domain\, we analyze the leading t
erm in the series. Numerical simulations show a fairly good coincidence wi
th the full solution despite the lack of smoothness of the potential in th
is case.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3978/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3978/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-ultralocality\, affine Gaudin models and Chern-Simons theory
DTSTART;VALUE=DATE-TIME:20190904T090000Z
DTEND;VALUE=DATE-TIME:20190904T093000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3968@indico.math.cnrs.fr
DESCRIPTION:Speakers: Benoit Vicedo (University of York)\nNon-ultralocalit
y is a long-standing open problem in classical integrable field theory whi
ch has precluded the first-principle quantisation of many important models
. I will review a recent proposal for dealing with this issue\, which rela
tes it to the study of Gaudin models associated with affine Kac-Moody alge
bras. I will then go on to discuss its relation to another very recent pro
posal of Costello and Yamazaki who's starting point is a four-dimensional
variant of Chern-Simons theory.\n\nhttps://indico.math.cnrs.fr/event/4493/
contributions/3968/
LOCATION: C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3968/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Electrical Impedance Tomography and the Novikov-Veselov equation
DTSTART;VALUE=DATE-TIME:20190905T090000Z
DTEND;VALUE=DATE-TIME:20190905T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3979@indico.math.cnrs.fr
DESCRIPTION:Speakers: Samuli Siltanen (University of Helsinki)\nThe D-bar
method\, introduced by Beals and Coifman in the 1980’s\, provides a solu
tion method for Calderón’s inverse conductivity problem in dimension tw
o\, as was shown by Nachman in 1996. This presentation shows how Nachman
’s proof can be developed further to yield the D-bar method\, a practica
l imaging algorithm for Electrical Impedance Tomography (EIT). Furthermore
\, demonstrated is how machine learning can be combined with the D-bar met
hod for the diagnosis of stroke. Finally\, the nonlinear Novikov-Veselov e
quation can be solved using the inverse scattering method and the same non
linear Fourier transform than the one used in EIT.\n\nhttps://indico.math.
cnrs.fr/event/4493/contributions/3979/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3979/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrable coupled sigma-models from affine Gaudin models
DTSTART;VALUE=DATE-TIME:20190904T093000Z
DTEND;VALUE=DATE-TIME:20190904T100000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3969@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sylvain Lacroix (Universtät Hamburg)\nIn this talk\
, we will discuss realisations of affine Gaudin models and their applicati
on to integrable sigma-models. After reviewing the properties of affine Ga
udin models and their relation with integrable sigma-models (see also B. V
icedo's talk)\, we will explain a systematic procedure allowing to assembl
e two affine Gaudin models into a unique one. As an application of this fo
rmalism\, we will present an integrable coupled sigma-model obtained by as
sembling together N copies of the Principal Chiral Model with Wess-Zumino
term.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3969/
LOCATION: C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3969/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a gas of soliton for the modified KdV equation
DTSTART;VALUE=DATE-TIME:20190904T073000Z
DTEND;VALUE=DATE-TIME:20190904T080000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3971@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tamara Grava (SISSA)\nWe study a gas of solitons in
the limit when the number of solitons goes to infinity.\nWe characterize t
he asymptotic behaviour and the long time behaviour of the soliton gas.\n\
nhttps://indico.math.cnrs.fr/event/4493/contributions/3971/
LOCATION: C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3971/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Riemann-Hilbert approach to the lower tail of the KPZ equation
DTSTART;VALUE=DATE-TIME:20190904T080000Z
DTEND;VALUE=DATE-TIME:20190904T083000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3972@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mattia Cafasso (Université d'Angers)\nFredholm dete
rminants associated to deformations of the Airy kernel are known to be clo
sely connected to the solution to the Khardar-Parisi-Zhang (KPZ) equation
with narrow wedge initial data\, and they also appear as largest particle
distribution in models of positive-temperature free fermions. It is of par
ticular importance in these models to understand the lower tail of the Fre
dholm determinants.\nWe show that logarithmic derivatives of the Fredholm
determinants can be expressed in terms of a 2×2 Riemann-Hilbert problem\,
and we use this to derive asymptotics for the Fredholm determinants. As a
n application of our result\, we derive precise lower tail asymptotics for
the solution of the KPZ equation with narrow wedge initial date\, thus re
fining recent results by Corwin and Ghosal.\n\nhttps://indico.math.cnrs.fr
/event/4493/contributions/3972/
LOCATION: C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3972/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrable and near-integrable long-wave models in stratified shea
r flows
DTSTART;VALUE=DATE-TIME:20190902T150000Z
DTEND;VALUE=DATE-TIME:20190902T153000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3959@indico.math.cnrs.fr
DESCRIPTION:Speakers: Karima Khusnutdinova (Loughborough University)\nIn t
his talk I will overview recent developments concerning a version of the K
adomtsev-Petviashvili (KP) equation for surface gravity waves related to e
lliptic-cylindrical geometry\, a system of coupled Ostrovsky equations der
ived for strongly interacting internal waves in the presence of background
rotation and a shear flow\, and 2+1-dimensional cylindrical Korteweg-de V
ries (cKdV)-type model describing ring waves in a stratified fluid in the
presence of a depth-dependent parallel shear flow.\n\nhttps://indico.math.
cnrs.fr/event/4493/contributions/3959/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3959/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stratified 2D Euler Flows: Hamiltonian aspects\, conserved quantit
ies and classes of solutions.
DTSTART;VALUE=DATE-TIME:20190904T070000Z
DTEND;VALUE=DATE-TIME:20190904T073000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3974@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gregorio Falqui (University of Milano-Bicocca)\nhttp
s://indico.math.cnrs.fr/event/4493/contributions/3974/
LOCATION: C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3974/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bloch spectrum for water waves
DTSTART;VALUE=DATE-TIME:20190902T070000Z
DTEND;VALUE=DATE-TIME:20190902T074500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3951@indico.math.cnrs.fr
DESCRIPTION:Speakers: Catherine Sulem (University of Toronto)\nWe examine
the motion of the free surface of a body of fluid with a periodically vary
ing bottom. We consider the water wave system linearized near a stationary
state and develop a Bloch theory. The analysis takes the form of a spectr
al problem for the Dirichlet– Neumann operator in a fluid domain with a
periodic bottom and a flat surface elevation. We find that\, generically\,
the presence of the bottom results in the splitting of double eigenvalues
creating a spectral gap. The analysis is uniform in the spectral paramete
r and provides the gap asymptotics.\n\nhttps://indico.math.cnrs.fr/event/4
493/contributions/3951/
LOCATION: Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3951/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrability of new class of hyperbolic two-dimensional linear eq
uations of second order
DTSTART;VALUE=DATE-TIME:20190902T153000Z
DTEND;VALUE=DATE-TIME:20190902T160000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3960@indico.math.cnrs.fr
DESCRIPTION:Speakers: Maxim Pavlov (Lebedev Physical Institute of Russian
Academy of Sciences)\nWe consider a linear two-dimensional hyperbolic equa
tion of second order\, whose coefficients are polynomials with respect to
one of independent variables.\n \nWe show that this equation possesses inf
initely many particular solutions\, determined by solutions of ordinary di
fferential equations.\n\nhttps://indico.math.cnrs.fr/event/4493/contributi
ons/3960/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3960/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrable Lagrangians and Picard modular forms
DTSTART;VALUE=DATE-TIME:20190905T131500Z
DTEND;VALUE=DATE-TIME:20190905T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3993@indico.math.cnrs.fr
DESCRIPTION:Speakers: Evgeny Ferapontov (Loughborough University)\nWe cons
ider first-order Lagrangians whose Euler-Lagrange equations belong to the
class of 3D dispersionless integrable systems. Our main results can be sum
marised as follows:\n(1) A link between integrable Lagrangians and Picard
curves/Picard modular forms studied by E. Picard as far back as in 1883 is
established.\n(2) A parametrisation of integrable Lagrangian densities by
generalised hypergeometric functions (solutions of the Picard-Fuchs syste
m governing periods of Picard curves) is obtained.\n(3) Conjectured theta
representations and power series expansions of the integrable Lagrangian d
ensities are proved.\n(based on joint work with F. Cl\\'ery A. Odesskii an
d D. Zagier)\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3993/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3993/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Novikov algebras and Darboux coordinate: the construction of flat
coordinates
DTSTART;VALUE=DATE-TIME:20190905T123000Z
DTEND;VALUE=DATE-TIME:20190905T131500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3992@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ian Strachan (University of Glasgow)\nThe classical
Muira maps transforms the second Hamiltonian structure of the KdV hierarch
y into constant\, or Darboux\, form. In this talk multi-component versions
of this map are constructed\, for Hamiltonian structures defined by Novik
ov algebras.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3992/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3992/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sine-Gordon field theory vs. relativistic Calogero-Moser $N$-parti
cle sytems
DTSTART;VALUE=DATE-TIME:20190905T094500Z
DTEND;VALUE=DATE-TIME:20190905T103000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3989@indico.math.cnrs.fr
DESCRIPTION:Speakers: Simon Ruijsenaars (University of Leeds)\nWe survey t
he relation between the relativistic sine-Gordon model and (a special case
of) the hyperbolic relativistic integrable $N$-particle systems of Caloge
ro-Moser type. More specifically\, we review the intimate link between the
classical version of the latter and the particle-like sine-Gordon solutio
ns\, and present compelling evidence that this soliton-particle correspond
ence turns into a physical equivalence on the quantum level\, in the sens
e that the same scattering amplitudes and bound state energies arise in
the quantum field-theoretic and $N$-particle models.\n\nhttps://indico.mat
h.cnrs.fr/event/4493/contributions/3989/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3989/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On some (non-integrable) KP type equations
DTSTART;VALUE=DATE-TIME:20190906T094500Z
DTEND;VALUE=DATE-TIME:20190906T103000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3987@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jean-Claude Saut (Universite Paris-Sud)\nWe present
recent results and open issues on KP-type equations arising in the modelin
g of internal waves\n\nhttps://indico.math.cnrs.fr/event/4493/contribution
s/3987/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3987/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Universality in Random Tiling Models
DTSTART;VALUE=DATE-TIME:20190906T070000Z
DTEND;VALUE=DATE-TIME:20190906T074500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3990@indico.math.cnrs.fr
DESCRIPTION:Speakers: Pierre van Moerbeke (University of Louvain and Brand
eis University)\nTilings of polygonal regions with non-convexities (cuts)
lead to a new kernel and a new statistics for the asymptotic fluctuations
of the tiles\, when the size of the region and the cuts gets large under a
n appropriate scaling. The limiting statistics has been observed in very d
ifferent circumstances.\n\nhttps://indico.math.cnrs.fr/event/4493/contribu
tions/3990/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3990/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiple rogue waves and integrable models: perspectives and retro
spectives
DTSTART;VALUE=DATE-TIME:20190906T074500Z
DTEND;VALUE=DATE-TIME:20190906T083000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3991@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vladimir Matveev (Université de Bourgogne)\nThis ta
lk is dedicated to the description of the modulation instabilities\, lea
ding to the appearance of phenomena of multiple rogue waves generation in
a frame of integrable hierarchies. It is mainly concentrated on the AKNS h
ierarchy and some related systems.\nAn essential part of the results is ex
posed in our recent article: V.B. Matveev\, A.O. Smirnov "AKNS and NLS hi
erarchies\, MRW solutions\, P_n breathers\, and beyond"\, J.Math. Phys. 59
\, 091419(2018)\; doi: 10.1063/1.5049949\n\nhttps://indico.math.cnrs.fr/ev
ent/4493/contributions/3991/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3991/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tropical limit of matrix solitons
DTSTART;VALUE=DATE-TIME:20190903T150000Z
DTEND;VALUE=DATE-TIME:20190903T153000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3984@indico.math.cnrs.fr
DESCRIPTION:Speakers: Folkert Müller-Hoissen (University of Goettingen)\n
The "tropical limit'' of a matrix (KdV\, Boussinesq\, or the like) soliton
solution in two-dimensional space-time consists of a piecewise linear gra
ph in space-time\, together with values of the dependent variable along it
s segments. In two space-time dimensions\, it associates with such waves
a point particle picture\, in which free "particles'' with internal degree
s of freedom interact at definite points in space-time. Whereas for KdV th
e values of the dependent variable attached to incoming and outgoing solit
ons at a vertex are related by a (highly nonlinear) Yang-Baxter map\, such
a map appears to be insufficient in the Boussinesq case to describe all p
ossible soliton interactions in the tropical limit. The interaction in cas
e of solitons in more than two dimensions is definitely richer. We will r
eport about some insights for soliton solutions of the KP equation. \nThis
talk is based on joint work with A. Dimakis [1\,2\,3] and X.-M. Chen [3].
\n[1] A. Dimakis and F. Müller-Hoissen: Matrix KP: tropical limit and Yan
g-Baxter maps\, Lett. Math. Phys. 109 (2019) 799-827.\n[2] A. Dimakis and
F. Müller-Hoissen: Matrix KP: tropical limit\, Yang-Baxter and pentagon m
aps\, Theor. Math. Phys. 196 (2018) 1164-1173.\n[3] A. Dimakis\, F. Mülle
r-Hoissen and X.-M. Chen: Matrix Boussinesq solitons and their tropical li
mit\, Physica Scripta 94 (2019) 035206.\n\nhttps://indico.math.cnrs.fr/eve
nt/4493/contributions/3984/
LOCATION: Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3984/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Strongly interacting soliton gas and the noise-induced modulation
instability
DTSTART;VALUE=DATE-TIME:20190905T150000Z
DTEND;VALUE=DATE-TIME:20190905T153000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-4019@indico.math.cnrs.fr
DESCRIPTION:Speakers: Andrey Gelash (Skolkovo Institute of Science and Tec
hnology)\nWe investigate the statistically stationary state of spontaneous
noise-driven modulation instability of a plane wave (condensate) backgrou
nd. As a model we use the integrable focusing one-dimensional nonlinear Sc
hrodinger equation (NLSE). The fundamental statistical characteristics of
the stationary state of the modulation instability obtained numerically by
Agafontsev and Zakharov in 2015 [1] have not been explained so far. When
the condensate is spatially wide the inverse scattering transform (IST) th
eory predicts that interacting solitons play the dominating role in the sy
stem evolution. Here we explain statistical characteristics of the modulat
ion instability by using N-soliton solutions (N-SS\, here N means the numb
er of solitons) of the NLSE. We determine parameters of the N-SS correspon
ding to the statistically stationary state of the integrable turbulence pr
oduced by the instability development. These N-SS are strongly interacting
bound states of solitons having specific distribution of the IST eigenval
ues and random phases. The condensate is a coherent state of the N-SS and
initial stage of the modulation instability development represents the los
s of coherence of the soliton phases. We use a special approach to constru
ct ensembles of the multi-soliton solutions with statistically large numbe
r of solitons N ~100 [2]. Our investigation demonstrates complete agreemen
t in spectral and statistical properties of the long-term evolution of the
condensate perturbed by noise and the constructed multisoliton bound stat
es [3]. Our results can be generalised to the broad class of integrable tu
rbulence problems in the cases when the wave filed dynamics is strongly no
nlinear and driven by solitons.\n\n[1] D. Agafontsev and V. E. Zakharov\,
Nonlinearity 28\, 2791 (2015)\n[2] A. A. Gelash and D. S. Agafontsev\, Phy
s. Rev. E 98\, 042210 (2018).\n[3] A. Gelash\, D. Agafontsev\, V. Zakharov
\, G. El\, S. Randoux and P. Suret\, Bound state soliton gas dynamics unde
rlying the noise-induced modulational instability\, In preparation.\n\nhtt
ps://indico.math.cnrs.fr/event/4493/contributions/4019/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/4019/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A complex-analysis friendly form of Schroedinger equation with a n
on-vanishing potential
DTSTART;VALUE=DATE-TIME:20190905T153000Z
DTEND;VALUE=DATE-TIME:20190905T160000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-4020@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmitry Ponomarev (TU Wien)\nThe aim of the talk is t
o introduce a transformation which reduces initial-value problem for one-d
imensional Schroedinger equation with a non-vanishing potential to an elem
entary homogeneous first-order nonlinear ODE. The latter exhibits nonlinea
rity merely as complex conjugation and hence is very amenable to applicati
on of transform methods and further complex-analytic treatment. The obtain
ed reformulation is beneficial for both analytical and practical purposes
such as simplification of construction of efficient hybrid asymptotical-nu
merical schemes for oscillatory quasi-classical regime\, a new form of Pru
fer equations and new classes of solvable potentials due to reduction to a
n integral equation of convolution type on a half-line.\n\nhttps://indico.
math.cnrs.fr/event/4493/contributions/4020/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/4020/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The quantum beating and its numerical simulation
DTSTART;VALUE=DATE-TIME:20190903T090000Z
DTEND;VALUE=DATE-TIME:20190903T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3963@indico.math.cnrs.fr
DESCRIPTION:Speakers: Claudia Negulescu (Univ. Paul Sabatier)\nQuantum bea
ting may nowadays refer to many\, often quite different phenomena studied
in various domains of quantum physics. A paradigmatic example is the inver
sion in the ammonia molecule\, observed experimentally in 1935. \nA theore
tical explanation of the quantum beating was obtained by modelling the nit
rogen atom as a quantum particle in a double well potential. The quantum e
nvironment of this particle can be modelled as a non-linear perturbation t
erm added to the double well potential.\n\nIn this talk\, I shall examine
numerically the suppression of the quantum beating in a one dimensional no
n-linear double well potential\, made up of two focusing nonlinear point i
nteractions. The study of the Schroedinger dynamics is reduced to the stud
y of a system of coupled nonlinear Volterra integral equations. I will sho
w that already for a nonlinearity exponent well below the critical value\,
there is complete suppression of the typical beating behaviour characteri
zing the linear quantum case.\n\nhttps://indico.math.cnrs.fr/event/4493/co
ntributions/3963/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3963/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monodromy dependence of Painlevé tau functions
DTSTART;VALUE=DATE-TIME:20190902T123000Z
DTEND;VALUE=DATE-TIME:20190902T130000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3955@indico.math.cnrs.fr
DESCRIPTION:Speakers: Oleg Lisovyi (Université de Tours)\nIn many interes
ting cases\, distribution functions of random matrix theory and correlatio
n functions of integrable models of statistical mechanics and quantum C-fi
eld theory are given by tau functions of Painlevé equations. I will discu
ss an extension of the Jimbo-Miwa-Ueno differential to the space of monodr
omy data and explain how this construction can be used to compute constant
terms in the tau function asymptotics.\n\nhttps://indico.math.cnrs.fr/eve
nt/4493/contributions/3955/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3955/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The direct problem of perturbed KPII multi-line solitons
DTSTART;VALUE=DATE-TIME:20190904T100000Z
DTEND;VALUE=DATE-TIME:20190904T103000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3982@indico.math.cnrs.fr
DESCRIPTION:Speakers: Derchyi Wu (Academica Sinica\, Taipei)\nBoiti-Pempin
elli-Pogrebkov's inverse scattering theories on the KPII equation provide
an integrable approach to solve the Cauchy problem of the perturbed KPII m
ulti-line soliton solutions and the stability problem of KPII multi-line s
olitons.\n\nIn this talk\, we will present rigorous analysis for the direc
t scattering theory of perturbed KPII multi line solitons\, illustrated
by perturbations of low dimensional Grassmannian cases.\n\nhttps://indico
.math.cnrs.fr/event/4493/contributions/3982/
LOCATION: C101
URL:https://indico.math.cnrs.fr/event/4493/contributions/3982/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On dressing factors of 2-dimensional Toda field theories and mul
ticomponent MKdV equations
DTSTART;VALUE=DATE-TIME:20190903T153000Z
DTEND;VALUE=DATE-TIME:20190903T160000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-4018@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vladimir Gerdjikov (Bulgarian Academy of Sciences)\n
https://indico.math.cnrs.fr/event/4493/contributions/4018/
LOCATION: Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/4018/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Extended Lagrangian approach for the defocusing Non-Linear Schröd
inger equation
DTSTART;VALUE=DATE-TIME:20190902T143000Z
DTEND;VALUE=DATE-TIME:20190902T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3958@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sergey Gavrilyuk (Aix-Marseille Université)\nWe stu
dy the defocusing Non-Linear Schrödinger (NLS) equation written in hydrod
ynamic form through the Madelung transform. From the mathematical point of
view\, the hydrodynamic form can be seen as the Euler-Lagrange equations
for a Lagrangian submitted to a differential constraint corresponding to
the mass conservation law. The dispersive nature of the NLS equation poses
some major numerical challenges. The idea is to introduce a two-parameter
family of extended Lagrangians\, depending on a greater number of variabl
es\, whose Euler-Lagrange equations are hyperbolic and accurately approxim
ate NLS equation in a certain limit. The corresponding hyperbolic equatio
ns are studied and solved numerically using Godunov type methods. Compari
son of exact and asymptotic solutions to the one-dimensional cubic NLS equ
ation (`grey' solitons and dispersive shocks) and the corresponding numer
ical solutions to the extended system was performed. A very good accuracy
of such a hyperbolic approximation was observed. This is a joint talk wit
h Firas Dhaouadi and Nicolas Favrie.\n\nhttps://indico.math.cnrs.fr/event/
4493/contributions/3958/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3958/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the derivative nonlinear Schrödinger equation related to symme
tric spaces
DTSTART;VALUE=DATE-TIME:20190903T133000Z
DTEND;VALUE=DATE-TIME:20190903T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3967@indico.math.cnrs.fr
DESCRIPTION:Speakers: Georgi Grahovski (University of Essex)\nWe will pres
ent multi-component generalizations of derivative nonlinear Schrödinger (
DNLS) type of equations having quadratic bundle Lax pairs related to $\\ma
thbb{Z}_2$-graded Lie algebras and A.III symmetric spaces. The Jost solut
ions and the minimal set of scattering data for the case of local and nonl
ocal reductions are constructed.\n\nFurthermore\, the fundamental analytic
solutions (FAS) are constructed and the spectral properties of the associ
ated Lax operators are briefly discussed. The Riemann-Hilbert problem (RHP
) for the multi-component generalizations of DNLS equation of Kaup-Newell
(KN) and Gerdjikov-Ivanov (GI) types is derived. A modification of the dre
ssing method is presented allowing the explicit derivation of the soliton
solutions for the multi-component GI equation with both local and nonloca
l reductions. \n\nThe infinite set of integrals of motion for these models
is briefly described at the end.\n\nBased on a joint work with Vladimir G
erdjikov and Rossen Ivanov.\n\n[1] Gerdjikov V.S\, Grahovski G.G. and Ivan
ov R.I.\, On integrable wave interactions and Lax pairs on symmetric space
s\, Wave Motion 71 (2017)\, 53--70\, E-print: arXiv:1607.06940.\n\nhttps:/
/indico.math.cnrs.fr/event/4493/contributions/3967/
LOCATION: Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3967/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The non-commutative KdV equation and enumerative geometry
DTSTART;VALUE=DATE-TIME:20190902T133000Z
DTEND;VALUE=DATE-TIME:20190902T140000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3957@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paolo Rossi (Università degli Studi di Padova)\nIn
the past years\, in a joint project with A. Buryak\, we have developed a g
eneral framework to construct classical and quantum field systems (in one
space and one time dimensions) from intersection theory of the moduli spac
e of stable curves. Recently a particularly interesting example came under
our attention\, which actually produces a integrable system of Hamiltonia
n PDEs in two space and one time dimensions. Computations of quadratic dou
ble ramification integrals\, an entirely natural problem in algebraic geom
etry\, turn out to produce a interesting generalization of the KdV hierarc
hy to 2 non-commutative space dimensions (KdV on a noncommutative Moyal to
rus).\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3957/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3957/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Birkhoff coordinates for the Benjamin-Ono equation on the torus
and applications to solutions with negative Sobolev regularity. Part 1
DTSTART;VALUE=DATE-TIME:20190902T074500Z
DTEND;VALUE=DATE-TIME:20190902T083000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3952@indico.math.cnrs.fr
DESCRIPTION:Speakers: Patrick Gérard (Université Paris-Sud)\nThis talk i
s a survey of a recent joint work with Thomas Kappeler about the construct
ion of Birkhoff coordinates for real valued\, spatially periodic and squar
e integrable solutions of the Benjamin-Ono equation.\n\nhttps://indico.mat
h.cnrs.fr/event/4493/contributions/3952/
LOCATION: Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3952/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Birkhoff coordinates of the Benjamin-Ono equation on the torus
and applications to solutions with negative Sobolev regularity. Part 2
DTSTART;VALUE=DATE-TIME:20190902T090000Z
DTEND;VALUE=DATE-TIME:20190902T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3953@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thomas Kappeler (University of Zurich)\nIn this talk
I report on joint work with Patrick Gérard and Peter Topalov concerning
properties of the flow map of the Benjamin-Ono equation on the torus. The
main result says that the flow map\, introduced in our previous work on th
e space $L^2_{r\,0}$ of real valued\, $2\\pi-$periodic $L^2-$functions wit
h mean $0$\, \ncan be extended to the Sobolev spaces $H^{-s}_{r\,0}$ for $
0 < s < 1/2$. The key ingredient is a corresponding extension of the Birkh
off coordinates to these Sobolev spaces.\n\nhttps://indico.math.cnrs.fr/ev
ent/4493/contributions/3953/
LOCATION: Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3953/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Short review of results on Isomonodromy Deformations and Applicati
ons
DTSTART;VALUE=DATE-TIME:20190902T130000Z
DTEND;VALUE=DATE-TIME:20190902T133000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3956@indico.math.cnrs.fr
DESCRIPTION:Speakers: Davide Guzzetti (SISSA)\nSome results on non-generic
isomonodormy deformations\, already presented in other conferences and se
minars is some detail\, will be here reviewed in 25 minutes\, stressing th
eir relevance for computations involving Painleve' equations and Dubrovin
-Frobenius Manifolds. From joint works with G. Cotti and B. Dubrovin\n\nht
tps://indico.math.cnrs.fr/event/4493/contributions/3956/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3956/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conformal Fishnet Theory
DTSTART;VALUE=DATE-TIME:20190903T070000Z
DTEND;VALUE=DATE-TIME:20190903T074500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3961@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vladimir Kazakov (Ecole Normale Superieure\, Univ. S
orbonne)\nI will review the propreties and recent results for conformal f
ishnet theory (FCFT) which was proposed by O.Gurdogan and myself as a spec
ial double scaling limit of gamma-twisted N=4 SYM theory. FCFT\, in its s
implest\, bi-scalar version\, is a UV finite strongly coupled 4-dimensionl
logarithmic CFT dominated by planar fishnet Feynman graphs (of the shape
of regular square lattice). FCFT inherits the planar integrability of N=
4 SYM which becomes manifest in this case: the fishnet graphs can be m
apped on the SO(2\,4) integrable spin chain (A.Zamolodchikov 1980). The D-
dimensional generalization of FCFT\, with SO(2\,D) conformal symmetry can
be also provided. A remarkable property of FCFT is the possibility of sp
ontaneous symmetry breaking\, which is not lifted by quantum corrections.
I will also discuss the exact computation of certain anomalous dimensions
and 4-point correlators\, and of related fishnet Feynman graphs (of "whe
el" or "spiral" type)\, using the quantum integrability tools: asymptotic
and thermodynamic Bethe ansatz and quantum spectral curve.\n\nhttps://indi
co.math.cnrs.fr/event/4493/contributions/3961/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3961/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Field-theoretical formulation of the Thermodynamic Bethe Ansatz
DTSTART;VALUE=DATE-TIME:20190903T074500Z
DTEND;VALUE=DATE-TIME:20190903T083000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3962@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ivan Kostov (IPhT Saclay)\nWe construct a quantum sy
stem which generates the finite size effects in massive integrable models
of QFT. The quantum system is built on a pair of operators creating partic
les wrapping the space and the time directions. The two wrapping operators
are given a representation as vertex operators for a pair of free bosonic
fields. The partition function at finite volume is represented as the exp
ectation value of an operator creating the ensemble of virtual particles w
rapping the space direction. This operator simplifies after approximating
the sum over mode numbers by an integral over the rapidities. The non-triv
ial measure in the rapidity space requires adding a pair of fermionic part
ners of the two bosonic fields. The expectation value is formulated as a p
ath integral which localises to the critical point described by the TBA eq
uations. We restrict ourselves to a field theory with a single particle wi
th factorised scattering and no bound states\, such as the sinh-Gordon mod
el. Both periodic and open boundary conditions are considered. In case of
periodic boundary conditions the loop effects due to bosons and fermions c
ompensate completely while for open boundary conditions the one-loop contr
ibution gives the universal part of the boundary free energy.\n\nhttps://i
ndico.math.cnrs.fr/event/4493/contributions/3962/
LOCATION: Amphi Gevrey
URL:https://indico.math.cnrs.fr/event/4493/contributions/3962/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asymptotic stability in 3d Zakharov-Kuznetsov equation
DTSTART;VALUE=DATE-TIME:20190906T090000Z
DTEND;VALUE=DATE-TIME:20190906T094500Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3988@indico.math.cnrs.fr
DESCRIPTION:Speakers: Svetlana Roudenko (Florida International University)
\nWe consider Zakharov-Kuznetsov (ZK) equation\, a higher-dimensional gene
ralization of the well-known KdV equation. We discuss the behavior of solu
tions close to the solitary wave given by Q(x-t\,y\,z) with Q being the st
andard ground state.\nWe discuss the stability of solitary waves in the 3d
quadratic (subcritical) ZK equation\, proving that solutions in the energ
y space that are orbitally stable (which is due to de Bouard) are also asy
mptotically stable\, that is\, as time goes to infinity\, they converge to
a rescaling and shift of Q(x-t\,y\,z) in some rightward moving window. Wh
ile the local and global well-posedness is currently available only in hig
her regularity spaces (than finite energy) and due to Ribaud-Vento and Mol
inet-Pilod\, we nevertheless obtain asymptotic stability in the energy spa
ce. This is a joint work with Luiz Gustavo Farah\, Justin Holmer\, and Kai
Yang.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3988/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3988/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Numerical study of the Davey-Stweartson equation
DTSTART;VALUE=DATE-TIME:20190903T143000Z
DTEND;VALUE=DATE-TIME:20190903T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3976@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nikola Stoilov (Université de Bourgogne)\nIn this w
ork we will look at the focusing Davey-Stewartson equation from two differ
ent angles\, using advanced numerical tools.\nAs a nonlinear dispersive PD
E and a generalisation of the non-linear Schrödinger equation\, DS posses
ses solutions that develop a singularity in finite time. We numerically st
udy the long time behaviour and potential blow-up of solutions to the focu
sing Davey-Stewartson II equation for various initial data and propose a c
onjecture describing the blow up rate and solution profiles near the singu
larity.\nSecondly\, DS is an integrable system and can be studied as an in
verse scat- tering problem. Both the forward and inverse scattering transf
ormation in this case are reduced to a d-bar system which plays the role t
hat Riemann-Hilbert problems play in one dimensional problems. We will pre
sent numerical solutions for Schwartzian and compactly supported potential
s. In all studied cases we use spectral methods and achieve machine precis
ion.\n\nBased on joint works with Christian Klein and Ken McLaughlin\n\nht
tps://indico.math.cnrs.fr/event/4493/contributions/3976/
LOCATION: Amphi Bernard
URL:https://indico.math.cnrs.fr/event/4493/contributions/3976/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hydrodynamics for integrable systems
DTSTART;VALUE=DATE-TIME:20190902T094500Z
DTEND;VALUE=DATE-TIME:20190902T103000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3954@indico.math.cnrs.fr
DESCRIPTION:Speakers: Benjamin Doyon (King's college London)\nHydrodynamic
s is a powerful framework for large-wavelength phenomena in many-body syst
ems. It was extended recently to include integrable models\, giving ``gene
ralised hydrodynamics”. In this talk\, I will review fundamental aspects
of the hydrodynamic of integrable systems\, with the simple examples of t
he quantum Lieb-Liniger and the classical Toda models. I will then show so
me of the exact results that can be obtained with this formalism\, such as
exact nonequilibrium steady states and exact asymptotic of correlation fu
nctions at large space-time separations in Gibbs and generalised Gibbs sta
tes\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3954/
LOCATION: Amphi Niepce
URL:https://indico.math.cnrs.fr/event/4493/contributions/3954/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rational spin chains at higher rank: new tools to solve\, complete
ness\, and separation of variables
DTSTART;VALUE=DATE-TIME:20190905T143000Z
DTEND;VALUE=DATE-TIME:20190905T150000Z
DTSTAMP;VALUE=DATE-TIME:20210419T020131Z
UID:indico-contribution-4493-3970@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dmytro Volin (Uppsala University and Nordita)\nWe pr
esent recent advances in solution of rational spin chains that build on re
sults from representation theory of Yangian and analytic Bethe Ansatz. Fir
st we show how to find spectrum of supersymmetric GL(N|M) chains using Q-s
ystem on Young diagrams. This approach can be more efficient than conventi
onal nested Bethe equations\, and also it provides one with means for expl
icitly counting solutions and hence for proving completeness. Second\, we
discuss the separation of variables program for GL(N) chains with generic
twist and inhomogeneities and\, notably\, in arbitrary finite-dimensional
representation. For them\, we present an SoV basis in which eigenstates ar
e products of Slater determinants of Baxter Q-functions and discuss its co
nnection to Gelfand-Tsetlin patterns and to generalisations of Sklyanin B-
operator.\n\nhttps://indico.math.cnrs.fr/event/4493/contributions/3970/
LOCATION: Amphi Paris
URL:https://indico.math.cnrs.fr/event/4493/contributions/3970/
END:VEVENT
END:VCALENDAR