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BEGIN:VEVENT
SUMMARY:Michael Roop
DTSTART;VALUE=DATE-TIME:20200427T120000Z
DTEND;VALUE=DATE-TIME:20200427T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/1
DESCRIPTION:Title: Sho
ck waves in Euler flows of gases\nby Michael Roop as part of Geometry
of differential equations seminar\n\n\nAbstract\nNon-stationary one-dimens
ional Euler flows of gases are studied. The system of differential equatio
ns describing such flows can be represented by means of 2-forms on zero-je
t space and we get some exact solutions by means of such a representation.
Solutions obtained are multivalued and we provide a method of finding cau
stics\, as well as wave front displacement. The method can be applied to a
ny model of thermodynamic state as well as to any thermodynamic process. W
e illustrate the method on adiabatic ideal gas flows.\n
LOCATION:https://researchseminars.org/talk/GDEq/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Lychagin
DTSTART;VALUE=DATE-TIME:20200504T120000Z
DTEND;VALUE=DATE-TIME:20200504T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/2
DESCRIPTION:Title: On
structure of linear differential operators of the first order\nby Vale
ntin Lychagin as part of Geometry of differential equations seminar\n\n\nA
bstract\nWe'll discuss the equivalence problem (local as well as global) f
or linear differential operators of the first order\, acting in vector bun
dles.\n\nThe slides will be in English and if preferred by anyone in the a
udience the talk itself can be switched from Russian to English.\n
LOCATION:https://researchseminars.org/talk/GDEq/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valery Yumaguzhin
DTSTART;VALUE=DATE-TIME:20200511T120000Z
DTEND;VALUE=DATE-TIME:20200511T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/3
DESCRIPTION:Title: Inv
ariants of forth order linear differential operators\nby Valery Yumagu
zhin as part of Geometry of differential equations seminar\n\n\nAbstract\n
The report is devoted to linear scalar differential operators of the fourt
h order on 2-dimensional manifolds. The field of rational differential inv
ariants of such operators will be described and their application to the e
quivalence problem with respect to the group of diffeomorphisms of the man
ifold will be shown.\n\nAlthough the talk will be in Russian\, the slides
will be in English and the discussion will be in both languages.\n
LOCATION:https://researchseminars.org/talk/GDEq/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Samokhin
DTSTART;VALUE=DATE-TIME:20200518T120000Z
DTEND;VALUE=DATE-TIME:20200518T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/4
DESCRIPTION:Title: Usi
ng the KdV conserved quantities in problems of splitting of initial data a
nd reflection / refraction of solitons in varying dissipation and/or dis
persion media\nby Alexey Samokhin as part of Geometry of differential
equations seminar\n\n\nAbstract\nAn arbitrary compact-support initial datu
m for the Korteweg-de Vries equation asymptotically splits into solitons a
nd a radiation tail\, moving in opposite direction. We give a simple metho
d to predict the number and amplitudes of resulting solitons and some inte
gral characteristics of the tail using only conservation laws.\n\nA simila
r technique allows to predict details of the behavior of a soliton which\
, while moving in non-dissipative and dispersion-constant medium encounter
s a finite-width barrier with varying dissipation and/or dispersion\; be
yond the layer dispersion is constant (but not necessarily of the same val
ue) and dissipation is null. The process is described with a special typ
e generalized KdV-Burgers equation $u_t=(u^2+f(x)u_{xx})_x$.\n\nThe transm
itted wave either retains the form of a soliton (though of different param
eters) or scatters a into a number of them. And a reflection wave may be n
egligible or absent. This models a situation similar to a light passing fr
om a humid air to a dry one through the vapor saturation/condensation area
. Some rough estimations for a prediction of an output are given using the
relative decay of the KdV conserved quantities\; in particular a formula
for a number of solitons in the transmitted signal is given.\n
LOCATION:https://researchseminars.org/talk/GDEq/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Tychkov
DTSTART;VALUE=DATE-TIME:20200525T120000Z
DTEND;VALUE=DATE-TIME:20200525T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/5
DESCRIPTION:Title: Con
tinuum mechanics of media with inner structures\nby Sergey Tychkov as
part of Geometry of differential equations seminar\n\n\nAbstract\nWe propo
se a geometrical approach to the mechanics of continuous media equipped wi
th inner structures and give the basic equations of their motion: the mass
conservation law\, the Navier-Stokes equation and the energy conservation
law.\n\nThis is a joint work with Anna Duyunova and Valentin Lychagin.\n
LOCATION:https://researchseminars.org/talk/GDEq/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleks Kleyn
DTSTART;VALUE=DATE-TIME:20200601T120000Z
DTEND;VALUE=DATE-TIME:20200601T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/6
DESCRIPTION:Title: Sys
tem of differential equations over quaternion algebra\nby Aleks Kleyn
as part of Geometry of differential equations seminar\n\n\nAbstract\nThe t
alk is based on the file\nhttps://gdeq.org/files/Aleks_Kleyn-2020.06.01.En
glish.pdf (Russian transl.: https://gdeq.org/files/Aleks_Kleyn-2020.06.01.
Russian.pdf)\n\nIn order to study homogeneous system of linear differentia
l equations\, I considered vector space over division D-algebra and the th
eory of eigenvalues in non commutative division D-algebra. I started from
section 1 dedicated to product of matrices. Since product in algebra is no
n-commutative\, I considered two forms of product of matrices and two form
s of eigenvalues (section 4). In sections 5\, 6\, 7\, I considered solving
of homogeneous system of differential equations. In the section 8\, I con
sidered the system of differential equations which has infinitely many fun
damental solutions. Following sections are dedicated to analysis of soluti
ons of system of differential equations. In particular\, if a system of di
fferential equations has infinitely many fundamental solutions\, then each
solution is envelope of a family of solutions of considered system of dif
ferential equations.\n
LOCATION:https://researchseminars.org/talk/GDEq/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Bobrova (HSE\, Moscow)
DTSTART;VALUE=DATE-TIME:20200608T120000Z
DTEND;VALUE=DATE-TIME:20200608T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/7
DESCRIPTION:Title: On
the second Painlevé equation and its higher analogues\nby Irina Bobro
va (HSE\, Moscow) as part of Geometry of differential equations seminar\n\
n\nAbstract\nSix Painlevé equations were obtained by Paul Painlevé and h
is school during the classification of ODE's of the form $w'' = P (z\, w\,
w')$\, where the function $P (z\, w\, w')$ is a polynomial in $w$ and $w'
$ and is an analytic function of $z$. These equations are widely used in p
hysics and have beautiful mathematical structures. My talk is devoted to t
he second Painlevé equation.\n\nWe will discuss the integrability of this
equation and introduce its Hamiltonian representation in terms of the Kaz
uo Okamoto variables. On the other hand\, the PII equation is integrable i
n the sense of the Lax pair and the isomonodromic representation\, that I
will present.\n\nThe Bäcklund transformation and the affine Weyl group ar
e another interesting question. Using these symmetries\, we are able to co
nstruct various rational solutions for the integer parameter PII equation.
\n\nThe second Painlevé equation has one more important representation in
terms of $\\sigma$-coordinates which are $log$-symplectic.\n\nThere are h
igher analogues of the PII equation\, which we will obtain by self-similar
reduction of the modified Korteveg-de Vries hierarchy.\n
LOCATION:https://researchseminars.org/talk/GDEq/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hovhannes Khudaverdian
DTSTART;VALUE=DATE-TIME:20200615T120000Z
DTEND;VALUE=DATE-TIME:20200615T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/8
DESCRIPTION:Title: Non
-linear homomorphisms and thick morphisms\nby Hovhannes Khudaverdian a
s part of Geometry of differential equations seminar\n\n\nAbstract\nIn 201
4\, Voronov introduced the notion of thick morphisms of (super)manifolds a
s a tool for constructing $L_{\\infty}$-morphisms of homotopy Poisson alge
bras. Thick morphisms generalise ordinary smooth maps\, but are not maps t
hemselves. Nevertheless\, they induce pull-backs on $C^{\\infty}$ function
s. These pull-backs are in general non-linear maps between the algebras o
f functions which are so-called "non-linear homomorphisms". By definition\
, this means that their differentials are algebra homomorphisms in the usu
al sense. The following conjecture was formulated: an arbitrary non-linear
homomorphism of algebras of smooth functions is generated by some thick m
orphism. We prove here this conjecture in the class of formal functionals.
In this way\, we extend the well-known result for smooth maps of manifold
s and algebra homomorphisms of $C^{\\infty}$ functions and\, more generall
y\, provide an analog of classical "functional-algebraic duality" in the n
on-linear setting.\n
LOCATION:https://researchseminars.org/talk/GDEq/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Morozov
DTSTART;VALUE=DATE-TIME:20200622T120000Z
DTEND;VALUE=DATE-TIME:20200622T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/9
DESCRIPTION:Title: Lax
representations via extensions and deformations of Lie symmetry algebras<
/a>\nby Oleg Morozov as part of Geometry of differential equations seminar
\n\n\nAbstract\nThe challenging problem in the theory of integrable partia
l differential equations is to find conditions that are formulated in inhe
rent terms of a PDE under study and ensure existence of a Lax representati
on. The talk will present the technique for constructing Lax representatio
ns via extensions of the contact symmetry algebras of PDEs. Also I will s
how examples that use deformations of infinite-dimensional Lie algebras fo
r searching new integrable PDEs.\n
LOCATION:https://researchseminars.org/talk/GDEq/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Druzhkov
DTSTART;VALUE=DATE-TIME:20200629T120000Z
DTEND;VALUE=DATE-TIME:20200629T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/10
DESCRIPTION:Title: Ex
tendable symplectic structures and the inverse problem of the calculus of
variations for systems of equations written in an extended Kovalevskaya fo
rm\nby Konstantin Druzhkov as part of Geometry of differential equatio
ns seminar\n\n\nAbstract\nThe talk is devoted to extendable symplectic str
uctures for systems of equations written in an extended Kovalevskaya form.
\n\nIt is shown\, that each extension of a symplectic structure to jets is
related to an extension of a special form.\n\nComplete description of all
extendable symplectic structures is obtained. Relation of this result wit
h the inverse problem of the calculus of variations is discussed.\n\nIt is
shown\, that each variational formulation for a system of evolution equat
ions is related to a two-sided invertible variational operator of a specia
l form.\n
LOCATION:https://researchseminars.org/talk/GDEq/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Grigoriev (Lebedev Physical Institute\, Institute for Theore
tical and Mathematical Physics of Moscow State University)
DTSTART;VALUE=DATE-TIME:20200706T120000Z
DTEND;VALUE=DATE-TIME:20200706T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/11
DESCRIPTION:Title: Pr
esymplectic structures and intrinsic Lagrangians\nby Maxim Grigoriev (
Lebedev Physical Institute\, Institute for Theoretical and Mathematical Ph
ysics of Moscow State University) as part of Geometry of differential equa
tions seminar\n\n\nAbstract\nIt is well-known that a Lagrangian induces a
compatible presymplectic form on the equation manifold (stationary surface
\, understood as a submanifold of the respective jet-space). Given an equa
tion manifold and a compatible presymplectic form therein\, we define the
first-order Lagrangian system which is formulated in terms of the intrinsi
c geometry of the equation manifold. It has a structure of a presymplectic
AKSZ sigma model for which the equation manifold\, equipped with the pres
ymplectic form and the horizontal differential\, serves as the target spac
e. For a wide class of systems (but not all) we show that if the presymple
ctic structure originates from a given Lagrangian\, the proposed first-ord
er Lagrangian is equivalent to the initial one and hence the Lagrangian pe
r se can be entirely encoded in terms of the intrinsic geometry of its sta
tionary surface. If the compatible presymplectic structure is generic\, th
e proposed Lagrangian is only a partial one in the sense that its stationa
ry surface contains the initial equation manifold but does not necessarily
coincide with it. I also plan to briefly discuss extension of this constr
uction to gauge PDEs (gauge theories in BV framework).\n
LOCATION:https://researchseminars.org/talk/GDEq/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d'Angers)
DTSTART;VALUE=DATE-TIME:20200713T120000Z
DTEND;VALUE=DATE-TIME:20200713T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/12
DESCRIPTION:Title: Po
lynomial Poisson algebras associated with elliptic curves. Part 1\nby
Vladimir Rubtsov (Université d'Angers) as part of Geometry of differentia
l equations seminar\n\n\nAbstract\nI shall give an introduction in a study
of Poisson algebras which are quasi classical limit of Sklyanin-Odesskii-
Feigin elliptic algebras. I will restrict my description to the algebras w
ith a "small" number of generators (n = 3\,4\,5).\n\nThe results are (almo
st) not new. The talk is based on my old papers with A. Odesskii\, G. Orte
nzi and S. Tagne Pelap.\n
LOCATION:https://researchseminars.org/talk/GDEq/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d'Angers)
DTSTART;VALUE=DATE-TIME:20200720T120000Z
DTEND;VALUE=DATE-TIME:20200720T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/13
DESCRIPTION:Title: Po
lynomial Poisson algebras associated with elliptic curves. Part 2\nby
Vladimir Rubtsov (Université d'Angers) as part of Geometry of differentia
l equations seminar\n\n\nAbstract\nI shall give an introduction in a study
of Poisson algebras which are quasi classical limit of Sklyanin-Odesskii-
Feigin elliptic algebras. I will restrict my description to the algebras w
ith a "small" number of generators (n = 3\,4\,5).\n\nThe results are (almo
st) not new. The talk is based on my old papers with A. Odesskii\, G. Orte
nzi and S. Tagne Pelap.\n
LOCATION:https://researchseminars.org/talk/GDEq/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Krasil'shchik (Independent University of Moscow)
DTSTART;VALUE=DATE-TIME:20200930T162000Z
DTEND;VALUE=DATE-TIME:20200930T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/14
DESCRIPTION:Title: No
nlocal conservation laws of PDEs possessing differential coverings\nby
Joseph Krasil'shchik (Independent University of Moscow) as part of Geomet
ry of differential equations seminar\n\nLecture held in room 303 of the In
dependent University of Moscow.\n\nAbstract\nIn his 1892 paper "Sulla tra
sformazione di Bäcklund per le superfici pseudosferiche" (Rend. Mat. Acc.
Lincei\, s. 5\, v. 1 (1892) 2\, pp. 3-12\; Opere\, vol. 5\, pp. 163-173)
Luigi Bianchi noticed\, among other things\, that quite simple transformat
ions of the formulas that describe the Bäcklund transformation of the sin
e-Gordon equation lead to what is called a nonlocal conservation law in mo
dern language. Using the techniques of differential coverings [I.S. Krasil
'shchik\, A.M. Vinogradov\, Nonlocal trends in the geometry of differentia
l equations: symmetries\, conservation laws\, and Bäcklund transformation
s\, Acta Appl. Math. 15 (1989) 161-209]\, we show that this observation is
of a quite general nature. We describe the procedures to construct such c
onservation laws and present a number of illustrative examples.\n
LOCATION:https://researchseminars.org/talk/GDEq/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Dafinger (University of Jena\, Germany)
DTSTART;VALUE=DATE-TIME:20201021T162000Z
DTEND;VALUE=DATE-TIME:20201021T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/15
DESCRIPTION:Title: A
converse to Noether's theorem\nby Markus Dafinger (University of Jena\
, Germany) as part of Geometry of differential equations seminar\n\n\nAbst
ract\nThe classical Noether's theorem states that symmetries of a variatio
nal functional lead to conservation laws of the corresponding Euler-Lagran
ge equation. It is a well-known statement to physicists with many applicat
ions. In the talk we investigate a reverse statement\, namely that a diffe
rential equation which satisfies sufficiently many symmetries and correspo
nding conservation laws leads to a variational functional whose Euler-Lagr
ange equation is the given differential equation. The aim of the talk is t
o provide some background of the so-called inverse problem of the calculus
of variations and then to discuss some new results\, for example\, how to
prove the reverse statement.\n
LOCATION:https://researchseminars.org/talk/GDEq/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Sheftel
DTSTART;VALUE=DATE-TIME:20201104T162000Z
DTEND;VALUE=DATE-TIME:20201104T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/17
DESCRIPTION:Title: No
nlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vec
tors\nby Mikhail Sheftel as part of Geometry of differential equations
seminar\n\n\nAbstract\nThe complex Monge-Ampère equation (CMA) in a two-
component form is treated as a bi-Hamiltonian system. I present explicitly
the first nonlocal symmetry flow in each of the two hierarchies of this s
ystem. An invariant solution of CMA with respect to these nonlocal symmetr
ies is constructed which\, being a noninvariant solution in the usual sens
e\, does not undergo symmetry reduction in the number of independent varia
bles. I also construct the corresponding 4-dimensional anti-self-dual (ASD
) Ricci-flat metric with either Euclidean or neutral signature. It admits
no Killing vectors which is one of characteristic features of the famous g
ravitational instanton K3.\n
LOCATION:https://researchseminars.org/talk/GDEq/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierandrea Vergallo (University of Salento)
DTSTART;VALUE=DATE-TIME:20201111T162000Z
DTEND;VALUE=DATE-TIME:20201111T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/18
DESCRIPTION:Title: Hy
drodynamic-type systems and homogeneous Hamiltonian operators: a necessary
condition of compatibility\nby Pierandrea Vergallo (University of Sal
ento) as part of Geometry of differential equations seminar\n\n\nAbstract\
nUsing the theory of coverings\, it is presented a necessary condition to
write a hydrodynamic-type system in Hamiltonian formulation. Explicit cond
itions for first\, second and third order homogeneous Hamiltonian operator
s are shown. In particular\, an alternative proof of Tsarev's theorem abou
t compatibility conditions for first order operators is obtained by using
this method.\n\nThen\, analogous conditions are presented for non local h
omogeneous Hamiltonian operators of first and third order.\n\nFinally\, it
is discussed the projective invariance for second and third order operato
rs.\n\nThe talk is based on a joint work with Raffaele Vitolo.\n
LOCATION:https://researchseminars.org/talk/GDEq/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Losev
DTSTART;VALUE=DATE-TIME:20201118T162000Z
DTEND;VALUE=DATE-TIME:20201118T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/19
DESCRIPTION:Title: Ta
u theory\, d=10 N=1 SUSY and BV\nby Andrey Losev as part of Geometry o
f differential equations seminar\n\n\nAbstract\nPlease\, see https://gdeq.
org/Losev for the abstract.\n
LOCATION:https://researchseminars.org/talk/GDEq/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Lychagin
DTSTART;VALUE=DATE-TIME:20201125T162000Z
DTEND;VALUE=DATE-TIME:20201125T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/20
DESCRIPTION:Title: Di
fferential equations\, their symmetries\, invariants and quotients\nb
y Valentin Lychagin as part of Geometry of differential equations seminar\
n\n\nAbstract\nWe'll discuss quotients of PDEs by their symmetry algebras
and show their applications for integrations.\n
LOCATION:https://researchseminars.org/talk/GDEq/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d'Angers)
DTSTART;VALUE=DATE-TIME:20201202T162000Z
DTEND;VALUE=DATE-TIME:20201202T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/21
DESCRIPTION:Title: Re
al Monge-Ampère operators and (almost) complex structures\nby Vladimi
r Rubtsov (Université d'Angers) as part of Geometry of differential equat
ions seminar\n\n\nAbstract\nWe observe some interesting geometric structur
es which are naturally linked with the geometric approach to Monge-Ampère
operators developed by Lychagin in late 70th.\n\nAmong them are: (almost
) complex\, (almost) product\, generalized complex\, hyperkahler\, hypersy
mplectic and many other geometric structures.\n\nI hope (if I have time) t
o show few interesting examples of its applications.\n
LOCATION:https://researchseminars.org/talk/GDEq/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Mikhailov (University of Leeds)
DTSTART;VALUE=DATE-TIME:20201209T162000Z
DTEND;VALUE=DATE-TIME:20201209T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/22
DESCRIPTION:Title: Qu
antisation ideals of nonabelian integrable systems\nby Alexander Mikha
ilov (University of Leeds) as part of Geometry of differential equations s
eminar\n\n\nAbstract\nIn my talk I'll discuss a new approach to the proble
m of quantisation of dynamical systems\, introduce the concept of quantisa
tion ideals and show meaningful examples. Traditional quantisation theorie
s start with classical Hamiltonian systems with dynamical variables taking
values in commutative algebras and then study their non-commutative defor
mations\, such that the commutators of observables tend to the correspondi
ng Poisson brackets as the (Planck) constant of deformation goes to zero.
I am proposing to depart from systems defined on a free associative algebr
a. In this approach the quantisation problem is reduced to a description o
f two-sided ideals which define the commutation relations (the quantisatio
n ideals) in the quotient algebras and which are invariant with respect to
the dynamics of the system. Surprisingly this idea works rather efficient
ly and in a number of cases I have been able to quantise the system\, i.e.
to find consistent commutation relations for the system. To illustrate t
his approach I'll consider the quantisation problem for the non-abelian Bo
goyavlensky N-chains and other examples\, including quantisation of nonabe
lian integrable ODEs on free associative algebras.\n\nThe talk is based on
: AVM\, Quantisation ideals of nonabelian integrable systems\, arXiv prepr
int arXiv:2009.01838\, 2020
(Published in Russ. Math. Surv. v.75:5\, pp 199-200\, 2020).\n
LOCATION:https://researchseminars.org/talk/GDEq/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Khavkine (Czech Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20201216T162000Z
DTEND;VALUE=DATE-TIME:20201216T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/23
DESCRIPTION:Title: Ki
lling compatibility complex on Kerr spacetime\nby Igor Khavkine (Czech
Academy of Sciences) as part of Geometry of differential equations semina
r\n\n\nAbstract\nThe Killing operator $K_{ab}[v] = \\nabla_a v_b + \\nabla
_b v_a$ on a Lorentzian spacetime $(M\,g)$ plays an important role in Gene
ral Relativity (GR): it generates infinitesimal gauge symmetries of the th
eory. Gauge symmetry invariants play the role of physical observables. In
PDE language\, this translates to the following: the components of a comp
atibility operator for $K_{ab}$ generate all local observables for lineari
zed GR on the background $(M\,g)$. In arXiv:1910.08756 we have explicitly constructed such a compatib
ility operator (indeed\, a full compatibility complex) on the astrophysica
lly interesting Kerr spacetime of a rotating black hole. I will motivate a
nd explain our approach and describe the complexity of the construction.\n
LOCATION:https://researchseminars.org/talk/GDEq/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Kruglikov (UiT the Arctic University of Norway)
DTSTART;VALUE=DATE-TIME:20201223T162000Z
DTEND;VALUE=DATE-TIME:20201223T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/24
DESCRIPTION:Title: Di
spersionless integrable hierarchies and GL(2) geometry\nby Boris Krugl
ikov (UiT the Arctic University of Norway) as part of Geometry of differen
tial equations seminar\n\n\nAbstract\n(joint work with Evgeny Ferapontov)\
n\nParaconformal or GL(2) geometry on an n-dimensional manifold M is defin
ed by a field of rational normal curves of degree n - 1 in the projectiviz
ed cotangent bundle $\\mathbb{P}T^*M$. In dimension n=3 this is nothing bu
t a Lorentzian metric. GL(2) geometry is known to arise on solution spaces
of ODEs with vanishing Wünschmann invariants.\n\nWe show that GL(2) stru
ctures also arise on solutions of dispersionless integrable hierarchies of
PDEs such as the dispersionless Kadomtsev-Petviashvili (dKP) hierarchy. I
n fact\, they coincide with the characteristic variety (principal symbol)
of the hierarchy. GL(2) structures arising in this way possess the propert
y of involutivity. For n=3 this gives the Einstein-Weyl geometry.\n\nThus
we are dealing with a natural generalization of the Einstein-Weyl geometry
. Our main result states that involutive GL(2) structures are governed by
a dispersionless integrable system whose general local solution depends on
2n - 4 arbitrary functions of 3 variables. This establishes integrability
of the system of Wünschmann conditions.\n
LOCATION:https://researchseminars.org/talk/GDEq/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chetverikov
DTSTART;VALUE=DATE-TIME:20210203T162000Z
DTEND;VALUE=DATE-TIME:20210203T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/25
DESCRIPTION:Title: Co
verings and multivector pseudosymmetries of differential equations\nby
Vladimir Chetverikov as part of Geometry of differential equations semina
r\n\n\nAbstract\nFinite-dimensional coverings from systems of differential
equations are investigated. This problem is of interest in view of its re
lationship with the computation of differential substitution\, nonlocal sy
mmetries\, recursion operators\, and Backlund transformations. We show tha
t the distribution specified by the fibers of a covering is determined by
an integrable pseudosymmetry of the system. Conversely\, every integrable
pseudosymmetry of a system defines a covering from this system. The vertic
al component of the pseudosymmetry is a matrix analog of the evolution dif
ferentiation. The corresponding generating matrix satisfies a matrix analo
g of the linearization of the equation. We consider also the exterior prod
uct of vector fields defining a pseudosymmetry. The definition of pseudosy
mmetry is rewritten in the language of the Schouten bracket of multivector
fields and total derivatives with respect to the independent variables of
the system. A method for constructing coverings is given and demonstrated
by the examples of the Laplace equation and the Kapitsa pendulum system.\
n
LOCATION:https://researchseminars.org/talk/GDEq/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Samokhin
DTSTART;VALUE=DATE-TIME:20210210T162000Z
DTEND;VALUE=DATE-TIME:20210210T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/26
DESCRIPTION:Title: On
monotonic pattern in periodic boundary solutions of cylindrical and spher
ical Kortweg-de Vries-Burgers equations\nby Alexey Samokhin as part of
Geometry of differential equations seminar\n\n\nAbstract\nWe studied\, fo
r the Kortweg-de Vries Burgers equations on cylindrical and spherical wave
s\, the development of a regular profile starting from an equilibrium unde
r a periodic perturbation at the boundary.\n\nThe regular profile at the v
icinity of perturbation looks like a periodical chain of shock fronts with
decreasing amplitudes. Further on\, shock fronts become decaying smooth q
uasi periodic oscillations. After the oscillations cease\, the wave develo
ps as a monotonic convex wave\, terminated by a head shock of a constant h
eight and equal velocity. This velocity depends on integral characteristic
s of a boundary condition and on spatial dimensions.\n\nThe explicit asymp
totic formulas for the monotonic part\, the head shock and a median of the
oscillating part are found.\n
LOCATION:https://researchseminars.org/talk/GDEq/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Pushkar
DTSTART;VALUE=DATE-TIME:20210217T162000Z
DTEND;VALUE=DATE-TIME:20210217T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/27
DESCRIPTION:Title: Mo
rse theory\, Bruhat cells and Unitriangular geometry\nby Petr Pushkar
as part of Geometry of differential equations seminar\n\n\nAbstract\nStron
g Morse function is a Morse function with pairwise different critical valu
es. For such a function we construct a collection of numbers\, which is a
(smooth) topological invariant of the strong Morse function.\n\nAlgebraica
lly our construction is a close relative of the construction of Bruhat cel
ls and belongs to Unitriangular geometry. We will present a generalization
of determinant of any linear map between finite dimensional vector spaces
.\n\nTalk based on a joint work with Misha Temkin.\n
LOCATION:https://researchseminars.org/talk/GDEq/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sokolov (Landau Institute for Theoretical Physics\, Chern
ogolovka\, Russia)
DTSTART;VALUE=DATE-TIME:20210224T162000Z
DTEND;VALUE=DATE-TIME:20210224T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/28
DESCRIPTION:Title: No
n-Abelian generalizations of integrable PDEs and ODEs\nby Vladimir Sok
olov (Landau Institute for Theoretical Physics\, Chernogolovka\, Russia) a
s part of Geometry of differential equations seminar\n\n\nAbstract\nA gene
ral procedure for nonabelinization of given integrable polynomial differen
tial equation is described. We consider NLS type equations as an example.
We also find nonabelinizations of the Euler top and of the Painleve-2 equa
tion.\n\nAlthough the talk will be in Russian\, the slides will be in Engl
ish and the discussion will be in both languages.\n
LOCATION:https://researchseminars.org/talk/GDEq/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d'Angers)
DTSTART;VALUE=DATE-TIME:20210303T162000Z
DTEND;VALUE=DATE-TIME:20210303T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/29
DESCRIPTION:Title: Re
al Monge-Ampère operators and (almost) complex structures. Part 2\nby
Vladimir Rubtsov (Université d'Angers) as part of Geometry of differenti
al equations seminar\n\n\nAbstract\nWe observe some interesting geometric
structures which are naturally linked with the geometric approach to Monge
-Ampère operators developed by Lychagin in late 70th. I shall concentrate
my attention on the Hitchin generalized complex structure\, hyper-Kahler/
symplectic and hope to show few interesting examples of its relations with
the Monge-Ampère operators and applications.\n
LOCATION:https://researchseminars.org/talk/GDEq/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Pavlov
DTSTART;VALUE=DATE-TIME:20210310T162000Z
DTEND;VALUE=DATE-TIME:20210310T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/30
DESCRIPTION:Title: Ne
w variational principles for one-dimensional gas dynamics and for Egorov h
ydrodynamic type systems\nby Maxim Pavlov as part of Geometry of diffe
rential equations seminar\n\n\nAbstract\nThe Statement. If some Egorov hyd
rodynamic type system has one local Hamiltonian structure of Dubrovin-Novi
kov type\, then such a system possesses infinitely many: local Hamiltonian
structures of all odd orders\, and infinitely many local Lagrangian repre
sentations.\n
LOCATION:https://researchseminars.org/talk/GDEq/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladislav Zhvick
DTSTART;VALUE=DATE-TIME:20210317T162000Z
DTEND;VALUE=DATE-TIME:20210317T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/31
DESCRIPTION:Title: No
nlocal conservation law in a submerged jet\nby Vladislav Zhvick as par
t of Geometry of differential equations seminar\n\nLecture held in room 30
3 of the Independent University of Moscow.\n\nAbstract\nLandau was the fir
st to obtain the exact solution of Navier-Stokes equations for an axisymme
tric submerged jet generated by a point momentum source. The Landau jet is
the main term of a coordinate expansion of the flow far field in the case
when the flow is generated by a finite size source (for example\, a tube
with flow). The next term of the expansion was calculated by Rumer. This t
erm has an indefinite coefficient. To determine this coefficient we need a
conservation law connecting the jet far field with the source. Well-known
conservation laws of mass\, momentum\, and angular momentum fail to calcu
late the coefficient. In my talk\, I will solve this problem for low visco
sity. In this case\, the flow satisfies the boundary layer equations that
possess a nonlocal conservation law closing the problem. The problem for a
n arbitrary viscosity remains open.\n
LOCATION:https://researchseminars.org/talk/GDEq/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anatolij Prykarpatski
DTSTART;VALUE=DATE-TIME:20210324T162000Z
DTEND;VALUE=DATE-TIME:20210324T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/32
DESCRIPTION:Title: On
integrability of some Riemann type hydrodynamical systems and Dubrovin in
tegrability classification of perturbed Korteweg-de Vries type equations\nby Anatolij Prykarpatski as part of Geometry of differential equations
seminar\n\n\nAbstract\nIn our report we will stop on two closely related
to each other integrability theory aspects. The first one concerns the obt
ained integrability results\, based on the gradient-holonomic integrabilit
y scheme\, devised and applied by me jointly with Maxim Pavlov and collabo
rators to a virtually new important Riemann type hierarchy $D_{t}^{N-1}u=z
_{x}^{s}$\, $D_{t}z=0$\, where $s$\, \;$N\\in N$ are arbitrary natural
numbers\, and proposed in our work (M. Pavlov\, A. Prykarpatsky\, at al.\
, arXiv:1108.0878) as a nont
rivial generalization of the infinite hierarchy of the Riemann type flows\
, suggested before by M. Pavlov and D. Holm in the form of dynamical syste
ms $D_{t}^{N}u=0$\, defined on a $2\\pi$-periodic functional manifold $M^{
N}\\subset C^{\\infty}( R/2\\pi Z\; R^{N})$\, the vector $(u\,D_{t}u\,D_{t
}²u\,...\,D_{t}^{N-1}u\,z)^{\\intercal}\\in M^{N}$\, the differentiations
$D_{x}:=\\partial/\\partial x$\, $D_{t}:=\\partial/\\partial t+u\\partial
/\\partial x$ satisfy as above the Lie-algebraic commutator relationship $
[D_{x}\,D_{t}]=u_{x}D_{x}$ and t\\in R is an evolution parameter. The seco
nd aspect of our report concerns the integrability results obtained by B.
Dubrovin jointly with Y. Zhang and collaborators\, devoted to classificati
on of a special perturbation of the Korteweg-de Vries equation in the form
$u_{t}=uu_{x}+\\epsilon^2[f_{31}(u)u_{xxx}+f_{32}(u)u_{xx}u_{x}+f_{33}(u)
u_{x}^3]$\, where $f_{jk}(u)\,~j=3\,~k=1\,~3$\, are some smooth functions
and \\epsiln\\in R is a real parameter. We will deal with classification s
cheme of evolution equations of a special type suspicious on being integra
ble which was devised some years ago by untimely passed away Prof. Boris D
ubrovin (19 March 2019) and developed with his collaborators\, mainly with
Youjin Zhang. We have reanalyzed in detail their interesting results on i
ntegrability classification of a suitably perturbed KdV type equation with
in our gradient-holonomic integrability scheme\, devised many years ago an
d developed by me jointly with Maxim Pavlov and collaborators\, and found
out that the Dubrovin's scheme has missed at least a one very interesting
integrable equation\, whose natural reduction became similar to the well-k
nown Krichever-Novikov equation\, yet different from it. As a consequence
of the analysis\, we presented one can firmly claim that the Dubrovin-Zhan
g integrability criterion inherits some important part of the mentioned ab
ove gradient-holonomic integrability scheme properties\, coinciding with t
he statement about the necessary existence of suitably ordered reduction e
xpansions with coefficients to be strongly homogeneous differential polyno
mials.\n\nJoint with Alex A. Balinsky\, Radoslaw Kycia and Yarema A. Pryka
rpatsky.\n\nAlthough the talk will be in Russian\, the slides will be in E
nglish and the discussion will be in both languages.\n
LOCATION:https://researchseminars.org/talk/GDEq/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hovhannes Khudaverdian
DTSTART;VALUE=DATE-TIME:20210331T162000Z
DTEND;VALUE=DATE-TIME:20210331T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/33
DESCRIPTION:Title: Od
d symplectic geometry in the BV-formalism\nby Hovhannes Khudaverdian a
s part of Geometry of differential equations seminar\n\nLecture held in ro
om 304 of the Independent University of Moscow.\n\nAbstract\nOdd symplecti
c geometry was considered by physicists as an exotic counterpart of even s
ymplectic geometry. Batalin and Vilkovisky changed this\npoint of view by
the seminal work considering the quantisation of general theory in Lagrang
ian framework\, where they considered odd symplectic superspace of fields
and antifields. [In the case of Lie group of symmetries BV receipt is redu
ced to the standard Faddeev-Popov method.]\n\nThe main ingredient of the t
heory\, the exponent of the master action\, is defined by the function $f$
such that $\\Delta f=0$\, where $\\Delta$ is second order differential op
erator of the second order: $\\Delta=\\frac{\\partial^2}{\\partial x^i \\p
artial\\theta_i}$\, ($x^i\,\\theta_j$ are the Darboux coordinates of an od
d symplectic superspace.) This operator has no analogy in the standard sym
plectic geometry.\n\nI consider in this talk the main properties of the BV
-formalism geometry.\n\nThe $\\Delta$-operator is defined in geometrical c
lear way\, and this operator depends on the volume form.\n\nIt is suggeste
d the canonical operator $\\Delta$ on half-densities. This operator is the
proper framework for BV geometry. We also study the groupoid property of
BV master-equation\; this leads us to the notion of BV groupoid. We also d
iscuss some constructions of invariants for odd symplectic structure.\n
LOCATION:https://researchseminars.org/talk/GDEq/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Lychagin
DTSTART;VALUE=DATE-TIME:20210407T162000Z
DTEND;VALUE=DATE-TIME:20210407T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/34
DESCRIPTION:Title: On
dynamics of molecular media and generalization of Navier-Stokes equations
\nby Valentin Lychagin as part of Geometry of differential equations s
eminar\n\nLecture held in room 304 of the Independent University of Moscow
.\n\nAbstract\nThis talk is a prolongation of my previous talk that was de
voted to continuum mechanics of media possessing inner structure.\n\nHere
we'll consider molecular media\, its geometry and thermodynamics.\n\nThe m
ain goal of this talk is to present in the explicit form necessary geometr
ical structures and to give the explicit form of the Navier-Stokes equatio
ns.\n
LOCATION:https://researchseminars.org/talk/GDEq/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Morozov
DTSTART;VALUE=DATE-TIME:20210421T162000Z
DTEND;VALUE=DATE-TIME:20210421T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/35
DESCRIPTION:Title: La
x representations via twisted extensions of infinite-dimensional Lie algeb
ras: some new results\nby Oleg Morozov as part of Geometry of differen
tial equations seminar\n\nLecture held in room 304 of the Independent Univ
ersity of Moscow.\n\nAbstract\nI will discuss the technique for constructi
ng integrable differential equations via twisted extensions of infinite-di
mensional Lie algebras. Examples will include a 3D generalization of the H
unter-Saxton equation with the special value of the parameter and the "deg
enerate heavenly equation".\n
LOCATION:https://researchseminars.org/talk/GDEq/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taras Skrypnyk
DTSTART;VALUE=DATE-TIME:20210428T162000Z
DTEND;VALUE=DATE-TIME:20210428T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/36
DESCRIPTION:Title: As
ymmetric variable separation for the Clebsch model\nby Taras Skrypnyk
as part of Geometry of differential equations seminar\n\n\nAbstract\nIn th
e present talk we present our result on separation of variables (SoV) for
the Clebsch model.\n\nIn particular\, we report on the development of two
methods in the variable separation theory:\n\n - the method of the
differential separability conditions\;
\n - the method of the vecto
r fields $Z$.
\n

\nUsing these two methods we construct an asymmet
ric variable separation for the Clebsch model. Our SoV is unusual: it is c
haracterized by two different curves of separation. We explicitly construc
t coordinates and momenta of separation\, the reconstruction formulae and
the Abel-type quadratures for the Clebsch system. The solution of the non-
standard Abel-Jacobi inversion problem is briefly discussed.\n
LOCATION:https://researchseminars.org/talk/GDEq/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Sachkov
DTSTART;VALUE=DATE-TIME:20210414T162000Z
DTEND;VALUE=DATE-TIME:20210414T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/37
DESCRIPTION:Title: Su
b-Riemannian geometry on the group of motions of the plane\nby Yuri Sa
chkov as part of Geometry of differential equations seminar\n\n\nAbstract\
nWe will discuss the unique\, up to local isometries\, contact sub-Riemann
ian struc\nture on the group SE(2) of proper motions of the plane (aka gro
up of rototransla\ntions).\nThe following questions will be addressed:\n\n \; geodesics\,\n &nb
sp\; their local and global optimality\,\n \; cut time\, cu
t locus\, and spheres\,\n \; infinite geodesics\,\n <
li> \; bicycle transform and relation of geodesics with Euler elastica
e\,\n \; group of isometries and homogeneous geodesics\,\n \; applications to imaging and robotics.\n\nJoint
work with Andrei Ardentov.\n
LOCATION:https://researchseminars.org/talk/GDEq/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Ferapontov (Loughborough University)
DTSTART;VALUE=DATE-TIME:20210505T162000Z
DTEND;VALUE=DATE-TIME:20210505T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/38
DESCRIPTION:Title: Se
cond-order PDEs in 3D with Einstein-Weyl conformal structure\nby Eugen
e Ferapontov (Loughborough University) as part of Geometry of differential
equations seminar\n\n\nAbstract\nI will discuss a general class of second
-order PDEs in 3D whose characteristic conformal structure satisfies the E
instein-Weyl conditions on every solution.\n\nThis property is known to be
equivalent to the existence of a dispersionless Lax pair\, as well as to
other equivalent definitions of dispersionless integrability.\n\nI will de
monstrate that (a) the Einstein-Weyl conditions can be viewed as an effici
ent contact-invariant test of dispersionless integrability\, (b) show some
partial classification results\, and (c) formulate a rigidity conjecture
according to which any second-order PDE with Einstein-Weyl conformal struc
ture can be reduced to a dispersionless Hirota form via a suitable contact
transformation.\n\nBased on joint work with S. Berjawi\, B. Kruglikov\, V
. Novikov.\n
LOCATION:https://researchseminars.org/talk/GDEq/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Zabrodin
DTSTART;VALUE=DATE-TIME:20210519T162000Z
DTEND;VALUE=DATE-TIME:20210519T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/39
DESCRIPTION:Title: Ka
domtsev-Petviashvili hierarchies of types B and C\nby Anton Zabrodin a
s part of Geometry of differential equations seminar\n\nLecture held in ro
om 303 or 304 of the Independent University of Moscow.\n\nAbstract\nThis i
s a short review of the Kadomtsev-Petviashvili hierarchies of types B and
C. The main objects are the $L$-operator\, the wave operator\, the auxilia
ry linear problems for the wave function\, the bilinear identity for the w
ave function and the tau-function. All of them are discussed in the paper.
The connections with the usual Kadomtsev-Petviashvili hierarchy (of the t
ype A) are clarified. Examples of soliton solutions and the dispersionless
limit of the hierarchies are also considered.\n
LOCATION:https://researchseminars.org/talk/GDEq/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgy Sharygin
DTSTART;VALUE=DATE-TIME:20210512T162000Z
DTEND;VALUE=DATE-TIME:20210512T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/40
DESCRIPTION:Title: Op
erations on universal enveloping algebra and the "argument shift" method\nby Georgy Sharygin as part of Geometry of differential equations semin
ar\n\nLecture held in room 303 or 304 of the Independent University of Mos
cow.\n\nAbstract\nIf a vector field X is given on a Poisson manifold M suc
h that the square of the Lie derivative in the X direction "kills" the Poi
sson bivector\, then there is a well-known simple method of "shifting the
argument" (along X) to construct a commutative subalgebra (with respect to
the Poisson bracket) inside the algebra of functions on M. In a particula
r case\, this method can be applied to the Poisson-Lie bracket on the symm
etric algebra of an arbitrary Lie algebra and gives (according to a well-k
nown result\, the proven Mishchenko-Fomenko conjecture) maximal commutativ
e subalgebras in the symmetric algebra. However\, the lifting of these alg
ebras to commutative subalgebras in the universal enveloping algebra\, alt
hough possible\, is based on very nontrivial results from the theory of in
finite-dimensional Lie algebras. In my talk\, I will describe partial resu
lts that allow one to construct on the universal enveloping algebra of the
algebra $gl_{n}$￼ the operators of "quasidifferentiation" and with thei
r help\, in some cases\, construct a commutative subalgebra in $Ugl_{n}$
￼. I will also describe how\, in the general case\, this question is red
uced to the combinatorial question of commuting a certain set of operators
in tensor powers $\\mathbb {R} ^{n}$￼. The story is based on collaborat
ions with Dmitry Gurevich\, Pavel Saponov and Ikeda Yasushi.\n
LOCATION:https://researchseminars.org/talk/GDEq/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Lychagin
DTSTART;VALUE=DATE-TIME:20210922T162000Z
DTEND;VALUE=DATE-TIME:20210922T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/41
DESCRIPTION:Title: On
metric invariants of spherical harmonics\nby Valentin Lychagin as par
t of Geometry of differential equations seminar\n\nLecture held in room 30
3 of the Independent University of Moscow.\n\nAbstract\nWe'll discuss the
algebraic and differential SO(3)-invariants of spherical harmonics and giv
e a description of fields of rational algebraic and rational differential
invariants together with their application to the description of regular S
O(3)-orbits of spherical harmonics.\n
LOCATION:https://researchseminars.org/talk/GDEq/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raffaele Vitolo (Università del Salento)
DTSTART;VALUE=DATE-TIME:20211006T162000Z
DTEND;VALUE=DATE-TIME:20211006T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/43
DESCRIPTION:Title: WD
VV equations and invariant bi-Hamiltonian formalism\nby Raffaele Vitol
o (Università del Salento) as part of Geometry of differential equations
seminar\n\n\nAbstract\nThe WDVV equations are central in Topological Field
Theory and Integrable Systems. We prove that in low dimensions the WDVV e
quations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalis
m is proved for N = 3. More examples in higher dimensions show that the re
sult might hold in general. The invariance group of the bi-Hamiltonian pai
rs is the group of projective reciprocal transformations. The significance
of projective invariance of WDVV equations is discussed in detail. Comput
er algebra programs that were used for calculations throughout the paper a
re provided at https://github.com/Jakub-Vasicek/WDVV-computations/.\n\nBas
ed on a joint work with Jakub Vašíček.\n
LOCATION:https://researchseminars.org/talk/GDEq/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Khavkine (Czech Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20211020T162000Z
DTEND;VALUE=DATE-TIME:20211020T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/44
DESCRIPTION:Title: Tr
iangular decoupling of systems of differential equations\, with applicatio
n to separation of variables on Schwarzschild spacetime\nby Igor Khavk
ine (Czech Academy of Sciences) as part of Geometry of differential equati
ons seminar\n\n\nAbstract\nCertain tensor wave equations admit a complete
separation of variables on the Schwarzschild spacetime (asymptotically fla
t\, static\, spherically symmetric black hole in 4d)\, resulting in compli
cated systems of radial mode ODEs. Almost none of the important questions
about these radial mode equations can be answered in their original form.
I will discuss a drastic simplification of these ODE systems to sparse upp
er triangular form\, which uncovers their general properties. Essential to
this simplification are geometric properties of the original tensor wave
equations\, ideas from homological algebra and from the theory of ODEs wit
h rational coefficients. Based on https://arxiv.org/abs/1711.00585 \, http
s://arxiv.org/abs/1801.09800 \, https://arxiv.org/abs/2004.09651\n
LOCATION:https://researchseminars.org/talk/GDEq/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Morozov
DTSTART;VALUE=DATE-TIME:20211027T162000Z
DTEND;VALUE=DATE-TIME:20211027T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/45
DESCRIPTION:Title: In
tegrable PDEs and extensions of Lie-Rinehart algebras\nby Oleg Morozov
as part of Geometry of differential equations seminar\n\nLecture held in
room 303 of the Independent University of Moscow.\n\nAbstract\nI will disc
uss extensions of Lie-Rinehart algebras and their application to the probl
em of recognizing whether a given PDE admits a Lax representation.\n
LOCATION:https://researchseminars.org/talk/GDEq/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Ferapontov (Loughborough University)
DTSTART;VALUE=DATE-TIME:20211201T162000Z
DTEND;VALUE=DATE-TIME:20211201T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/46
DESCRIPTION:Title: Se
cond order integrable Lagrangians and WDVV equations\nby Eugene Ferapo
ntov (Loughborough University) as part of Geometry of differential equatio
ns seminar\n\n\nAbstract\nI will discuss integrability of 2D and 3D Euler-
Lagrange equations for second-order Lagrangians. A link to WDVV equations
will be established. Based on joint work with Maxim Pavlov and Lingling Xu
e.\n
LOCATION:https://researchseminars.org/talk/GDEq/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Kotov
DTSTART;VALUE=DATE-TIME:20211013T162000Z
DTEND;VALUE=DATE-TIME:20211013T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/48
DESCRIPTION:Title: Ri
emannian Cartan-Lie algebroids and groupoids and curved Yang-Mills-Higgs m
odels\nby Alexei Kotov as part of Geometry of differential equations s
eminar\n\n\nAbstract\nIn this talk the generalization of the Yang-Mills-Hi
ggs model will be presented\, based upon the notion of Cartan structures a
nd compatible metrics on Lie algebroids and groupoids.\n
LOCATION:https://researchseminars.org/talk/GDEq/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Doubrov
DTSTART;VALUE=DATE-TIME:20211124T162000Z
DTEND;VALUE=DATE-TIME:20211124T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/49
DESCRIPTION:Title: On
Cartan's C-class differential equations\nby Boris Doubrov as part of
Geometry of differential equations seminar\n\nLecture held in room 303 of
the Independent University of Moscow.\n\nAbstract\nWe consider a very spec
ial class of differential equations\, which is characterized by the condit
ion that all its local differential invariants (under the action of a suit
able Lie pseudogroup) become first integrals when restricted to the equati
on manifold. Such differential equations were introduced in a short note o
f Elie Cartan (Les espaces généralisés et l'intégration de certaines c
lasses d'équations différentielles\, C.R.\, 1938\, V.206\, N.23\, 1689-1
693)\, who characterized them in two simplest cases: scalar 2nd order ODEs
viewed under the pseudogroup of point transformations and scalar 3rd orde
r ODEs under the group of contact transformations. We show how these resul
ts generalize to any systems of ODEs and\, more generally\, differential e
quations of finite type. The same question for arbitrary systems of PDEs s
till remains open.\n
LOCATION:https://researchseminars.org/talk/GDEq/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eivind Schneider
DTSTART;VALUE=DATE-TIME:20211110T162000Z
DTEND;VALUE=DATE-TIME:20211110T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/50
DESCRIPTION:Title: Di
fferential invariants of Kundt spacetimes\nby Eivind Schneider as part
of Geometry of differential equations seminar\n\n\nAbstract\nWe compute g
enerators for the algebra of rational scalar differential invariants of ge
neral and degenerate Kundt spacetimes. Special attention is given to dimen
sions 3 and 4 since in those dimensions the degenerate Kundt metrics are k
nown to be exactly the Lorentzian metrics that can not be distinguished by
polynomial curvature invariants constructed from the Riemann tensor and i
ts covariant derivatives.\n\nThe talk is based on joint work with Boris Kr
uglikov.\n
LOCATION:https://researchseminars.org/talk/GDEq/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Duyunova and Sergey Tychkov
DTSTART;VALUE=DATE-TIME:20211103T162000Z
DTEND;VALUE=DATE-TIME:20211103T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/51
DESCRIPTION:Title: Th
e Euler system on a space curve\nby Anna Duyunova and Sergey Tychkov a
s part of Geometry of differential equations seminar\n\n\nAbstract\nWe con
sider flows of an inviscid medium on a space curve in a constant gravitati
onal field (the Euler system). We discuss symmetries and differential inva
riants of the Euler system\, and give their classification based on symmet
ries group of the system. Using differential invariants for this system\,
we obtain its quotient. The solutions of the quotient equation that are co
nstant along characteristic vector field provide some solutions of the Eul
er system.\n\nJoint work with Valentin Lychagin.\n
LOCATION:https://researchseminars.org/talk/GDEq/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Igonin
DTSTART;VALUE=DATE-TIME:20211229T162000Z
DTEND;VALUE=DATE-TIME:20211229T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/52
DESCRIPTION:Title: Al
gebra and geometry of Lax representations and Bäcklund transformations fo
r (1+1)-dimensional partial differential and differential-difference equat
ions\nby Sergei Igonin as part of Geometry of differential equations s
eminar\n\n\nAbstract\nSee IgoninSeminar20211229abstract.pdf\n
LOCATION:https://researchseminars.org/talk/GDEq/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hynek Baran
DTSTART;VALUE=DATE-TIME:20211208T162000Z
DTEND;VALUE=DATE-TIME:20211208T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/53
DESCRIPTION:Title: Je
ts\, a computer algebra on diffieties\nby Hynek Baran as part of Geome
try of differential equations seminar\n\n\nAbstract\nJets is a set of Mapl
e procedures to facilitate solution of differential equations in total der
ivatives on diffieties. Otherwise said\, Jets is a tool to compute symmetr
ies\, conservation laws\, zero-curvature representations\, recursion opera
tors\, any many other invariants of systems of partial differential equati
ons.\n
LOCATION:https://researchseminars.org/talk/GDEq/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Grigoriev
DTSTART;VALUE=DATE-TIME:20211117T162000Z
DTEND;VALUE=DATE-TIME:20211117T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/54
DESCRIPTION:Title: Pr
esymplectic gauge PDEs and Batalin-Vilkovisky formalism\nby Maxim Grig
oriev as part of Geometry of differential equations seminar\n\nLecture hel
d in room 303 of the Independent University of Moscow.\n\nAbstract\nGauge
PDE is a geometrical object underlying what physicists call a local gauge
field theory defined at the level of equations of motion (i.e. without sp
ecifying Lagranian) in terms of BV-BRST formalism. Although gauge PDE can
be defined as a PDE equipped with extra structures\, the generalization is
not entirely straightforward as\, for instance\, two gauge PDEs can be eq
uivalent even if the underlying PDEs are not. As far as Lagrangian gauge s
ystems are concerned the powerful framework is provided by the BV formalis
m on jet-bundles. However\, just like in the case of usual PDEs it is diff
icult to encode the BV extension of the Lagrangian in terms of the intrins
ic geometry of the equation manifold while working on jet-bundles is often
very restrictive\, especially in analyzing boundary behaviour\, e.g.\, in
the context of AdS/CFT correspondence. We show that BV Lagrangian (or its
weaker analogs) can be encoded in the compatible graded presymplectic str
ucture on the gauge PDE. In the case of genuine Lagrangian systems this pr
esymplectic structure is related to a certain completion of the canonical
BV symplectic structure. A presymplectic gauge PDE gives rise to a BV form
ulation of the underlying system through an appropriate generalization of
the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) sigma-model constructi
on followed by taking the symplectic quotient. The construction is illustr
ated on the standard examples of gauge theories with particular emphasis o
n the Einstein gravity\, where this naturally leads to an elegant presympl
ectic AKSZ representation of the BV extension of the Cartan-Weyl formulati
on of gravity.\n
LOCATION:https://researchseminars.org/talk/GDEq/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Vojčák
DTSTART;VALUE=DATE-TIME:20211208T162000Z
DTEND;VALUE=DATE-TIME:20211208T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/55
DESCRIPTION:Title: On
the algebras of nonlocal symmetries for the (modified) 4D Martı́nez Alo
nso-Shabat equation\nby Petr Vojčák as part of Geometry of different
ial equations seminar\n\n\nAbstract\nWe consider two four-dimensional Lax-
integrable equations known as the 4D Martı́nez Alonso-Shabat equation an
d the modified Martı́nez Alonso-Shabat equation\, respectively. We const
ruct two differential coverings for both of them and describe the algebras
of nonlocal symmetries in these coverings. We also analyze the actions of
the known recursion operators on these nonlocal symmetries.\n\nPartially
based on a joint work with Joseph Krasil'shchik.\n
LOCATION:https://researchseminars.org/talk/GDEq/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Agafonov
DTSTART;VALUE=DATE-TIME:20220209T162000Z
DTEND;VALUE=DATE-TIME:20220209T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/56
DESCRIPTION:Title: Da
rboux integrability for diagonal systems of hydrodynamic type\nby Serg
ey Agafonov as part of Geometry of differential equations seminar\n\nLectu
re held in room 303 of the Independent University of Moscow.\n\nAbstract\n
We prove that diagonal systems of hydrodynamic type are Darboux integrable
if and only if the Laplace transformation sequences of the system for com
muting flows terminate\, give geometric interpretation for Darboux integra
bility of such systems in terms of congruences of lines and in terms of so
lution orbits with respect to symmetry subalgebras\, show that Darboux int
egrable systems are necessarily semihamiltonian\, and discuss known and ne
w examples.\n
LOCATION:https://researchseminars.org/talk/GDEq/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Kruglikov (UiT the Arctic University of Norway)
DTSTART;VALUE=DATE-TIME:20220223T162000Z
DTEND;VALUE=DATE-TIME:20220223T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/57
DESCRIPTION:Title: OD
Es with essential contact or point symmetries\nby Boris Kruglikov (UiT
the Arctic University of Norway) as part of Geometry of differential equa
tions seminar\n\nLecture held in room 303 of the Independent University of
Moscow.\n\nAbstract\n(joint work with Eivind Schneider)\n\nWe observe tha
t\, up to conjugation\, a majority of higher order ODEs and ODE systems ha
ve only point fiber-preserving symmetries (surprisingly this is also true
for "most interesting" ODEs). We describe all the exceptions in the case o
f scal ar ODEs and systems of pairs of ODEs on a pair of functions. We exp
loit classifications of Lie algebras of vector fields in 2 and 3 dimension
s.\n\nWhile we can express scalar ODEs with essentially contact or point s
ymmetry algebras via absolute and relative differential invariants\, we ha
ve to invoke also conditional differential invariants in the case of ODE s
ystems to deal with singular orbits of the action. In the scalar case the
result is partially due to Lie\, but we consider the global classification
and discuss the algebra of relative invariants. For systems the result is
new.\n\nInvestigating prolongations of the actions\, we observe some inte
resting relations between different realizations of Lie algebras. We also
note that prolongation of a finite-dimensional Lie algebra acting on a dif
ferential equation may not eventually become free. An example of underdete
rmined ODE with this phenomenon shows limitations of the method of moving
frames.\n
LOCATION:https://researchseminars.org/talk/GDEq/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitri Alekseevsky
DTSTART;VALUE=DATE-TIME:20220316T162000Z
DTEND;VALUE=DATE-TIME:20220316T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/59
DESCRIPTION:Title: Sp
ecial Vinberg cones and their applications\nby Dmitri Alekseevsky as p
art of Geometry of differential equations seminar\n\nLecture held in room
303 of the Independent University of Moscow.\n\nAbstract\nThe talk is base
d on joint works with Vicete Cortes\, Andrea Spiro and Alessio Marrani.\n\
nA short survey of the Vinberg theory of convex cones (including its infor
mational geometric interpretation) and homogeneous convex cones will be pr
esented. Then we concentrate on the theory of rank 3 special Vinberg cones
\, associated to metric Clifford $Cl({\\mathbb R}^n)$ modules.\n\nA genera
lization of the theory to the indefinite special Vinberg cones\, associate
d to indefinite metric Clifford $Cl({\\mathbb R}^{p\,q})$ modules is indic
ated. An application of special Vinberg cones to $N=2 \, \\\, d=5\,4\,3$ S
upergravity will be considered.\n\nWe will discuss also applications of th
eory of homogeneous convex cones to convex programming\, information geome
try and Frobenius manifolds.\n
LOCATION:https://researchseminars.org/talk/GDEq/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d'Angers)
DTSTART;VALUE=DATE-TIME:20220309T162000Z
DTEND;VALUE=DATE-TIME:20220309T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/60
DESCRIPTION:Title: Mu
ltiplicative kernels\, Non-abelian Abel theorem\, Kontsevich polynomials a
nd around. Part 1\nby Vladimir Rubtsov (Université d'Angers) as part
of Geometry of differential equations seminar\n\n\nAbstract\nWe discuss re
cent progress (published and unpublished yet ) in studies of multiplicativ
e kernels\, initiated by M. Konstevich. We will try to explain various lin
ks and applications of this notion in geometry\, differential equations an
d integrable systems. My talk is based on the paper arXiv:2102.09511 and on two ongoing projects with
I. Gaiur and D. Van Straten.\n
LOCATION:https://researchseminars.org/talk/GDEq/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Lychagin
DTSTART;VALUE=DATE-TIME:20220413T162000Z
DTEND;VALUE=DATE-TIME:20220413T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/61
DESCRIPTION:Title: Na
tural invariants and classification of quasilinear second-order differenti
al operators\nby Valentin Lychagin as part of Geometry of differential
equations seminar\n\nLecture held in room 303 of the Independent Universi
ty of Moscow.\n\nAbstract\nThis talk is based on joint research with Valer
y Yumaguzhin.\n\nIn the first part\, we outline the method of finding rati
onal natural differential invariants of a class of quasilinear second-orde
r differential operators\, and then we show how these invariants could be
used to get local as well as global classification of such type operators
with respect to the diffeomorphism group.\n
LOCATION:https://researchseminars.org/talk/GDEq/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitri Gurevich
DTSTART;VALUE=DATE-TIME:20220330T162000Z
DTEND;VALUE=DATE-TIME:20220330T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/62
DESCRIPTION:Title: Qu
antum Matrix Algebras and their applications\nby Dimitri Gurevich as p
art of Geometry of differential equations seminar\n\n\nAbstract\nQuantum M
atrix Algebras are very interesting objects from algebraic viewpoint. Part
icular examples of these algebras are related to Drinfeld-Jimbo Quantum Gr
oups. Some of these QMA admit defining analogs of partial derivatives. In
a limit it is possible to develop a new calculus on the enveloping algebra
s $U(gl(N))$.\n\nOther applications will be discussed.\n
LOCATION:https://researchseminars.org/talk/GDEq/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d'Angers)
DTSTART;VALUE=DATE-TIME:20220406T162000Z
DTEND;VALUE=DATE-TIME:20220406T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/63
DESCRIPTION:Title: Mu
ltiplicative kernels\, Non-abelian Abel theorem\, Kontsevich polynomials a
nd around. Part 2\nby Vladimir Rubtsov (Université d'Angers) as part
of Geometry of differential equations seminar\n\n\nAbstract\nA continuatio
n of the talk on 9 Ma
rch.\n\nWe discuss recent progress (published and unpublished yet) in
studies of multiplicative kernels\, initiated by M. Konstevich. We will tr
y to explain various links and applications of this notion in geometry\, d
ifferential equations and integrable systems. My talk is based on the pape
r arXiv:2102.09511 and on t
wo ongoing projects with I. Gaiur and D. Van Straten.\n
LOCATION:https://researchseminars.org/talk/GDEq/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Marshall
DTSTART;VALUE=DATE-TIME:20220504T162000Z
DTEND;VALUE=DATE-TIME:20220504T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/64
DESCRIPTION:Title: On
action-angle duality\nby Ian Marshall as part of Geometry of differen
tial equations seminar\n\nLecture held in room 303 of the Independent Univ
ersity of Moscow.\n\nAbstract\nAction-angle duality is a property enjoyed
by systems of Ruijsenaars type - many body systems\; relativistic analogue
s of Calogero-Moser-Sutherland systems - whereby families of integrable sy
stems come in natural pairs: the canonical coordinates of one system are t
he action-angle variables of the other\, and together they generate the wh
ole phase space. I will explain this property\, and why it is special. Whe
n transported to quantum systems\, the action-angle duality property is re
presented in the form of bispectral operators.\n\nI hope also to describe
results obtained with László Fehér in which Hamiltonian reduction is us
ed to obtain systems in action-angle duality relation with one an other.\n
LOCATION:https://researchseminars.org/talk/GDEq/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Gaiur (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20220511T162000Z
DTEND;VALUE=DATE-TIME:20220511T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/65
DESCRIPTION:Title: Ha
miltonian reduction and rational Calogero system\nby Ilia Gaiur (Unive
rsity of Birmingham) as part of Geometry of differential equations seminar
\n\n\nAbstract\nIn my talk I am going to give an introduction to the theor
y of the moment map for the Hamiltonian group action on the symplectic man
ifolds with the focus on Hamiltonian reduction and integrable systems. In
particular\, I will show how to translate symmetries of the Hamiltonian sy
stem to the first integrals using the moment map and what kind of systems
we may obtain by performing such reduction. As the main example\, I will d
emonstrate how to obtain a rational Calogero system from the free particle
system on the cotangent bundle to the Lie algebra $su(n)$.\n
LOCATION:https://researchseminars.org/talk/GDEq/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Smilga
DTSTART;VALUE=DATE-TIME:20220518T162000Z
DTEND;VALUE=DATE-TIME:20220518T180000Z
DTSTAMP;VALUE=DATE-TIME:20220528T073854Z
UID:GDEq/66
DESCRIPTION:Title: No
ncommutative quantum mechanical systems associated with Lie algebras\n
by Andrei Smilga as part of Geometry of differential equations seminar\n\n
\nAbstract\nWe consider quantum mechanics on the noncommutative spaces cha
racterized by the commutation relations\n$$ [x_a\, x_b] \\ =\\ i\\theta f_
{abc} x_c\\\,\, $$\nwhere $f_{abc}$ are the structure constants of a Lie a
lgebra. We note that this problem can be reformulated as an ordinary quant
um problem in a commuting {\\it momentum} space. The coordinates are then
represented as linear differential operators $\\hat x_a = -i \\hat D_a = -
iR_{ab} (p)\\\, \\partial /\\partial p_b $. Generically\, the matrix $R_{a
b}(p)$ represents a certain infinite series over the deformation parameter
$\\theta$: $R_{ab} = \\delta_{ab} + \\ldots$. The deformed Hamiltonian\,
$\\hat H \\ =\\ - \\frac 12 \\hat D_a^2\\\,\, $ describes the motion alon
g the corresponding group manifolds with the characteristic size of order
$\\theta^{-1}$. Their metrics are also expressed into certain infinite se
ries in $\\theta$.\n\nFor the algebras $su(2)$ and $u(2)$\, it has been po
ssible to represent the operators $\\hat x_a$ in a simple finite form. A b
yproduct of our study are new nonstandard formulas for the metrics on $SU(
2) \\equiv S^3$ and on $SO(3)$.\n
LOCATION:https://researchseminars.org/talk/GDEq/66/
END:VEVENT
END:VCALENDAR