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BEGIN:VEVENT
SUMMARY:Monomial combinatorics of polynomial ideals and related algorithms
DTSTART;VALUE=DATE-TIME:20231213T090000Z
DTEND;VALUE=DATE-TIME:20231213T094000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-630@indico.eimi.ru
DESCRIPTION:Speakers: Nikolay Vasilyev (PDMI)\nMonomial combinatorics desc
 ribes the geometric and combinatorial properties of supports of  polynomia
 ls belonging to polynomial ideals. A classic example is the theory of Grö
 bner bases\, which allows us to find sets of polynomials in an ideal  with
  minimal leading  terms\, with respect to any  admissible orderings. Other
  tasks\, the simplest in terms of formulation\, but by no means simple alg
 orithmically\, is the search for monomials or binomials in ideals.  The fi
 rst task is equivalent to determining the intersection of an ideal with a 
 lattice of monomials.  The second problem  is closely related to the toric
 al geometry. I will describe various methods and algorithms of monomial co
 mbinatorics that allow\, for example\, to build monomial bases in factoral
 gebras\, as well as alternative methods to Buchberger's algorithm for cons
 tructing Gröbner bases of polynomial ideals based on interesting combinat
 orial structures such as involutive divisions. We will also discuss  some 
  applications of monomial combinatorics to  the tropical varieties and giv
 e tropical interpretation of the universal Gröbner basis.\n\nhttps://indi
 co.eimi.ru/event/1405/contributions/630/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/630/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A curious hypergeometric identity and perfectness of Meixner--Soro
 kin system of weights
DTSTART;VALUE=DATE-TIME:20231212T143500Z
DTEND;VALUE=DATE-TIME:20231212T151000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-616@indico.eimi.ru
DESCRIPTION:Speakers: Alexander Dyachenko (Keldysh Institute RAS)\nOn two 
 integer lattices with interlacing nodes let us introduce two discrete meas
 ures for which a point weight is determined by the product of two classica
 l Meixner weights. It turns out that the resulting measures are positive w
 hen the lattices alternate.\n\nThis generalisation of the Meixner weight w
 as introduced by Sorokin in 2010. He studied asymptotic behaviour of the c
 orresponding orthogonal polynomials~$P_{n\,n}$ with diagonal indices. The 
 orthogonal polynomials may be constructed using the (discrete) Rodrigues f
 ormula\, but the question whether they are uniquely defined remained open.
 \n\nIndeed\, such a system of measures does not form a Nikishin system as 
 the measures have disjoint supports\; it does not form an Angelesco system
 s either since one of these supports lies in the convex hull of the other.
 \nNevertheless\, the uniqueness of the orthogonal polynomials (i.e. the no
 rmality of diagonal indices for Sorokin's system of measures) would be use
 ful for applying Sorokin's result.\n\nThe talk will be aimed at showing th
 at this system of measures is perfect (that is all indices are normal). In
  the course of our proof we derive an intriguing hypergeometric identity. 
 We also rely on an extension of the aforementioned Rodrigues formula.\n\nT
 his is a joint research with Alexander Aptekarev and Vladimir Lysov.\n\nht
 tps://indico.eimi.ru/event/1405/contributions/616/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/616/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Approximation by sums of shifts of one function
DTSTART;VALUE=DATE-TIME:20231216T092000Z
DTEND;VALUE=DATE-TIME:20231216T101000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-637@indico.eimi.ru
DESCRIPTION:Speakers: Petr Borodin (Moscow state university)\nThe talk pre
 sents a survey of results on the density of the additive semigroup generat
 ed by shifts of one function in various function spaces.\n\nhttps://indico
 .eimi.ru/event/1405/contributions/637/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/637/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weissler type inequalities in Bergman spaces
DTSTART;VALUE=DATE-TIME:20231215T124000Z
DTEND;VALUE=DATE-TIME:20231215T131500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-645@indico.eimi.ru
DESCRIPTION:Speakers: Diana Khammatova (Kazan Federal university)\nFor $r\
 \in(0\,1)$ let $f_r(z) = f(rz)$.  A well-known Weissler inequality states 
 that for the Hardy spaces $H^p$ and $H^q$\, $p\\leq q$\, \n$\\|f_r\\|_{H^q
 }\\leq \\|f\\|_{H^p}\\qquad \\Longleftrightarrow \\qquad r\\leq \\sqrt{\\f
 rac pq}.$\n\nWe consider Bergman spaces $A^p(w)$ with the weight $w(r)\\ge
 q0$\, consisting of functions $f$ analytic in the unit \ndisk $\\mathbb{D}
 $ and such that\n$\\|f\\|_{A^p(w)} :=\\left( \\frac1{2\\pi}\\int\\limits_{
 \\mathbb{D}}  |f(z)|^p  w(|z|) \\\, dz\\right)^{1/p} 1$\, a significant pr
 ogress was achieved by K.Seip\, F. Bayart\, O.F. Brevig\, J. Ortega-Cerdà
 \, K.-M. Perfekt and\, recently\, A. Kulikov\, and P. Melentijević. \n\nI
 n our work\, we considered a counterpart of the Weissler inequality for Be
 rgman spaces $A^{2n}(w)$ and $A^{2}(w)$ with general radial weights. We fo
 und the conditions on the weight $w$ in terms of its moments ensuring that
  the counterpart is true for $n\\in\\mathbb{N}$ and $0 < r$ $\\leq \\frac{
 1}{\\sqrt{n}} $. \n\nWe also examined the case of noninteger exponents for
  the particular function $f(z) = e^z$. Then the corresponding inequality c
 an be considered as a certain analog of the Bernoulli inequality. An examp
 le of a monotonic weight was constructed for which these inequalities are 
 no longer true. \n\nThe talk is based on a joint work with A.D. Baranov\, 
 I.R. Kayumov and R.Sh. Khasyanov.\n\nhttps://indico.eimi.ru/event/1405/con
 tributions/645/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/645/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the scalar approach to the weak asymptotic problem for the mode
 l $\\mathcal{GN}$-system
DTSTART;VALUE=DATE-TIME:20231215T150500Z
DTEND;VALUE=DATE-TIME:20231215T154000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-652@indico.eimi.ru
DESCRIPTION:Speakers: Elijah Lopatin (Steklov Institute RAS)\nTraditionall
 y\, weak asymptotics of Hermite--Padé polynomials for various systems of 
 Markov functions (such as the Angelesco and Nikishin systems) is described
  in terms of the vector potential problem on the complex plane. This appro
 ach has a number of limitations in context of generalisation of Stahl’s 
 theory on Hermite--Padé polynomials. Development of the alternative langu
 age was initiated by Sergey Suetin \n(Steklov Institute\, Moscow) in 2018.
  He considered a very special generalised Nikishin system ($\\mathcal{GN}$
  system) of two functions\; corresponding weak asymptotic problem was solv
 ed via scalar potential problem with a harmonic exterior field on a Rieman
 n surface of genus zero. This technique was generalised on the slightly wi
 der class of $\\mathcal{GN}$ systems by me in 2021\; the corresponding pot
 ential problem lives on a Riemann surface on genus $g>0$. In this talk I w
 ill summarise recent results on the development of this scalar approach.\n
 \nhttps://indico.eimi.ru/event/1405/contributions/652/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/652/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the construction of the Green's function for strongly elliptic 
 systems in domains on the plane
DTSTART;VALUE=DATE-TIME:20231215T142500Z
DTEND;VALUE=DATE-TIME:20231215T150000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-651@indico.eimi.ru
DESCRIPTION:Speakers: Astamur Bagapsh (Bauman Moscow State Technical Unive
 rsity)\nWe consider strongly elliptic second-order systems with constant c
 oefficients in domains on the plane reduced to the canonical form with onl
 y two real parameters $\\tau$\, $\\sigma\\in[0\, 1)$ and written in comple
 x form. When both parameters are equal to zero\, we obtain the complex Lap
 lace equation. When only $\\sigma=0$\, we have the skew-symmetric system w
 hich is a perturbation of the Laplace one by the parameter $\\tau$. Its so
 lutions are represented as a sum of two holomorphic functions of variables
  $z_\\tau=z-\\tau\\overline z$ and $\\overline z$. In some regions\, it is
  possible to construct the Green's function for a skew-symmetric system us
 ing the analogue of Schwarz function which holomorphically expresses $z_\\
 tau$ on the boundary in terms of $\\overline z$. Although different Schwar
 z functions may arise for different parts of the boundary\, for such domai
 ns as\, for example\, a strip or an angle\, it is possible to select funct
 ions that are invariant under the replacement of one Schwarz function by a
 nother. Using such functions\, the Green's function is constructed. The ge
 neral case of a two-parameter system is studied by considering it as a per
 turbation of a skew-symmetric system with respect to the parameter $\\sigm
 a$.\n\nhttps://indico.eimi.ru/event/1405/contributions/651/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/651/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Characterization of non-adaptive Clifford channels
DTSTART;VALUE=DATE-TIME:20231215T141500Z
DTEND;VALUE=DATE-TIME:20231215T144000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-650@indico.eimi.ru
DESCRIPTION:Speakers: Vsevolod Yashin (Steklov Institute RAS)\nWe show tha
 t multiqubit quantum channels which may be realised via stabilizer circuit
 s without classical control (Clifford channels) have a particularly simple
  structure. They can be equivalently defined as channels that preserve mix
 ed stabilizer states\, or the channels with stabilizer Choi state. Up to u
 nitary encoding and decoding maps any Clifford channel is a product of sta
 bilizer state preparations\, qubit discardings\, identity channels and dep
 hasing channels. This simple structure allows to characterise information-
 theoretic properties of such channels.\n\nhttps://indico.eimi.ru/event/140
 5/contributions/650/
LOCATION:MCS 217б
URL:https://indico.eimi.ru/event/1405/contributions/650/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Example of a non-covariant channel constructed using the unitary i
 rreducible  representation of a finite group\, for which classical capacit
 y is calculated
DTSTART;VALUE=DATE-TIME:20231215T134500Z
DTEND;VALUE=DATE-TIME:20231215T141000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-649@indico.eimi.ru
DESCRIPTION:Speakers: Lev Ryskin (Moscow Institute of Physics and Technolo
 gy)\nRecently\, classical capacity of quantum channels generated by projec
 tive unitary irreducible representations of finite group was calculated fo
 r some strong limitations of the group structure\, on the representation $
 U_g$\, on the probability distribution $\\pi_g$\, on the finite group $G$ 
 and finally that the obtained channel $\\Phi_G$ has to be covariant with r
 espect \nto representation $U_g$. \n \nThe channel $\\Phi_G$ is not always
  covariant regarding to representation $U_g$ when the group $G$ is not abe
 lian --\nit depends on $\\pi_g$. But\, fortunately\, the limitation of cov
 ariance of the quantum channel $\\Phi_G$ can be omitted if other condition
 s are preserved.\nIn addition\, the real example of such non covariant qua
 ntum channel will be given on the group $S_4\\times S_3$.\n\nhttps://indic
 o.eimi.ru/event/1405/contributions/649/
LOCATION:MCS 217б
URL:https://indico.eimi.ru/event/1405/contributions/649/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Gaudin model and isomonodromic deformations
DTSTART;VALUE=DATE-TIME:20231215T134500Z
DTEND;VALUE=DATE-TIME:20231215T142000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-648@indico.eimi.ru
DESCRIPTION:Speakers: Ilya Tolstukhin (Higher School of Economics)\nThe Ga
 udin model is a quantum integrable system originally introduced to describ
 e the interaction of multiple charged particles on a line. It consists of 
 $n$ commuting Hamiltonian operators\, dependent on $n$ pairwise distinct c
 omplex parameters and acting on the tensor product of $n$ irreducible repr
 esentations of the Lie algebra $\\mathfrak{sl}_2$. One of the main tasks o
 f the Gaudin model is to diagonalize these operators and understand how th
 eir joint spectrum changes as the parameters vary. In joint work with Nata
 lia Amburg\, branched coverings of the parameter space with joint spectra 
 of Hamiltonians were studied in the case of $n = 3$. The base of such cove
 rings is the Riemann sphere\, and algebraic curves act as total spaces. Th
 e remarkable structure of these curves will be described\, along with thei
 r connection to isomonodromic deformations.\n\nhttps://indico.eimi.ru/even
 t/1405/contributions/648/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/648/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Entanglement-based approach to quantum coherence\, path informatio
 n\, and uncertainty
DTSTART;VALUE=DATE-TIME:20231215T124000Z
DTEND;VALUE=DATE-TIME:20231215T131500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-647@indico.eimi.ru
DESCRIPTION:Speakers: Aleksei Kodukhov (Terra Quantum AG)\, Dmitry Kronber
 g (Steklov Institute RAS)\nWe propose a framework in which quantum measure
 ment is applied to a subsystem of an entangled state\, thus producing a qu
 antum ensemble in the other part. This approach generalizes the seminal mu
 ltibeam Young's interference experiment \nwhich established the wave-parti
 cle duality principle\, connecting quantum properties (interference) and p
 ath information. Our framework provides a connection between such fundamen
 tal quantum information concepts as entanglement\, coherence\, and uncerta
 inty.\n\nhttps://indico.eimi.ru/event/1405/contributions/647/
LOCATION:MCS 217b
URL:https://indico.eimi.ru/event/1405/contributions/647/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Symmetries of $C^*$-algebras
DTSTART;VALUE=DATE-TIME:20231215T120000Z
DTEND;VALUE=DATE-TIME:20231215T123500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-646@indico.eimi.ru
DESCRIPTION:Speakers: Ekaterina Turilova (Kazan Federal university)\nThere
  are many faces of $C^*$-algebras whose symmetries encode important aspect
 s of their structures. We show that in surprisingly different situations t
 hese symmetries are implemented by Jordan $*$-isomorphisms and lead to ful
 l Jordan invariants. In this respect we study the following structures: on
 e dimensional projections in a Hilbert space with transition probability a
 nd orthogonality relation (Wigner type theorems)\;  projection lattices of
  von Neumann algebras and $AW^*$-algebras (Dye type theorems)\; abelian $C
 ^*$-subalgebras with set theoretic inclusion (Bohrification program in qua
 ntum theory).\n\nhttps://indico.eimi.ru/event/1405/contributions/646/
LOCATION:MCS 217b
URL:https://indico.eimi.ru/event/1405/contributions/646/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conformal spectral estimates of the Dirichlet-Laplacian
DTSTART;VALUE=DATE-TIME:20231215T120000Z
DTEND;VALUE=DATE-TIME:20231215T123500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-644@indico.eimi.ru
DESCRIPTION:Speakers: Valerii Pchelintsev (Tomsk state university)\nIn thi
 s talk we give applications of the conformal geometry to the spectral esti
 mates of the Dirichlet-Laplace operator in bounded simply connected domain
 s with highly non-rectifiable boundaries.\nOur method is based on the geom
 etrical theory of composition operators on Sobolev spaces. These compositi
 on operators are generated by conformal mappings.\nThe talk is based on a 
 joint work with Ivan Kolesnikov.\n\nResearch was supported by RSF Grant No
 . 23-21-00080.\n\nhttps://indico.eimi.ru/event/1405/contributions/644/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/644/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mellin--Barnes integrals and equivalences of  triangulated categor
 ies
DTSTART;VALUE=DATE-TIME:20231215T092000Z
DTEND;VALUE=DATE-TIME:20231215T101000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-624@indico.eimi.ru
DESCRIPTION:Speakers: Mauricio Romo Jorquera (Yau Mathematical Science Cen
 ter)\nIn this talk we will present a pedagogical survey on how convergence
  of certain Mellin--Barnes integrals\, that arise from open quantum field 
 theory\, can be used to predict equivalences between different triangulate
 d categories. We will focus on the case of  how monodromies give rise to a
 utoequivalences of derived categories of coherent sheaves and present seve
 ral examples\, as time allows.\n\nhttps://indico.eimi.ru/event/1405/contri
 butions/624/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/624/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Dirichlet problem for bianalytic functions and for solutions of
  general second-order non-strongly elliptic systems with constant coeffici
 ents
DTSTART;VALUE=DATE-TIME:20231215T082000Z
DTEND;VALUE=DATE-TIME:20231215T091000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-623@indico.eimi.ru
DESCRIPTION:Speakers: Konstantin Fedorovskiy (Moscow state university)\nIn
  the talk we plan to discuss Dirichlet problem for non-strongly elliptic s
 econd-order PDE with constant complex coefficients in bounded simply conne
 cted domains in the complex plane. Starting with the most known case of bi
 analytic functions (that corresponds to the  Bitsadze equation)\, we will 
 proceed to discuss the case of solutions to general non-strongly elliptic 
 second order PDEs with constant complex coefficients and\, moreover\, solu
 tions to general non-strongly elliptic  systems of second-order PDEs with 
 constant coefficients. We will show that any Jordan domain in the complex 
 plane with sufficiently regular (smooth) boundary is not regular with resp
 ect to the Dirichlet problem for any non-strongly elliptic system under co
 nsideration\, which means that there always exists a continuous complex-va
 lued function on the boundary of the domain under consideration that can n
 ot be continuously extended to this domain to a function satisfying the co
 rresponding system therein. Since there exists a Jordan domain with Lipsch
 itz boundary\, which is regular with respect to the Dirichlet problem for 
 bianalytic functions\, the result obtained is near to be sharp. The discov
 ered phenomena that domains with sufficiently smooth boundaries are not re
 gular with  respect to the Dirichlet problem for systems under considerati
 on\, while domains having worse boundaries may be regular is rather unexpe
 cted and essentially new.\n\nhttps://indico.eimi.ru/event/1405/contributio
 ns/623/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/623/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bipolar Green function and Nuttall decomposition of a three-sheete
 d torus
DTSTART;VALUE=DATE-TIME:20231211T092000Z
DTEND;VALUE=DATE-TIME:20231211T101000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-622@indico.eimi.ru
DESCRIPTION:Speakers: Semen Nasyrov (Kazan Federal university)\nWe study t
 he Nuttall decomposition of a three-sheeted torus $T$ which is a Riemann s
 urface $S$ of the algebraic function $w=\\sqrt[3]{(z-a_1)(z-a_2)(z-a_3)}$.
  This decomposition is induced by a harmonic function $U$ with two logarit
 hmic singularities\, it is called bipolar Green function. It is important 
 to describe this function and investigate its properties. With the help of
  Weierstrass elliptic functions\, we construct the universal covering of $
 T$ by the complex plane $\\mathbb{C}$ and  study the harmonic function $\\
 widetilde{U}$ on $\\mathbb{C}$ corresponding to $U$. The sets $\\widetilde
 {U}(z)=0$\, $\\widetilde{U}(e^{2\\pi i/3}z)=0$ and $\\widetilde{U}(e^{-2\\
 pi i/3}z)=0$ fully define decomposition of the complex plane into three pa
 rts which induces the  Nuttall decomposition of $T$. According to the Nutt
 all conjecture\,  this decomposition defines the convergence domains for t
 he Hermite--Padé approximants.\n\nThe study was supported by the grant of
  the Russian Science Foundation No. 23-11-00066.\n\nhttps://indico.eimi.ru
 /event/1405/contributions/622/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/622/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Continuation of the family of projectors to a positive operator-va
 lued measure and restoration of the quantum state after measurement
DTSTART;VALUE=DATE-TIME:20231214T140000Z
DTEND;VALUE=DATE-TIME:20231214T142500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-643@indico.eimi.ru
DESCRIPTION:Speakers: Anton Alekseev (Moscow Institute of Physics and Tech
 nology)\nWe build POVM\, which is absolutely continuous relative to the sc
 alar measure with a projector-valued density\, and  study the quantum chan
 nel generated by it. Also\, we consider the possibility of restoring state
 s when measured by the Davis--Lewis instrument. An experiment with two out
 comes is considered\, and we compare two cases: with post-selection and wi
 thout post-selection.  We study how states are transformed in these cases 
 and whether it is possible to restore them.\n\nhttps://indico.eimi.ru/even
 t/1405/contributions/643/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/643/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A semigroup approach to describing the stochastic dynamics of a qu
 antum system
DTSTART;VALUE=DATE-TIME:20231214T130000Z
DTEND;VALUE=DATE-TIME:20231214T133500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-642@indico.eimi.ru
DESCRIPTION:Speakers: Andrey Utkin (Moscow Institute of Physics and Techno
 logy & Steklov International Mathematical Center)\nThe talk is devoted to 
 one method to derive the equation of stochastic dynamics of a quantum syst
 em for a wave function and its applications in quantum information theory.
  The main example of stochastic dynamics is the process of continuous-time
  weak measurements of an observable $L=L^*$ described \nby the stochastic 
 differential Belavkin equation \n\n  $  d|\\psi_t\\rangle =-iH|\\psi_t\\ra
 ngle dt-\\frac{1}{2}L^2|\\psi_t\\rangle dt+L|\\psi_t\\rangle dW_t.$\n\nHer
 e $|\\psi_t\\rangle =|\\psi_t(\\omega)\\rangle \\in \\mathcal{H}$ is a wav
 e function\, as a random vector process on the probability space $\\Omega$
 \, $H$ is a Hamiltonian\, $W_t$ is a real Wiener process.\n \nIn my talk w
 e obtain a generalization of the Belavkin equation by writing the equation
  not for a random vector $|\\psi_t\\rangle$\, but for its distribution. Th
 us\, we get rid of stochasticity and deal with Markov semigroups and their
  generators. The conditions of approximation of semigroups of diffusion pr
 ocesses corresponding to a continuous random process in Hilbert space by d
 iscrete ones are investigated.  Formally\, the semigroup operators are con
 sidered on the space of bounded weakly continuous functions $C_{BW}(\\math
 cal{H})$ on the Hilbert space\, which carry out the evolution of the chara
 cteristic functions $\\varphi_t(v)=\\mathbb{E} e^{i\\langle v|\\psi_t \\ra
 ngle_{\\mathbb{R}}}$ of the process. The proof uses the developed powerful
  theory of continuous and bi-continuous semigroups on a Banach space.\n \n
 In quantum physics\, stochastic processes continuous in time find interest
 ing applications: from models of collisions of particles in a gas to rando
 m circuits.\n\nhttps://indico.eimi.ru/event/1405/contributions/642/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/642/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On some properties of classical and quantum random walks
DTSTART;VALUE=DATE-TIME:20231214T123000Z
DTEND;VALUE=DATE-TIME:20231214T125500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-641@indico.eimi.ru
DESCRIPTION:Speakers: Stanislav Grishin (Moscow Institute of Physics and T
 echnology)\nThis talk is devoted to homogeneous random walks on a line. In
  the classical case\, the generating function for the positive half-line f
 irst passage time is discussed. It often turns out to admit an algebraic e
 quation and is useful in statistical computations. Besides\, the correspon
 ding algebraic curve sometimes is rational and has a positive genus which 
 can be accounted via analyzing singularities. An open quantum system $\\rh
 o \\mapsto \\sum _i V_i \\rho V_i^*$ where $V_i$ are operators of shift on
  $a_i$ with coefficients $\\sqrt{p_i}$ is similar to the classical random 
 walk with increases $a_i$ and their probabilities $p_i$. Some characterist
 ics of it are computed.\n\nhttps://indico.eimi.ru/event/1405/contributions
 /641/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/641/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On generating quantum channels
DTSTART;VALUE=DATE-TIME:20231214T120000Z
DTEND;VALUE=DATE-TIME:20231214T122500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-640@indico.eimi.ru
DESCRIPTION:Speakers: Renat Gumerov (Kazan Federal university)\, Ruslan Kh
 azhin (Kazan federal university)\nFor composite quantum systems\, we consi
 der quantum channels that uniquely determine the channels of subsystems. S
 uch channels of composite systems are called generating quantum channels.\
 nThe talk is devoted to  properties of those quantum channels. We give a c
 riterion for a quantum channel to be generating. Algebraic and topological
  properties of sets of generating quantum channels are discussed. For comp
 osite systems consisting of two qubits\, we construct generating phase-dam
 ping channels which generate phase-damping and depolarizing quantum channe
 ls of subsystems.\n\nhttps://indico.eimi.ru/event/1405/contributions/640/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/640/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the range of a convolution operator in spaces of ultradifferent
 iable functions
DTSTART;VALUE=DATE-TIME:20231213T094500Z
DTEND;VALUE=DATE-TIME:20231213T102000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-639@indico.eimi.ru
DESCRIPTION:Speakers: Daria Polyakova (Southern Federal university)\nWe co
 nsider a nonsurjective convolution operator in the Beurling space of ultra
 differentiable functions of mean type generated by  the weight function $\
 \omega$. We establish necessary and (separately) sufficient conditions on 
 the symbol under which the range of the operator contains the space define
 d by another weight function and of another type. These results are applie
 d to convolution operators in the Roumieu spaces of mean type.\n\nhttps://
 indico.eimi.ru/event/1405/contributions/639/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/639/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Avkhadiev--Wirths' conjecture for  Hardy inequalities on balls
DTSTART;VALUE=DATE-TIME:20231213T090000Z
DTEND;VALUE=DATE-TIME:20231213T093500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-638@indico.eimi.ru
DESCRIPTION:Speakers: Ramil Nasibullin  (Kazan Federal university)\nThe co
 njecture states that among all $n$-dimensional domains with given inradius
  $\\delta_0$  the maximum of the best Brezis--Marcus constants $\\lambda(\
 \Omega)$ is given by $\\lambda(B_n)$\, where $B_n$ is the $n$-dimensional 
 ball \nof radius $\\delta_0$. In the talk  the known results in Hardy type
  inequalities with additional terms are presented and we will give review 
 of our own results  in this subject. We improve estimates of $\\lambda(\\O
 mega)$.\n\nhttps://indico.eimi.ru/event/1405/contributions/638/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/638/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.V. Chernikov’s method for investigating functionals on the cla
 ss of conformal univalent mappings
DTSTART;VALUE=DATE-TIME:20231213T074500Z
DTEND;VALUE=DATE-TIME:20231213T082000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-618@indico.eimi.ru
DESCRIPTION:Speakers: Ivan Kolesnikov (Tomsk state university)\nThe variat
 ional method is one of the main methods for finding a region of a function
 al and boundary mappings. The greatest difficulty of this method is the st
 udy of the functional differential equation for the boundary mapping. V.V.
  Chernikov proposed a way for finding a solution to such a functional diff
 erential equation using the area method. We use the idea of V.V. Chernikov
  to study some functionals defined on the class $S$\, and consider questio
 ns about improving the method.\n\nThe work was supported by RSF Grant No. 
 23-21-00080.\n\nhttps://indico.eimi.ru/event/1405/contributions/618/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/618/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analytic continuation of power series by means of coefficients int
 erpolation
DTSTART;VALUE=DATE-TIME:20231213T070000Z
DTEND;VALUE=DATE-TIME:20231213T073500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-617@indico.eimi.ru
DESCRIPTION:Speakers: Alex Mkrtchyan (Siberian Federal university and Inst
 itute of Mathematics  NAS RA)\nWe consider the problem  of analytic contin
 uation of  power series in the sectoral domain by means of interpolation o
 f coefficients by holomorphic functions. We explore the relationship betwe
 en the growth (indicator) of the interpolating function and the set\, to w
 hich the series can be extended. \nTo estimate the growth of a holomorphic
  function of several complex variables\, we use a multidimensional indicat
 or \nafter Ivanov\, which is one of generalizations of the indicator intro
 duced by Phragmén and Lindelöf for analytic \nfunctions of one complex v
 ariable. Also\, a piecewise affine majorant for some subclass of functions
  will be used.\n\nWe obtain a multivariate version of the Le Roy and Linde
 löf theorem\, i.e.\, establish a connection between the growth of the int
 erpolating function of the coefficients on the imaginary subspace and the 
 multivariate sectoral domain to which the multiple series extends analytic
 ally.\n\nhttps://indico.eimi.ru/event/1405/contributions/617/
LOCATION:SPBU MCS MCS 201
URL:https://indico.eimi.ru/event/1405/contributions/617/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integral formulas and inequalities for meromorphic functions and d
 ifferences of subharmonic functions with applications
DTSTART;VALUE=DATE-TIME:20231212T135000Z
DTEND;VALUE=DATE-TIME:20231212T142500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-615@indico.eimi.ru
DESCRIPTION:Speakers: Bulat Khabibullin (Ufa Institute of Mathematics with
  Computing Centre)\, Enzhe Menshikova (Ufa Institute of Mathematics with C
 omputing Centre)\nWe consider various formulas relating integrals of delta
 -subharmonic functions to their Riesz distributions of charges.\nThese new
  formulas represent far-reaching developments and generalizations of the c
 lassical Poisson--Jensen\, Shimizu--Ahlfors\,  I.I. Privalov\, T. Carleman
 \,  B.Ya. Levin and other integral formulas. \nA distinctive feature of th
 e new formulas is the absence in them of any derivatives or function value
 s at individual points. \nThe inequalities obtained from these formulas wi
 ll be applied to uniqueness theorems for entire functions\, to approximati
 on in spaces of functions on subsets of the complex plane\, etc. We will a
 lso indicate possible multidimensional complex generalizations of these re
 sults.\n\nhttps://indico.eimi.ru/event/1405/contributions/615/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/615/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Removable sets for Newtonian space $N^{1\,p}$
DTSTART;VALUE=DATE-TIME:20231212T124500Z
DTEND;VALUE=DATE-TIME:20231212T132000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-614@indico.eimi.ru
DESCRIPTION:Speakers: Vladimir Shlyk (Far Eastern federal university)\, Yu
 ri Dymchenko (adm. G.I. Nevelskoy Maritime state university)\nLet $X=(X\,d
 \,\\mu)$ be a complete $p$-Poincaré metric space with distance $d$ and a 
 Borel regular doubling measure $\\mu$\, $1\n\nhttps://indico.eimi.ru/event
 /1405/contributions/614/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/614/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Free topololgical groups
DTSTART;VALUE=DATE-TIME:20231212T092000Z
DTEND;VALUE=DATE-TIME:20231212T101000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-612@indico.eimi.ru
DESCRIPTION:Speakers: Leonid Genze (Tomsk state university)\nThe talk will
  be devoted to free $n$-periodic and free Abelian $n$-periodic topological
  groups of the Tikhonoff space $X$. A classification of these groups will 
 be given for the case when $X$ is a compact segment of ordinals. The secon
 d part of the report will compare some properties of $n$-periodic (Abelian
 ) groups with the properties of free (Abelian) topological groups\, which 
 were introduced and studied in the classical works of A.A. Markov and M.I.
  Graev in 1945 and 1948\, respectively.\n\nhttps://indico.eimi.ru/event/14
 05/contributions/612/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/612/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random matrices ensembles and multiple orthogonal polynomials
DTSTART;VALUE=DATE-TIME:20231212T082000Z
DTEND;VALUE=DATE-TIME:20231212T091000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-611@indico.eimi.ru
DESCRIPTION:Speakers: Alexander Aptekarev (Keldysh Institute RAS)\nLet $\\
 mu(x):=(\\mu_1(x)\,\\dots \, \\mu_d(x))$ be a vector of positive measures.
  For a given multiindex $n=(n_1\,  \\dots  \, n_d)$ we consider a polynomi
 al $P_n(x)$  of degree $|n|:=n_1+ \\cdots +n_p$\, which satisfies $n_j$ or
 thogonality  relations to the degrees of the scalar variable $x$ with resp
 ect to the measure  $\\mu_j$\, $j=1\, \\dots \, p$.  Such polynomials alwa
 ys exist and they are called multiple orthogonal polynomials. For $p=1$ we
  have usual orthogonal polynomials.   We discuss several examples of ensem
 bles of random matrices related to the multiple orthogonal polynomials (na
 mely: random matrix model with external source\, two matrix model and norm
 al matrix model). An application to the Brownian bridges will be highlight
 ed.\n\nhttps://indico.eimi.ru/event/1405/contributions/611/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/611/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Time-frequency localization operator
DTSTART;VALUE=DATE-TIME:20231212T070000Z
DTEND;VALUE=DATE-TIME:20231212T075000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-610@indico.eimi.ru
DESCRIPTION:Speakers: Aleksei Kulikov (Tel-Aviv university)\nGiven a measu
 rable set $U\\subset \\mathbb{R}$\, we define the projection onto $U$ as $
 P_U:L^2(\\mathbb{R})\\to L^2(\\mathbb{R})$ given by $(P_U f)(x) = f(x)\\ch
 i_U(x)$. Similarly\, for the set $V\\subset \\mathbb{R}$ we define the Fou
 rier projection onto $V$ as $Q_V = \\mathcal{F}^{-1}P_V \\mathcal{F}$\, wh
 ere $\\mathcal{F}$ is a Fourier transform. The operator $S_{U\, V} = P_UQ_
 VP_U$ is called a time-frequency localization operator\, associated with $
 U$ and $V$.\n\nIt is easy to see that $S_{U\, V}$ is a non-negative defini
 te operator of norm at most $1$. If both $U$ and $V$ have finite measure i
 t turns out that $S_{U\, V}$ is a Hilbert--Schmidt operator with $||S_{U\,
  V}||_{HS}^2 = |U| |V|$. In particular\, it is a compact operator and as s
 uch it has a sequence of eigenvalues $1 \\ge \\lambda_1(U\, V) \\ge \\lamb
 da_2(U\, V) \\ge \\ldots > 0$.\n\nIn this talk\, we will focus on the case
  when both $U$ and $V$ are intervals. In this case the eigenvalues depend 
 only on the product of length of the intervals $c = |U| |V|$\, so we have 
 a sequence $1 > \\lambda_1(c) > \\lambda_2(c) > \\ldots > 0$. It turns out
  that these eigenvalues exhibit a phase transition: first $\\approx c$ of 
 them are very close to $1$\, then there are $\\approx \\log c$ intermediat
 e ones and the remaining eigenvalues decay to zero extremely fast. We will
  discuss the behaviour of eigenvalues in these regimes\, with focus on the
  most interesting\, intermediate region. If time permits we will also ment
 ion a new exponential lower bound for the eigenvalues $\\lambda_n(c)$ when
  $n < (1-\\varepsilon)c\, \\varepsilon > 0$.\n\nhttps://indico.eimi.ru/eve
 nt/1405/contributions/610/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/610/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On numerical differentiation of analytic functions  by differences
  of $h$-sums
DTSTART;VALUE=DATE-TIME:20231211T143500Z
DTEND;VALUE=DATE-TIME:20231211T151000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-609@indico.eimi.ru
DESCRIPTION:Speakers: Mikhail Komarov (Vladimir state university)\nIn 2006
 \, V.I. Danchenko suggested the method of $h$-sums \nfor approximation pro
 blems and numerical analysis (by $ h-sum$ $of$ $order$ $n$ we mean an expr
 ession of the form\n\n$H_n(z)=\\sum_{k=1}^n \\lambda_k h(\\lambda_k z)\, \
 \quad \\lambda_k\\in \\mathbb{C}\,$\n\nwhere $h(z)$ is a fixed function\, 
 analytic in the disk $D=\\{z:|z|<1\\}$\,  and $\\lambda_1\,\\dots\,\\lambd
 a_n$ are independent numeric parameters).\nIn particular\, it was proved t
 hat for every $n=1\,2\,\\dots$ there are numbers $\\lambda_{n\,1}\,\\dots\
 ,\\lambda_{n\,n}$ such that the corresponding $h$-sum $H_n$ interpolates t
 he differentiation operator $(zh(z))'$ at the node $z_0=0$ with the multip
 licity $n$:\n\n$(zh(z))'=\\sum_{k=1}^n\\lambda_{n\,k} h(\\lambda_{n\,k}z)+
 O(z^n)\,$\n\nand $H_n(z)$ converges uniformly to $(zh(z))'$ as $n\\to \\in
 fty$ on compact subsets $K\\subset D$ with exponential rate.\n\nWe conside
 r an analogous problem of numerical differentiation $ by$ $the$ $differenc
 e$ $of$ $two$ $h-sums$ $of$ $order$ $n$. It can be shown that under this m
 odified approach the rate of approximation  is much higher.\n\nhttps://ind
 ico.eimi.ru/event/1405/contributions/609/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/609/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The spaces of delta-subharmonic functions of finite order with res
 pect to the model function of growth
DTSTART;VALUE=DATE-TIME:20231211T135000Z
DTEND;VALUE=DATE-TIME:20231211T142500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-608@indico.eimi.ru
DESCRIPTION:Speakers: Konstantin Malyutin (Kursk state university)\nThe cl
 asses of standard functions introduced by B.N. Khabibullin are considered.
  The concept of a model function of growth covers a large class of functio
 ns. Functions $f$ of finite order with respect to the model function can h
 ave an order of growth in the classical sense equal to infinity or zero. F
 or example\, the model functions of growth  include functions of $r>0$ of 
 the form $\\exp^{\\circ n}r$\,  where $\\exp^{\\circ n}$ is the $n$-th sup
 erposition with $n=1\,2\,\\dots$ of the exponential function $\\exp$\, deg
 ree of the logarithmic function $\\ln^p(e+r)$ for any $p\\geq 1$\, and in 
 general any differentiable function $M(r)>0$ such that the function $rM'(r
 )>0$ increases for $r>0$. We prove that for any function $f$ defined on $\
 \mathbb{R}^+$ whose growth is determined by a model function of growth $M$
 \, there exist its own proximate growth functions with respect to the mode
 l growth function $M$ that estimate $f$ above and below. Thus\, we solve t
 he extended Hadamard problem for a fairly wide class of entire and subharm
 onic functions. The proof is constructive.\n\nThe research is  supported b
 y Russian Science Foundation (project No. 22-21-00012).\n\nhttps://indico.
 eimi.ru/event/1405/contributions/608/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/608/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On primitive recursive and automatic structures
DTSTART;VALUE=DATE-TIME:20231213T070000Z
DTEND;VALUE=DATE-TIME:20231213T072500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-627@indico.eimi.ru
DESCRIPTION:Speakers: Nikolay Bazhenov (Sobolev Institute RAS)\nIn the tal
 k we consider subrecursive algebraic structures. One of the key notions in
  this direction is the notion of a punctual structure introduced by Kalimu
 llin\, Melnikov\, and Ng (2017). An infinite algebraic structure S is punc
 tual if the domain of S is equal to the set of natural numbers\, and the s
 ignature functions and relations of the structure S are primitive recursiv
 e. The methods of punctual structure theory found their applications not o
 nly in the classical constructive model theory\, but also in other areas o
 f mathematical logic and theoretical computer science. In particular\, the
  paper "Automatic and polynomial-time algebraic structures" (2019) proves 
 that the class of automatic structures (in the sense of Khoussainov and Ne
 rode) does not admit a simple syntactic characterization (even within the 
 framework of infinitary logic). In the talk\, we discuss recent results on
  punctual structure theory\, and its applications to the theory of numberi
 ngs and equivalence relations. The talk is based on joint works with Harri
 son-Trainor\, Kalimullin\, Melnikov\, and Ng.\n\nhttps://indico.eimi.ru/ev
 ent/1405/contributions/627/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/627/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lower bounds for monotone minimal perfect hashing revisited
DTSTART;VALUE=DATE-TIME:20231214T143000Z
DTEND;VALUE=DATE-TIME:20231214T145500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-635@indico.eimi.ru
DESCRIPTION:Speakers: Dmitry Kosolobov (Ural Federal University)\nThe mono
 tone minimal perfect hash (MMPH) is a data structure that\, for a set of n
  integers k1\n\nhttps://indico.eimi.ru/event/1405/contributions/635/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/635/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Recursion elimination: from olympiad problems to program optimizat
 ion
DTSTART;VALUE=DATE-TIME:20231213T080000Z
DTEND;VALUE=DATE-TIME:20231213T082500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-629@indico.eimi.ru
DESCRIPTION:Speakers: Nikolay Shilov (Innopolis University)\nThe problem o
 f recursion elimination is a broad topic\, including purely mathematical a
 s well as practical formulations. Mathematical formulation may be presente
 d as follows: What are decidable sufficient conditions to find a primitive
  recursive function that is equivalent to a given recursive function. A pr
 actical formulation\, for instance\, may be presented as follows: what are
  syntactic conditions for functional programs that are sufficient for impl
 ementation of recursion via iteration with static memory. In the talk I wi
 ll provide an overview of known results in this direction and present some
  new results.\n\nhttps://indico.eimi.ru/event/1405/contributions/629/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/629/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Coefficient approach to the problem of describing homogeneous mani
 folds
DTSTART;VALUE=DATE-TIME:20231211T124500Z
DTEND;VALUE=DATE-TIME:20231211T132000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-607@indico.eimi.ru
DESCRIPTION:Speakers: Alexander Loboda (Voronezh state university)\nThe pr
 oblem of describing holomorphically homogeneous real hypersurfaces of spac
 es $ \\mathbb{C}^n$\, $n=2\,3\,4$\, is discussed as well as some close que
 stions about the homogeneity of embedded submanifolds. We consider an appr
 oach related to the normalization of the surfaces themselves and the Lie a
 lgebras of vector fields associated with them\, as well as to the determin
 ation of these objects through the lower Taylor coefficients of the functi
 ons representing them.\n \nThe use of canonical (Moser normal) equations o
 f real hypersurfaces in the space $\\mathbb{C}^2 $ made it possible to obt
 ain a complete description of holomorphically homogeneous hypersurfaces of
  this space. By using a similar technique in the space $\\mathbb{C}^3 $ a 
 local description was given of fairly representative families of homogeneo
 us Levi-nondegenerate hypersurfaces with ``rich'' symmetry algebras.\n \nR
 eduction to canonical form of the basic holomorphic vector fields of 5-dim
 ensional Lie algebras in the space $\\mathbb{C}^3$ made it possible to obt
 ain a complete description of all holomorphically homogeneous Levi-nondege
 nerate hypersurfaces with trivial symmetry algebras. A similar prospect em
 erges for 7-dimensional Lie algebras in the space $\\mathbb{C}^4$. At the 
 same time\, questions about the dimension of the symmetry algebras of the 
 resulting homogeneous manifolds can also be studied using normal equations
 \, the coefficient approach and computer programs of symbolic calculations
 .\n\nhttps://indico.eimi.ru/event/1405/contributions/607/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/607/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Correct use of Padé approximants and Hermite--Padé polynomials i
 n practice
DTSTART;VALUE=DATE-TIME:20231211T102000Z
DTEND;VALUE=DATE-TIME:20231211T105500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-606@indico.eimi.ru
DESCRIPTION:Speakers: Aleksandr Komlov (Steklov Institute RAS)\nLet $f$ be
  an algebraic function and $f_0$ be its germ at some point $z_0\\in\\mathb
 b C$. Padé approximants are the best rational approximations of a given d
 egree for the germ $f_0$. The convergence and the asymptotic behaviour of 
 Padé approximants is described by Stahl theory. Nevertheless\, sometimes 
 this theory is used incorrectly in practice even in industrial application
 s. We give one example\, where such mistake led to collapses in global ele
 ctrical networks. We explain this mistake and explain how it was fixed by 
 Trias in 2012 due to correct understanding of Stahl theory. Further we con
 sider such generalizations of Padé polynomials as Hermite--Padé polynomi
 als. Unfortunatelly\, for these polynomials there is no analogue of Stahl 
 theory for general $f$. But\, sometimes Hermite--Padé polynomials are als
 o used in practical applications without theoretical justification. Moreov
 er\, in some problems they are much more effective than usual Padé polyno
 mials. We give such example from the molecular chemistry and justify it in
  the model case\, when the function $f$ is 3-valued.\n\nhttps://indico.eim
 i.ru/event/1405/contributions/606/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/606/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Three versions of the nonlinear Fourier transform for real-analyti
 c signals in optical fibers
DTSTART;VALUE=DATE-TIME:20231215T070000Z
DTEND;VALUE=DATE-TIME:20231215T075000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-605@indico.eimi.ru
DESCRIPTION:Speakers: Andrey Domrin (Moscow state university)\nThe evoluti
 on of the complex envelopes of signals in fiber-optics communications is d
 escribed by the focusing nonlinear Schr\\"odinger equation. This equation 
 is integrable by the inverse scattering method\, which has three versions 
 corresponding to rapidly decaying\, periodic and local holomorphic signals
  respectively. We mention the remarkable recent advances in the study of t
 he pointwise convergence and time-frequency localization properties of the
  direct scattering transform (in the first and second versions)\, which is
  regarded as the nonlinear Fourier transform. We use the third version to 
 prove the global-in-time real-analytic solvability of the Cauchy problem f
 or any real-analytic initial data and discuss the natural isomorphism betw
 een the third version and each of the first two versions in the case of re
 al-analytic signals satisfying the corresponding boundary conditions.\n\nh
 ttps://indico.eimi.ru/event/1405/contributions/605/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/605/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiplicative chaos
DTSTART;VALUE=DATE-TIME:20231211T082000Z
DTEND;VALUE=DATE-TIME:20231211T091000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-604@indico.eimi.ru
DESCRIPTION:Speakers: Alexander Bufetov (Steklov Institute RAS & Kharkevic
 h Institute for Transmission Problems & Saint-Petersburg state university)
 \nIn this survey talk\, we will consider different approaches to  construc
 ting and studying the exponential of a random field\, with a special empha
 sis on proving the convergence to Gaussian multiplicative chaos of random 
 Euler-like products assigned to \nrealizations of the sine-process.\n\nhtt
 ps://indico.eimi.ru/event/1405/contributions/604/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/604/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seiberg-Witten equations and pseudoholomorphic curves
DTSTART;VALUE=DATE-TIME:20231211T070000Z
DTEND;VALUE=DATE-TIME:20231211T075000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-603@indico.eimi.ru
DESCRIPTION:Speakers: Armen Sergeev (Steklov Institute RAS)\nSeiberg--Witt
 en equations (SW-equations for short) were proposed in order to produce a 
 new kind of invariant for smooth 4-dimensional manifolds. These equations\
 , opposite to the conformally invariant Yang--Mills equations\, are not in
 variant under scale transformations. So to draw a useful information from 
 these equations one should plug the scale parameter $\\lambda$ into them a
 nd take the limit $\\lambda\\to\\infty$.\n\nIf we consider such limit in t
 he case of 4-dimensional symplectic manifolds solutions of SW-equations wi
 ll concentrate in a neighborhood of some pseudoholomorphic curve (more pre
 cisely\, pseudoholomorphic divisor) while SW-equations reduce to some vort
 ex equations in normal planes of the curve. The vortex equations are in fa
 ct static Ginzburg--Landau equations known in the superconductivity theory
 . So solutions of the limiting adiabatic SW-equations are given by familie
 s of vortices in the complex plane parameterized by the point z running al
 ong the limiting pseudoholomorphic curve. This parameter plays the role of
  complex time while the adiabatic SW-equations coincide with a nonlinear $
 \\bar\\partial$-equation with respect to this parameter.\n\nhttps://indico
 .eimi.ru/event/1405/contributions/603/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/603/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exact real computation for differential equations
DTSTART;VALUE=DATE-TIME:20231214T140000Z
DTEND;VALUE=DATE-TIME:20231214T142500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-634@indico.eimi.ru
DESCRIPTION:Speakers: Svetlana Selivanova (Ershov Institute of Informatics
  Systems\, RAS)\nIn this talk we discuss the exact real computation paradi
 gm\, which turns into practice the rigorous but theoretical computable ana
 lysis approach (see\, e.g.\, [Weihrauch 2000]). We also highlight some of 
 its recent applications in computing solutions of differential equations w
 ith guaranteed prescribed precision. Exact real computation packages allow
  to conveniently implement imperative algorithms involving real numbers\, 
 converging sequences\, and smooth functions without using the Turing machi
 nes formalism (which computability analysis heavily relies on). This appro
 ach differs from traditional reliable numerics in considering real numbers
  as exact entities (as opposed to intervals) while guaranteeing output app
 roximations up to error 1/2^n (as opposed to intermediate precision propag
 ation). Here n is the output error parameter\, i.e.\, the number of comput
 ed digits of the output\, which can be arbitrary and is given by the user.
  One of the crucial theoretical problems to address within this approach i
 s estimating the bit-complexity of computation w.r.t. the parameter n (see
 \, e.g.\, [Ko 2003] on complexity theory for real functions)\, which refle
 cts the speed of implementations. Thus\, the talk also contains a brief di
 scussion on algorithmic complexity classification of differential equation
 s\, compared to their other known classifications.\n\nhttps://indico.eimi.
 ru/event/1405/contributions/634/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/634/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phase shift and multi-controlled Z-type gates
DTSTART;VALUE=DATE-TIME:20231214T150000Z
DTEND;VALUE=DATE-TIME:20231214T152500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-636@indico.eimi.ru
DESCRIPTION:Speakers: Andrey Novikov (Sobolev Institute RAS)\nOne of the m
 ost famous algorithms in quantum computations is the Grover search algorit
 hm. Under certain assumptions\, this algorithm provides quantum speedup fo
 r the search problem. We always assume that we can build it efficiently\, 
 but assume for a moment that you are limited in the gates you are allowed 
 to use for the implementation of the Grover diffusion operator. For exampl
 e\, if you need to use at most two-channel gates. What would be the comple
 xity of the decomposition circuit for the diffusion operator itself? Here 
 we show that it is sufficient to use just only the Z-base operators (such 
 2n√Z and controlled CZ) and Hadamard operators\, but also we show that i
 n this case\, the number of used gates can grow exponentially. At least\, 
 the number of the multi-controlled Z-gates needed to build diffusion opera
 tor decomposition circuit only of the following gates: Z\, controlled Z\, 
 multi-controlled Z-gates\, or is summed into 2n − 1 for the n-dimensiona
 l phase shift and cannot be decreased if we will not allow other gates.\n\
 nhttps://indico.eimi.ru/event/1405/contributions/636/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/636/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Information disclosure in networks
DTSTART;VALUE=DATE-TIME:20231214T070000Z
DTEND;VALUE=DATE-TIME:20231214T075000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-619@indico.eimi.ru
DESCRIPTION:Speakers: Nikolay K. Vereshchagin (Moscow State University)\nW
 e consider the network consisting of three nodes 1\, 2\, 3 connected by tw
 o open channels 1 → 2 and 1 → 3. The information present in the node 1
  consists of four strings x\, y\, z\, w. The nodes 2\, 3 know x\, w and ne
 ed to know y\, z\, respectively. We want to arrange transmission of inform
 ation over the channels so that both nodes 2 and 3 learn what they need an
 d the disclosure of information is as small as possible. By information di
 sclosure we mean the amount of information in the strings transmitted thro
 ugh channels about x\, y\, z\, w (or about x\, w). We are also interested 
 in whether it is possible to minimize the disclosure of information and si
 multaneously minimize the length of words transferred through the channels
 .\n\nhttps://indico.eimi.ru/event/1405/contributions/619/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/619/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum fingerprinting and hashing for computing\, processing and 
 transmitting information
DTSTART;VALUE=DATE-TIME:20231214T082000Z
DTEND;VALUE=DATE-TIME:20231214T091000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-620@indico.eimi.ru
DESCRIPTION:Speakers: Farid M. Ablayev (Kazan Federal University)\nQuantum
  fingerprinting is a family of quantum functions that began to be used in 
 quantum algorithms in the early 2000s. They map classical objects to quant
 um states in such a way that different arguments can be effectively distin
 guished. To further highlight the additional cryptographic characteristics
  of quantum fingerprinting\, our group uses the name “quantum hashing.
 ” The talk introduces the basic concepts of quantum fingerprinting and h
 ashing\, as well as their use in communications protocols\, cryptographic 
 signatures\, and pattern searching in text.\n\nhttps://indico.eimi.ru/even
 t/1405/contributions/620/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/620/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the decision problem for quantified probability logic
DTSTART;VALUE=DATE-TIME:20231213T073000Z
DTEND;VALUE=DATE-TIME:20231213T075500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-628@indico.eimi.ru
DESCRIPTION:Speakers: Stanislav Speranski (Steklov Institute RAS)\nWe shal
 l be concerned with a natural one-sorted language L for talking about prob
 ability spaces\, where quantifiers are intended to range over events in a 
 given space. In this language one can express statements like `for every e
 vent E\, if P(E) > 0\, then there exists an event F such that 0 < P(F) < P
 (E)' — here P denotes the measure in question. It is known that the vali
 dity problem for arbitrary L-sentences is highly undecidable. So one may w
 ish to know more about prefix fragments of L. It turns out that the validi
 ty problem for AE-sentences in L is decidable\, while that for EA-sentence
 s is not. This solves the decision problem for prefix fragments of L. More
 over\, similar results can be obtained for some natural one-sorted fragmen
 ts of Halpern's first-order logics of probability.\n\nhttps://indico.eimi.
 ru/event/1405/contributions/628/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/628/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Complexity for theories with Kleene star
DTSTART;VALUE=DATE-TIME:20231214T124500Z
DTEND;VALUE=DATE-TIME:20231214T132500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-633@indico.eimi.ru
DESCRIPTION:Speakers: Stepan Kuznetsov (Steklov Institute RAS)\nWe give a 
 survey of algorithmic complexity results for theories of algebraic structu
 res including Kleene star. Those include Kleene algebras\, Kleene lattices
 \, and their extensions with division operations\, also called action alge
 bras / lattices. We focus on equational and Horn theories\, since already 
 on this level of expressivity we get high levels of undecidability. The ta
 lk includes both well-known old results (following Kozen 2002 and Buszkows
 ki 2007)\, as well as new ones recently obtained by the speaker. The latte
 r include undecidability and complexity of the logic of action algebras\, 
 both non-commutative and commutative\, and that of the logic of Kleene alg
 ebras with commutativity conditions.\n\nhttps://indico.eimi.ru/event/1405/
 contributions/633/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/633/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lower bounds for regular resolution over parities
DTSTART;VALUE=DATE-TIME:20231214T120000Z
DTEND;VALUE=DATE-TIME:20231214T124000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-632@indico.eimi.ru
DESCRIPTION:Speakers: Dmitry Itsykson (Ben-Gurion University)\nThe proof s
 ystem resolution over parities (Res(⊕)) operates with disjunctions of li
 near equations (linear clauses) over GF(2)\; it extends the resolution pro
 of system by incorporating linear algebra over GF(2). Over the years\, sev
 eral exponential lower bounds on the size of tree-like  Res(⊕) refutatio
 ns have been established. However\, proving a superpolynomial lower bound 
 on the size of dag-like  Res(⊕) refutations remains a highly challenging
  open question. We prove an exponential lower bound for regular  Res(⊕).
  Regular  Res(⊕) is a subsystem of dag-like  Res(⊕) that naturally ext
 ends regular resolution. This is the first known superpolynomial lower bou
 nd for a fragment of dag-like  Res(⊕) which is exponentially stronger th
 an tree-like Res(⊕). The talk is based on joint work with Klim Efremenko
  and Michal Garlik.\n\nhttps://indico.eimi.ru/event/1405/contributions/632
 /
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/632/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Search of structures computable in polynomial time
DTSTART;VALUE=DATE-TIME:20231213T094500Z
DTEND;VALUE=DATE-TIME:20231213T102500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-631@indico.eimi.ru
DESCRIPTION:Speakers: Pavel Alaev (Sobolev Institute RAS)\nWe consider som
 e questions related to the problem of searching a structure A computable i
 n polynomial time (in short\, P-computable)\, which is isomorphic to a giv
 en abstract structure B. In particular\, a general criterion for the exist
 ence of such a P-computable structure B is formulated. As an application\,
  we discuss some questions about the existence of P-computable presentatio
 ns for a series of classical objects\, including fields and Abelian groups
 .\n\nhttps://indico.eimi.ru/event/1405/contributions/631/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/631/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiplication formulas for Gaussian operators
DTSTART;VALUE=DATE-TIME:20231216T082000Z
DTEND;VALUE=DATE-TIME:20231216T091000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-626@indico.eimi.ru
DESCRIPTION:Speakers: Alexander Holevo (Steklov Institute RAS)\nhttps://in
 dico.eimi.ru/event/1405/contributions/626/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/626/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Domains of univalence for classes of bounded holomorphic functions
DTSTART;VALUE=DATE-TIME:20231216T070000Z
DTEND;VALUE=DATE-TIME:20231216T075000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-625@indico.eimi.ru
DESCRIPTION:Speakers: Aleksei Solodov (Moscow state university)\nThe probl
 em of finding domains of univalence for classes of holomorphic self-mappin
 gs of the disc is concidered. In 1926\, E. Landau found sharp radius of th
 e disc of univalence for the class of such mappings with a given value of 
 derivative at the inner fixed point. \nIn 2017\, V.V. Goryainov discovered
  the existence of domains of univalence for the classes of holomorphic sel
 f-mappings of the disc with two fixed points and conditions on the values 
 of angular derivatives at the boundary fixed points. The report is devoted
  to the development of these results. The sharp domains of univalence for 
 classes of holomorphic self-mappings of the disc with repulsive boundary f
 ixed point are found depending on the localization of the attracting fixed
  point and the value of the angular derivative at the repulsive fixed poin
 t.\n\nhttps://indico.eimi.ru/event/1405/contributions/625/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/625/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soft Riemann--Hilbert problems and planar orthogonal polynomials
DTSTART;VALUE=DATE-TIME:20231214T092000Z
DTEND;VALUE=DATE-TIME:20231214T101000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-621@indico.eimi.ru
DESCRIPTION:Speakers: Håkan Hedenmalm (Royal Institute of Technology and 
 Saint-Petersburg state university)\nRecent advances on planar orthogonal p
 olynomials with respect to exponentially varying weights become much easie
 r to work with if we introduce the concept of ``soft'' Riemann--Hilbert pr
 oblems. These are actually $\\overline{\\partial}$-problems but the underl
 ying thinking in terms of jump problems helps a lot. The method applies al
 so in the hard edge case where our work with A. Wennman gives a far-reachi
 ng generalization of Carleman’s theorem from 1921.\n\nhttps://indico.eim
 i.ru/event/1405/contributions/621/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/621/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Left-invariant diffusions on compact groups through Dirichlet form
  perturbation
DTSTART;VALUE=DATE-TIME:20231212T120000Z
DTEND;VALUE=DATE-TIME:20231212T123500Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-613@indico.eimi.ru
DESCRIPTION:Speakers: Qi Hou (Beijing Institute of Mathematical Sciences a
 nd Applications)\nGaussian convolution semigroups (also called heat semigr
 oups) on infinite dimensional compact groups exhibit a rich variety of ana
 lytic properties. The current knowledge mostly restricts to the product or
  central types\, corresponding to bi-invariant diffusions. In this talk we
  explain how to obtain heat kernel information for certain (non-product-ty
 pe\, noncentral) Gaussian semigroups through Dirichlet form perturbations.
  They correspond to certain left-invariant elliptic or sub-elliptic diffus
 ions on compact groups\, with generators left-invariant (sub-)Laplacians. 
 This is based on joint work with Laurent Saloff-Coste.\n\nhttps://indico.e
 imi.ru/event/1405/contributions/613/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/613/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Opening of the conference and a greeting word from organizers
DTSTART;VALUE=DATE-TIME:20231211T065000Z
DTEND;VALUE=DATE-TIME:20231211T070000Z
DTSTAMP;VALUE=DATE-TIME:20260815T220412Z
UID:indico-contribution-1405-602@indico.eimi.ru
DESCRIPTION:https://indico.eimi.ru/event/1405/contributions/602/
LOCATION:St. Petersburg University\, MCS faculty
URL:https://indico.eimi.ru/event/1405/contributions/602/
END:VEVENT
END:VCALENDAR