Name: Discrete and Continuous Signals: Analysis, Information and Applications
Start: 2023-12-11T09:50:00+03:00
End: 2023-12-16T18:00:00+03:00
Location: St. Petersburg University, MCS faculty

Discrete and Continuous Signals: Analysis, Information and Applications

from Monday, 11 December 2023 (09:50) to Saturday, 16 December 2023 (18:00)

Monday, 11 December 2023

09:50 Opening of the conference and a greeting word from organizers
Opening of the conference and a greeting word from organizers
09:50 - 10:00
10:00 Seiberg-Witten equations and pseudoholomorphic curves - Armen Sergeev (Steklov Institute RAS)
Seiberg-Witten equations and pseudoholomorphic curves
- Armen Sergeev (Steklov Institute RAS)
10:00 - 10:50
Seiberg--Witten 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 invariant under scale transformations. So to draw a useful information from these equations one should plug the scale parameter $\lambda$ into them and take the limit $\lambda\to\infty$. If we consider such limit in the case of 4-dimensional symplectic manifolds solutions of SW-equations will concentrate in a neighborhood of some pseudoholomorphic curve (more precisely, pseudoholomorphic divisor) while SW-equations reduce to some vortex equations in normal planes of the curve. The vortex equations are in fact static Ginzburg--Landau equations known in the superconductivity theory. So solutions of the limiting adiabatic SW-equations are given by families of vortices in the complex plane parameterized by the point z running along 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.
10:50 Coffee-break
Coffee-break
10:50 - 11:20
11:20 Multiplicative chaos - Alexander Bufetov (Steklov Institute RAS & Kharkevich Institute for Transmission Problems & Saint-Petersburg state university)
Multiplicative chaos
- Alexander Bufetov (Steklov Institute RAS & Kharkevich Institute for Transmission Problems & Saint-Petersburg state university)
11:20 - 12:10
In this survey talk, we will consider different approaches to constructing and studying the exponential of a random field, with a special emphasis on proving the convergence to Gaussian multiplicative chaos of random Euler-like products assigned to realizations of the sine-process.
12:20 Bipolar Green function and Nuttall decomposition of a three-sheeted torus - Semen Nasyrov (Kazan Federal university)
Bipolar Green function and Nuttall decomposition of a three-sheeted torus
- Semen Nasyrov (Kazan Federal university)
12:20 - 13:10
We study the Nuttall decomposition of a three-sheeted torus $T$ which is a Riemann surface $S$ 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 logarithmic 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 parts which induces the Nuttall decomposition of $T$. According to the Nuttall conjecture, this decomposition defines the convergence domains for the Hermite--Padé approximants. The study was supported by the grant of the Russian Science Foundation No. 23-11-00066.
13:20 Correct use of Padé approximants and Hermite--Padé polynomials in practice - Aleksandr Komlov (Steklov Institute RAS)
Correct use of Padé approximants and Hermite--Padé polynomials in practice
- Aleksandr Komlov (Steklov Institute RAS)
13:20 - 13:55
Let $f$ be an algebraic function and $f_0$ be its germ at some point $z_0\in\mathbb C$. Padé approximants are the best rational approximations of a given degree 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 applications. We give one example, where such mistake led to collapses in global electrical networks. We explain this mistake and explain how it was fixed by Trias in 2012 due to correct understanding of Stahl theory. Further we consider such generalizations of Padé polynomials as Hermite--Padé polynomials. Unfortunatelly, for these polynomials there is no analogue of Stahl theory for general $f$. But, sometimes Hermite--Padé polynomials are also used in practical applications without theoretical justification. Moreover, in some problems they are much more effective than usual Padé polynomials. We give such example from the molecular chemistry and justify it in the model case, when the function $f$ is 3-valued.
14:10 Lunch
Lunch
14:10 - 15:45
15:45 Coefficient approach to the problem of describing homogeneous manifolds - Alexander Loboda (Voronezh state university)
Coefficient approach to the problem of describing homogeneous manifolds
- Alexander Loboda (Voronezh state university)
15:45 - 16:20
The problem of describing holomorphically homogeneous real hypersurfaces of spaces $ \mathbb{C}^n$, $n=2,3,4$, is discussed as well as some close questions about the homogeneity of embedded submanifolds. We consider an approach related to the normalization of the surfaces themselves and the Lie algebras of vector fields associated with them, as well as to the determination of these objects through the lower Taylor coefficients of the functions representing them. The use of canonical (Moser normal) equations of real hypersurfaces in the space $\mathbb{C}^2 $ made it possible to obtain 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 homogeneous Levi-nondegenerate hypersurfaces with ``rich'' symmetry algebras. Reduction to canonical form of the basic holomorphic vector fields of 5-dimensional Lie algebras in the space $\mathbb{C}^3$ made it possible to obtain a complete description of all holomorphically homogeneous Levi-nondegenerate hypersurfaces with trivial symmetry algebras. A similar prospect emerges 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.
16:20 Coffee-break
Coffee-break
16:20 - 16:50
16:50 The spaces of delta-subharmonic functions of finite order with respect to the model function of growth - Konstantin Malyutin (Kursk state university)
The spaces of delta-subharmonic functions of finite order with respect to the model function of growth
- Konstantin Malyutin (Kursk state university)
16:50 - 17:25
The classes of standard functions introduced by B.N. Khabibullin are considered. The concept of a model function of growth covers a large class of functions. Functions $f$ of finite order with respect to the model function can have an order of growth in the classical sense equal to infinity or zero. For 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 superposition with $n=1,2,\dots$ of the exponential function $\exp$, degree 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 model growth function $M$ that estimate $f$ above and below. Thus, we solve the extended Hadamard problem for a fairly wide class of entire and subharmonic functions. The proof is constructive. The research is supported by Russian Science Foundation (project No. 22-21-00012).
17:35 On numerical differentiation of analytic functions by differences of $h$-sums - Mikhail Komarov (Vladimir state university)
On numerical differentiation of analytic functions by differences of $h$-sums
- Mikhail Komarov (Vladimir state university)
17:35 - 18:10
In 2006, V.I. Danchenko suggested the method of $h$-sums for approximation problems and numerical analysis (by $ h-sum$ $of$ $order$ $n$ we mean an expression of the form $H_n(z)=\sum_{k=1}^n \lambda_k h(\lambda_k z), \quad \lambda_k\in \mathbb{C},$ where $h(z)$ is a fixed function, analytic in the disk $D=\{z:|z|<1\}$, and $\lambda_1,\dots,\lambda_n$ are independent numeric parameters). In particular, it was proved that 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 the differentiation operator $(zh(z))'$ at the node $z_0=0$ with the multiplicity $n$: $(zh(z))'=\sum_{k=1}^n\lambda_{n,k} h(\lambda_{n,k}z)+O(z^n),$ and $H_n(z)$ converges uniformly to $(zh(z))'$ as $n\to \infty$ on compact subsets $K\subset D$ with exponential rate. We consider an analogous problem of numerical differentiation $ by$ $the$ $difference$ $of$ $two$ $h-sums$ $of$ $order$ $n$. It can be shown that under this modified approach the rate of approximation is much higher.
19:00 Welcome Party
Welcome Party
19:00 - 21:00
Tuesday, 12 December 2023
10:00 Time-frequency localization operator - Aleksei Kulikov (Tel-Aviv university)
Time-frequency localization operator
- Aleksei Kulikov (Tel-Aviv university)
10:00 - 10:50
Given a measurable 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 $(P_U f)(x) = f(x)\chi_U(x)$. Similarly, for the set $V\subset \mathbb{R}$ we define the Fourier projection onto $V$ as $Q_V = \mathcal{F}^{-1}P_V \mathcal{F}$, where $\mathcal{F}$ is a Fourier transform. The operator $S_{U, V} = P_UQ_VP_U$ is called a time-frequency localization operator, associated with $U$ and $V$. It is easy to see that $S_{U, V}$ is a non-negative definite operator of norm at most $1$. If both $U$ and $V$ have finite measure it 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 such it has a sequence of eigenvalues $1 \ge \lambda_1(U, V) \ge \lambda_2(U, V) \ge \ldots > 0$. In 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 $\approx \log c$ intermediate 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 mention a new exponential lower bound for the eigenvalues $\lambda_n(c)$ when $n < (1-\varepsilon)c, \varepsilon > 0$.
10:50 Coffee-break
Coffee-break
10:50 - 11:20
11:20 Random matrices ensembles and multiple orthogonal polynomials - Alexander Aptekarev (Keldysh Institute RAS)
Random matrices ensembles and multiple orthogonal polynomials
- Alexander Aptekarev (Keldysh Institute RAS)
11:20 - 12:10
Let $\mu(x):=(\mu_1(x),\dots , \mu_d(x))$ be a vector of positive measures. For a given multiindex $n=(n_1, \dots , n_d)$ we consider a polynomial $P_n(x)$ of degree $|n|:=n_1+ \cdots +n_p$, which satisfies $n_j$ orthogonality relations to the degrees of the scalar variable $x$ with respect to the measure $\mu_j$, $j=1, \dots , p$. Such polynomials always exist and they are called multiple orthogonal polynomials. For $p=1$ we have usual orthogonal polynomials. We discuss several examples of ensembles of random matrices related to the multiple orthogonal polynomials (namely: random matrix model with external source, two matrix model and normal matrix model). An application to the Brownian bridges will be highlighted.
12:20 Free topololgical groups - Leonid Genze (Tomsk state university)
Free topololgical groups
- Leonid Genze (Tomsk state university)
12:20 - 13:10
The 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 second 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.
13:10 Lunch
Lunch
13:10 - 15:00
15:00 Left-invariant diffusions on compact groups through Dirichlet form perturbation - Qi Hou (Beijing Institute of Mathematical Sciences and Applications)
Left-invariant diffusions on compact groups through Dirichlet form perturbation
- Qi Hou (Beijing Institute of Mathematical Sciences and Applications)
15:00 - 15:35
Gaussian convolution semigroups (also called heat semigroups) on infinite dimensional compact groups exhibit a rich variety of analytic 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-type, noncentral) Gaussian semigroups through Dirichlet form perturbations. They correspond to certain left-invariant elliptic or sub-elliptic diffusions on compact groups, with generators left-invariant (sub-)Laplacians. This is based on joint work with Laurent Saloff-Coste.
15:45 Removable sets for Newtonian space $N^{1,p}$ - Yuri Dymchenko (adm. G.I. Nevelskoy Maritime state university) Vladimir Shlyk (Far Eastern federal university)
Removable sets for Newtonian space $N^{1,p}$
- Yuri Dymchenko (adm. G.I. Nevelskoy Maritime state university)
- Vladimir Shlyk (Far Eastern federal university)
15:45 - 16:20
Let $X=(X,d,\mu)$ be a complete $p$-Poincaré metric space with distance $d$ and a Borel regular doubling measure $\mu$, $1<p<\infty$. Following Vodop'yanov and Gol'dstein, we introduce an analogue of $NC_p$-sets in the domain $\Omega$ of $X$ and give the criterion of equality $N^{1,p}(\Omega\setminus E)=N^{1,p}(\Omega)$ in terms of $E$ as an $NC_p$-set in $\Omega$. As a consequence, we obtain that the domains $\Omega_1$ and $\Omega$, $\Omega_1 \subset\Omega$, are $(1,p)$-equivalent if and only if $\Omega\setminus\Omega_1$ is an $NC_p$-set in $\Omega$. Moreover, for a quasisymmetric map $f:X\to Y$ of two complete $p$-regular, $p$-Poincaré metric spaces $X$ and $Y$, we show that $f(E)$ is an $NC_p$-set in the image $f(\Omega)$ if and only if $E$ is an $NC_p$-set in $\Omega\subset X$.
16:20 Coffee-break
Coffee-break
16:20 - 16:50
16:50 Integral formulas and inequalities for meromorphic functions and differences of subharmonic functions with applications - Enzhe Menshikova (Ufa Institute of Mathematics with Computing Centre) Bulat Khabibullin (Ufa Institute of Mathematics with Computing Centre)
Integral formulas and inequalities for meromorphic functions and differences of subharmonic functions with applications
- Enzhe Menshikova (Ufa Institute of Mathematics with Computing Centre)
- Bulat Khabibullin (Ufa Institute of Mathematics with Computing Centre)
16:50 - 17:25
We consider various formulas relating integrals of delta-subharmonic functions to their Riesz distributions of charges. These new formulas represent far-reaching developments and generalizations of the classical Poisson--Jensen, Shimizu--Ahlfors, I.I. Privalov, T. Carleman, B.Ya. Levin and other integral formulas. A distinctive feature of the new formulas is the absence in them of any derivatives or function values at individual points. The inequalities obtained from these formulas will be applied to uniqueness theorems for entire functions, to approximation in spaces of functions on subsets of the complex plane, etc. We will also indicate possible multidimensional complex generalizations of these results.
17:35 A curious hypergeometric identity and perfectness of Meixner--Sorokin system of weights - Alexander Dyachenko (Keldysh Institute RAS)
A curious hypergeometric identity and perfectness of Meixner--Sorokin system of weights
- Alexander Dyachenko (Keldysh Institute RAS)
17:35 - 18:10
On two integer lattices with interlacing nodes let us introduce two discrete measures for which a point weight is determined by the product of two classical Meixner weights. It turns out that the resulting measures are positive when the lattices alternate. This generalisation of the Meixner weight was introduced by Sorokin in 2010. He studied asymptotic behaviour of the corresponding orthogonal polynomials~$P_{n,n}$ with diagonal indices. The orthogonal polynomials may be constructed using the (discrete) Rodrigues formula, but the question whether they are uniquely defined remained open. Indeed, such a system of measures does not form a Nikishin system as the measures have disjoint supports; it does not form an Angelesco systems either since one of these supports lies in the convex hull of the other. Nevertheless, the uniqueness of the orthogonal polynomials (i.e. the normality of diagonal indices for Sorokin's system of measures) would be useful for applying Sorokin's result. The talk will be aimed at showing that 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. This is a joint research with Alexander Aptekarev and Vladimir Lysov.
Wednesday, 13 December 2023
10:00 Complex Analysis Session talks
Complex Analysis Session talks
10:00 - 11:30
Room: MCS 201
Contributions

10:00 Analytic continuation of power series by means of coefficients interpolation - Alex Mkrtchyan (Siberian Federal university and Institute of Mathematics NAS RA)

10:45 V.V. Chernikov’s method for investigating functionals on the class of conformal univalent mappings - Ivan Kolesnikov (Tomsk state university)
10:00 - 11:30
Contributions

10:00 On primitive recursive and automatic structures - Nikolay Bazhenov (Sobolev Institute RAS)

10:30 On the decision problem for quantified probability logic - Stanislav Speranski (Steklov Institute RAS)

11:00 Recursion elimination: from olympiad problems to program optimization - Nikolay Shilov (Innopolis University)
11:30 Coffee-break
Coffee-break
11:30 - 12:00
12:00 Complex Analysis Session talks
Complex Analysis Session talks
12:00 - 13:30
Room: MCS 201
Contributions

12:00 Avkhadiev--Wirths' conjecture for Hardy inequalities on balls - Ramil Nasibullin (Kazan Federal university)

12:45 On the range of a convolution operator in spaces of ultradifferentiable functions - Daria Polyakova (Southern Federal university)
Theoretical Computer Science Session
Theoretical Computer Science Session
12:00 - 13:30
Contributions

12:00 Monomial combinatorics of polynomial ideals and related algorithms - Nikolay Vasilyev (PDMI)

12:45 Search of structures computable in polynomial time - Pavel Alaev (Sobolev Institute RAS)
13:30 Lunch
Lunch
13:30 - 15:00
Thursday, 14 December 2023
10:00 Information disclosure in networks - Nikolay K. Vereshchagin (Moscow State University)
Information disclosure in networks
- Nikolay K. Vereshchagin (Moscow State University)
10:00 - 10:50
We consider the network consisting of three nodes 1, 2, 3 connected by two 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 need to know y, z, respectively. We want to arrange transmission of information over the channels so that both nodes 2 and 3 learn what they need and the disclosure of information is as small as possible. By information disclosure we mean the amount of information in the strings transmitted through 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 simultaneously minimize the length of words transferred through the channels.
10:50 Coffee-break
Coffee-break
10:50 - 11:20
11:20 Quantum fingerprinting and hashing for computing, processing and transmitting information - Farid M. Ablayev (Kazan Federal University)
Quantum fingerprinting and hashing for computing, processing and transmitting information
- Farid M. Ablayev (Kazan Federal University)
11:20 - 12:10
Quantum fingerprinting is a family of quantum functions that began to be used in quantum algorithms in the early 2000s. They map classical objects to quantum states in such a way that different arguments can be effectively distinguished. 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 hashing, as well as their use in communications protocols, cryptographic signatures, and pattern searching in text.
12:20 Soft Riemann--Hilbert problems and planar orthogonal polynomials - Håkan Hedenmalm (Royal Institute of Technology and Saint-Petersburg state university)
Soft Riemann--Hilbert problems and planar orthogonal polynomials
- Håkan Hedenmalm (Royal Institute of Technology and Saint-Petersburg state university)
12:20 - 13:10
Recent advances on planar orthogonal polynomials with respect to exponentially varying weights become much easier to work with if we introduce the concept of ``soft'' Riemann--Hilbert problems. These are actually $\overline{\partial}$-problems but the underlying thinking in terms of jump problems helps a lot. The method applies also in the hard edge case where our work with A. Wennman gives a far-reaching generalization of Carleman’s theorem from 1921.
13:10 Lunch
Lunch
13:10 - 15:00
15:00
15:00 - 16:35
Contributions

15:00 On generating quantum channels - Renat Gumerov (Kazan Federal university) Ruslan Khazhin (Kazan federal university)

15:30 On some properties of classical and quantum random walks - Stanislav Grishin (Moscow Institute of Physics and Technology)

16:00 A semigroup approach to describing the stochastic dynamics of a quantum system - Andrey Utkin (Moscow Institute of Physics and Technology & Steklov International Mathematical Center)
15:00 - 16:30
Contributions

15:00 Lower bounds for regular resolution over parities - Dmitry Itsykson (Ben-Gurion University)

15:45 Complexity for theories with Kleene star - Stepan Kuznetsov (Steklov Institute RAS)
16:35 Coffee-break
Coffee-break
16:35 - 17:00
17:00
17:00 - 17:25
Contributions

17:00 Continuation of the family of projectors to a positive operator-valued measure and restoration of the quantum state after measurement - Anton Alekseev (Moscow Institute of Physics and Technology)
17:00 - 18:30
Contributions

17:00 Exact real computation for differential equations - Svetlana Selivanova (Ershov Institute of Informatics Systems, RAS)

17:30 Lower bounds for monotone minimal perfect hashing revisited - Dmitry Kosolobov (Ural Federal University)

18:00 Phase shift and multi-controlled Z-type gates - Andrey Novikov (Sobolev Institute RAS)
19:00 Conference Dinner
Conference Dinner
19:00 - 21:00
Friday, 15 December 2023
10:00 Three versions of the nonlinear Fourier transform for real-analytic signals in optical fibers - Andrey Domrin (Moscow state university)
Three versions of the nonlinear Fourier transform for real-analytic signals in optical fibers
- Andrey Domrin (Moscow state university)
10:00 - 10:50
The evolution of the complex envelopes of signals in fiber-optics communications is described 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 the 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 for any real-analytic initial data and discuss the natural isomorphism between the third version and each of the first two versions in the case of real-analytic signals satisfying the corresponding boundary conditions.
10:50 Coffee-break
Coffee-break
10:50 - 11:20
11:20 On Dirichlet problem for bianalytic functions and for solutions of general second-order non-strongly elliptic systems with constant coefficients - Konstantin Fedorovskiy (Moscow state university)
On Dirichlet problem for bianalytic functions and for solutions of general second-order non-strongly elliptic systems with constant coefficients
- Konstantin Fedorovskiy (Moscow state university)
11:20 - 12:10
In the talk we plan to discuss Dirichlet problem for non-strongly elliptic second-order PDE with constant complex coefficients in bounded simply connected domains in the complex plane. Starting with the most known case of bianalytic 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, solutions 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 respect to the Dirichlet problem for any non-strongly elliptic system under consideration, which means that there always exists a continuous complex-valued function on the boundary of the domain under consideration that can not be continuously extended to this domain to a function satisfying the corresponding system therein. Since there exists a Jordan domain with Lipschitz boundary, which is regular with respect to the Dirichlet problem for bianalytic functions, the result obtained is near to be sharp. The discovered phenomena that domains with sufficiently smooth boundaries are not regular with respect to the Dirichlet problem for systems under consideration, while domains having worse boundaries may be regular is rather unexpected and essentially new.
12:20 Mellin--Barnes integrals and equivalences of triangulated categories - Mauricio Romo Jorquera (Yau Mathematical Science Center)
Mellin--Barnes integrals and equivalences of triangulated categories
- Mauricio Romo Jorquera (Yau Mathematical Science Center)
12:20 - 13:10
In 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 triangulated categories. We will focus on the case of how monodromies give rise to autoequivalences of derived categories of coherent sheaves and present several examples, as time allows.
13:10 Lunch
Lunch
13:10 - 15:00
15:00
15:00 - 16:15
Room: MCS 201
Contributions

15:00 Conformal spectral estimates of the Dirichlet-Laplacian - Valerii Pchelintsev (Tomsk state university)

15:40 Weissler type inequalities in Bergman spaces - Diana Khammatova (Kazan Federal university)
15:00 - 16:15
Room: 217b
Contributions

15:00 Symmetries of $C^*$-algebras - Ekaterina Turilova (Kazan Federal university)

15:40 Entanglement-based approach to quantum coherence, path information, and uncertainty - Aleksei Kodukhov (Terra Quantum AG) Dmitry Kronberg (Steklov Institute RAS)
16:15 Coffee-break
Coffee-break
16:15 - 16:45
16:45
16:45 - 18:40
Room: MCS 201
Contributions

16:45 Quantum Gaudin model and isomonodromic deformations - Ilya Tolstukhin (Higher School of Economics)

17:25 On the construction of the Green's function for strongly elliptic systems in domains on the plane - Astamur Bagapsh (Bauman Moscow State Technical University)

18:05 On the scalar approach to the weak asymptotic problem for the model $\mathcal{GN}$-system - Elijah Lopatin (Steklov Institute RAS)
16:45 - 17:40
Room: 217б
Contributions

16:45 Example of a non-covariant channel constructed using the unitary irreducible representation of a finite group, for which classical capacity is calculated - Lev Ryskin (Moscow Institute of Physics and Technology)

17:15 Characterization of non-adaptive Clifford channels - Vsevolod Yashin (Steklov Institute RAS)
Saturday, 16 December 2023
10:00 Domains of univalence for classes of bounded holomorphic functions - Aleksei Solodov (Moscow state university)
Domains of univalence for classes of bounded holomorphic functions
- Aleksei Solodov (Moscow state university)
10:00 - 10:50
The problem of finding domains of univalence for classes of holomorphic self-mappings of the disc is concidered. In 1926, E. Landau found sharp radius of the disc of univalence for the class of such mappings with a given value of derivative at the inner fixed point. In 2017, V.V. Goryainov discovered the existence of domains of univalence for the classes of holomorphic self-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 fixed point are found depending on the localization of the attracting fixed point and the value of the angular derivative at the repulsive fixed point.
10:50 Coffee-break
Coffee-break
10:50 - 11:20
11:20 Multiplication formulas for Gaussian operators - Alexander Holevo (Steklov Institute RAS)
Multiplication formulas for Gaussian operators
- Alexander Holevo (Steklov Institute RAS)
11:20 - 12:10
12:20 Approximation by sums of shifts of one function - Petr Borodin (Moscow state university)
Approximation by sums of shifts of one function
- Petr Borodin (Moscow state university)
12:20 - 13:10
The talk presents a survey of results on the density of the additive semigroup generated by shifts of one function in various function spaces.
13:10 Lunch
Lunch
13:10 - 15:00