Lecture Series 27 —— April 7, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/C745583AE3B73B5E4E69ABDBAE6C8459
Valid Until: 2026-05-31 23:59

 

Lecture 1——Extending periodic maps on surfaces over the 4-sphere

 

Speaker: Prof. Shicheng Wang, Peking University

 

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

 

Abstract: The topic indicated by the title has been addressed by Montesinos (1982) and Hirose (2002) using Rohlin intersection form, and by Ding-Liu-Wang-Yao (2012) using spin structures.

    Based on the work above, we deduce a more computable criterion for extending periodic maps on surfaces over the 4-sphere.

    Some applications are given. Results including:

(1) Let $F_g$ be the closed orientable surface of genus $g$ and $w_g$ be a periodic map of maximum order on $F_g$.

    Then $w_g$ is extendable over $S^4$ for some smooth embedding $e: F_g\ to S^4$ if and only if $g=4k, 4k+3$.

(2) For infinitely many primes $p$, each periodic map of order $p$ on $F_g$ is extendable over $S^4$ for some smooth embedding $e: F_g\ to S^4$.

    This is joint work with Zhongzi Wang.

 

Bio: Prof. Shicheng Wang is currently a Distinguished Professor at the Department of Mathematics, Peking University. He received a master's degree from Peking University in 1981 and a doctorate degree from UCLA in 1988. He has won the Shiing-Shen Chern Mathematics Award and the second prize of the National Natural Science Awards (China). Prof. Wang was an invited speaker at the ICM’2002 in Beijing. His research focuses on low-dimensional topology, involving geometric group theory, dynamical systems, and algebraic topology.

 

Lecture 2——A Mozaic from Geometry, Dynamics, PDEs, and maybe more.

 

Speaker: Prof. Dimitri Yu. Burago, Pennsylvania State University, State College PA

 

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

 

Abstract: I am going to begin with some unsolved problems, which, in my opinion, deserve more attention that they receive. For some problems, there are partial solutions, which I would try to sketch or at least discuss. I plan then to go to problems where the progress is more substantial, as time permits. What I plan is indeed a mozaic. I am not sure how many topics I would be able to touch upon and which ones would be more of interest, my collaborators include D. Chen, S. Ivanov, B. Kleiner, Ya. Kurylev, M. Lassas, J. Lu, A. Novikov, L. Polterovich. Maybe, I would concentrate оn two or three topics, maybe many more short stories, depending on the reaction.

 

Bio: Dimitri Yurievich Burago is a worldwide renowned expert in Geometry, Topology and Dynamical Systems. He graduated from Saint Petersburg State University and has got his doctorate in 1994 under the supervision of Prof. Anatoly Vershik. Now he is working at Pennsylvania State University where he received the title of Distinguished Professor in Mathematics. Besides, Prof. Burago received many prestigious prizes including the Leroy P. Steele Prize by the American Mathematical Society. Also, he was an invited speaker of the ICM’1998 in Berlin.

 

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Lecture Series 26 —— March 24, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).
 

Video: https://disk.pku.edu.cn:443/link/EE1E0EAC2E77FE3CF97E4E2B48DAAEA3
Valid Until：2026-04-30 23:59

 

Lecture 1——On Lyapunov exponents of quasi-periodic cocycles

Speaker: Jiangong You (Chern Institute of Mathematics, Nankai University)

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: Lyapunov exponents are dynamical invariants. Quasi-periodic cocycles are a special important class of dynamical systems having strong background in quantum physics. Lyapunov exponents of a quasi-periodic cocycle depends sensitively on the smoothness of the cocycle, arithmetic property of the frequency and profile of the potential. So far the behind mechanism of the sensitivity has not been completely understood. In this talk, I will discuss the continuity, Holder regularity of the Lyapunov exponent as well as the quantitative version of Avila’s global theory. The talk is based on joint works with L. Ge, S. Jitomirskaya, Y. Wang, X. Zhao and Q. Zhou.

Bio: Jiangong You is a professor at Chern Institute of Mathematics of Nankai University. His research interests include Hamiltonian dynamics (especially KAM theory for Hamiltonian ODEs and PDEs), smooth ergodic theory (especially Lyapunov exponents) and mathematical physics (especially spectral theory of quasi-periodic Schrodinger operators).

 

Lecture 2——Systems of isometries: dynamics and topology

Speaker: Alexandra Skripchenko

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract: Systems of partial isometries of the interval represent a simple combinatorial object which appears in topology in connection with measured foliations on a surface (orientable or non-orientable), in dynamics as a nice model to study billiards in rational polygons and in geometric group theory as a way to describe actions of free groups on R-trees. We will discuss several classes of systems of isometries (interval exchange transformations, interval exchange transformations with flips, interval translation mappings, band complexes) and compare their basic dynamical properties: minimality, ergodicity, invariant measures etc. The talk is mainly based on the joint works with Artur Avila and Pascal Hubert and with Serge Troubetzkoy.

Bio: Prof. Alexandra Skripchenko is the Dean of Faculty of Mathematics at Higher School of Economics (HSE), Moscow. She is expert in Dynamical Systems, Low-dimensional Topology and Geometric Group Theory. In particular, she has got some outstanding results concerning interval exchange mappings and interval translation mappings. Having graduated from Moscow State University in 2009, Alexandra Skripchenko has got her PhD in 2012 and works at HSE since 2014.

 

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Lecture Series 25 —— March 8, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).

 

Recording: https://disk.pku.edu.cn:443/link/EDA3BDF8D06B8765C1542BE7278C7D3B
Valid Until: 2026-06-30 23:59

 

Lecture 1——Sharp asymptotics for arm events in critical planar percolation

Lecture Series 24 —— December 16, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).
 

Video: https://disk.pku.edu.cn:443/link/D51CB6937C05AB71E2B6F5627F6ECB52
Valid Until：2026-04-30 23:59

 

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Lecture Series 23 —— December 02, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/A863DD4C00B98F1807DB384C8909F353
Valid Until：2026-04-30 23:59

 

Lecture 1——Gabor analysis for rational functions

Speaker: Prof. Yuri Belov

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract:   Let $g$ be a function in $L^2(\mathbb{R})$. By $G_\Lambda$, $\Lambda\subset R^2$  we denote the system of time-frequency shifts of $g$, $G_\Lambda=\{e^{2\pi i \omega x}g(x-t)\}_{(t,\omega)\in\Lambda}$.

 A typical  model set $\Lambda$ is the rectangular lattice  $\Lambda_{\alpha, \beta}:= \alpha\mathbb{Z}\times\beta\mathbb{Z}$  and one of the basic  problems of the Gabor analysis is the description of the frame set of $g$ i.e., all pairs $\alpha, \beta$ such that  $G_\Lambda_{\alpha,\beta}$ is a frame   in $L^2(\mathbb{R})$. It follows from the general theory that $\alpha\beta \leq 1$ is a necessary condition (we assume $\alpha, \beta > 0$, of course). Do all such $\alpha, \beta $  belong to the frame set of $g$? Up to 2011 only few such functions $g$ (up to translation, modulation, dilation and Fourier transform) were known. In 2011  K. Grochenig and J. Stockler extended this class by including the totally positive functions of finite type(uncountable family yet depending on finite number of parameters) and later added the Gaussian finite type totally positive functions. We suggest another approach to the problem and prove that  all Herglotz rational functions with imaginary poles  also belong to this class. This  approach also gives  new results for general rational functions.  In particular, we are able to confirm Daubechies conjecture for rational functions and irrational densities.

 

Lecture 2——Planar Sobolev extension domains and quasiconformal mappings.  

Speaker: Yi Zhang

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract: In 1979, Goldshtein et al. pointed out that a bounded simply connected planar domain is a W^{1,\,2}-extension domain if and only if it is a quasidisk. This result was later generalized by Jone to all dimensions, showing that uniform domains are W^{1,\,p}-extension domain for any 1\le p<\infty. However, there are simply connected W^{1,\,p}-extension domains in the plane which are not uniform when p\neq 2, pointed out by e.g. Maz'ya. In this talk I will present my joint work with Koskela and Rajala on this problem, and show its connection to the Ahlfors' quasiconformal reflection theorem.  

Bio:   My main background is in complex analysis and geometric function theory. I have also done works on harmonic analysis, functional analysis, nonlinear elliptic partial differential equations (p-Laplacians and infinity Laplacian), free boundary problems, calculus of variations, eigenvalue problems of p-Laplacians and so on. Especially, I am interested in problems in the intersection of analysis and geometry.

B.S., Math & Applied Math, Beihang University, September 1, 2009 – June 30, 2013.

M.S., Mathematics, University of Jyväskylä (Supervisor: Pekka Koskela), August 1, 2013 – July 30, 2014.

Ph.D., Mathematics, University of Jyväskylä (Supervisor: Pekka Koskela), August 1, 2014 – July 30, 2017.

Doctoral Dissertation: Planar Sobolev extension domains. (Defended on May 5th, 2017)

 

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Video: https://disk.pku.edu.cn:443/link/5B3295FADF4652F5B3814A5112999F28
Valid Until：2026-04-30 23:59

Lecture 1——Symmetry Results in Two-Dimensional Inequalities for Aharonov–Bohm Magnetic Fields.
Speaker: Prof. Ari Laptev,  
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Lecture 2——Microscopic conservation laws for the derivative nonlinear Schrodinger equation
Speaker: Guixiang Xu (Beijing Normal University)
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

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Lecture Series 21 —— November 04, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).
 

Video: https://disk.pku.edu.cn:443/link/6D11936873F0A5E492B553AC48F3E6C6
Valid Until：2026-04-30 23:59

 

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Lecture Series 20 — October 21, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/90A35E4EF58FF4E7D0841D0217747F5D
Valid Until：2026-04-30 23:59

 

Lecture 1——Multiplication Between (Local) Hardy Spaces and Their Dual Spaces

Speaker: Yang Dachun

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: It is well known that bilinear decompositions of products of (local) Hardy spaces and their dual spaces play an important role in the study on various problems from analysis. In this talk, we present some recent progresses on such bilinear decompositions of products of (local) Hardy spaces and their dual spaces. Some open questions are also mentioned in this talk.

Bio: Yang Dachun, Professor, School of Mathematical Sciences, Beijing Normal University. Focus on the research of the real-variable theory of function spaces and its applications. Rewarded by National Science Foundation for Distinguished Young Scholars of China in 2005.

 

Lecture 2 ——  Elementwise sub-representations of groups, and their automorphic analogue.

Speaker: Dipendra Prasad, Prof.

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract:  Suppose V and W are two finite dimensional representations of a group G such that for each element g of G, the eigenvalues of g (counted with multiplicity) on V are contained in  the eigenvalues of g on W. What can we say about V and W? Such a question appears naturally in Automorphic representations which we will briefly discuss, but then focus on the abstract question on group representations.

Bio: Professor Dipendra Prasad works at the Indian Institute of Technology Bombay (Mumbai, India) having the second position at Saint - Petersburg State University where he heads the Laboratory ‘Modern Algebra and Applications’ at the Department of Mathematics and Computer Science. He obtained his bachelor’s degree from the St. Xavier College, Mumbai in 1978 before moving to the Indian Institute of Technology Kanpur which he completed in 1980. From 1980–1985, Prasad worked as a research scholar at the Tata Institute of Fundamental Research, Mumbai (TIFR Mumbai). He then completed his PhD under the supervision of Benedict Gross at Harvard, in 1989.

Prof. Prasad is a worldwide known expert in Number Theory, Group Theory and Representation Theory (mainly, on Automorphic Representations and the Gan-Gross-Prasad conjecture).  

He has got a big number of prestigious awards on national and international levels. In 2018, he was an invited speaker at the ICM in Rio de Janeiro.

 

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Lecture Series 19 — October 7, 2021（19:00-21:00 Beijing time or 14:00-16:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/F1CEAE494B34A35B67CBA8BD214CB2FD
Valid Until：2026-04-30 23:59

 

Lecture 1——Norm-resolvent convergence to zero-range models with internal structure in models with strong inhomogeneities

Speaker: Alexander V. Kiselev

Time: 19:00-20:00 Beijing time (14:00-15:00 St Petersburg time)

Abstract:

Bio: Dr. Alexander Kiselev, an outstanding expert in Mathematical Physics, whose interested include but not are limited to:
- Functional model for non-selfadjoint linear operators in Hilbert spaces
- Functional analysis;
- Stability Theory and Similarity Theory for non-selfadjoint linear operators;
- Theory of perturbations.
    Having graduated from Saint Petersburg State University in 1996 (Faculty of Physics), Dr. Kiselev obtained his PhD degree in 2001. After that he was working in a big number of top-level universities including Dublin Institute of Technology, Universidad Nacional Autónoma de México, University College London, University of Bath, and Lomonosov Moscow State University,
    The number of Alexander Kiselev’s collaborators and coauthors is very impressive as well as the number and scientific diversity of his research projects and students.
    Now Dr. Kiselev is working at the Department of Mathematics and Computer Science of Saint Petersburg State University.
 

Lecture 2 ——  Elementwise sub-representations of groups, and their automorphic analogue.

Speaker: Mingying Zhong

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: By identifying a norm capturing the effect of the forcing governed by the Poisson equation, we give a detailed spectrum analysis on the linearized Vlasov-Poisson-Boltzmann system around a global Maxwellian. It is shown  that the  electric field governed by the self-consistent Poisson equation plays a key role in the  analysis so that the spectrum structure is genuinely different from the well-known one of the Boltzmann equation. Based on this, we give the optimal time decay rates  of solutions to the equilibrium. 

Bio: Zhong Mingying, Professor, College of Mathematics and Information Science, Guangxi University. Focus on the spectral analysis, Green's function and fluid dynamical limits of the kinetic equations with external force, such as the Vlasov-Poisson(Maxwell)-Boltzmann systems, and so on. Rewarded by National Natural Science Foundation--Outstanding Youth Foundation, 2019.

 

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Lecture Series 18 — June 3, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/15CD646FE11B67512C30EDD28E594410
Valid Until：2026-04-30 23:59

 

Lecture 1——Nevanlinna  factorization in classes of analytic functions smooth up to the boundary.

Speaker: N.A. Shirokov

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: The definition of all objects used in this announcement will be given in the talk. Let an analytical function f belong to the Hardy class Hp in the unit disc D. Then f may be represented as the product, f=IOf, where I is the so-called inner function, it means that |I(z)|<1 for z belonging D, and |I(z)|=1 for almost every z on the unit circle, and the so-called outer function Of  is defined  by values  of |f(z)| on the unit circle. One of those two factors  may be absent. The cited statement is the classical result, the factors I and Of are in a sense independent for the functions  f from Hp. Let us  consider a class X which is contained in H1 and consists of functions f continuous in the closed disc D--. Then f=IOf ,the inner function I is in general  discontinuous in D--  what  implies that the outer function  Of is to compensate the points of  discontinuity of the inner function I. The talk is devoted to the concrete way of  this compensation and to the specific properties of outer functions  belonging  to the analytical Holder classes and to the classes of functions of variable smoothness. The consequences about the half-smoothness of an analytical  function in comparison with the  smoothness  of its modulus on the boundary will be given too.

Bio: Professor Nikolai A. Shirokov is a worldwide renowned expert in harmonic and complex analysis which includes the theory of approximations, boundary properties of holomorphic functions and the theory of singular integrals. Having graduated from Saint Petersburg State University in 1971, he has got his Ph.D.in 1973, became Doctor of Science (Saint Petersburg department of Steklov Institute) in 1985 and got his Professor degree in 1988. Professor Shirokov is the author of 82 research publications (Scopus) and a supervisor of a big number of students (both graduate and undergraduate). In 2014 he was officially recognized as ‘the best teacher’ of Higher School of Economics which is one of the most prestigious Russian Universities. N.A. Shirokov heads the department of Math.Analysis of Saint Petersburg State University since 2005 and the Department of Applied Mathematics at Higher School of Economics (Saint Petersburg branch) since 2013.

 

Lecture 2 ——  Factoring Quasiconformal & quasisymmetric mappings

Speaker: Jinsong Liu (Institute of Mathematics, Chinese Academy of Sciences)

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract: It follows from the Measurable Riemann Mapping Theorem that we can always present a 2-dimensional quasi-conformal mapping as a composition of quasi-conformal mappings with smaller dilatation. In this talk we will construct n (≥3)-dimensional quasi-conformal homeomorphism between Euclidean spaces which admit no minimal factorization in linear, inner, or outer dilatation. If time permits, I will discuss the composition of quasi-symmetric mappings between metric spaces.

Bio: Jinsong Liu is a professor of institute of mathematics, Chinese Academy of Sciences. His research field is complex analysis and Teichmuller theory.

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Lecture Series XVII — May 20, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/820DF463C85B66E00CB1FB0C1DDFB027
Valid Until：2026-04-30 23:59

 

Lecture 1——Fractional Calculus for m-accretive Operators

Speaker: Dr. Maxim Kukushkin,  Moscow State University for Civil Engineering; Institute for Applied Mathematics and Automatization

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: In this report we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is understood as an interpretation of concrete differential operators in terms of the infinitesimal generator of a corresponding semigroup. We study such operators as a Kipriyanov operator, Riesz potential, difference operator. Along with this, we consider transforms of m-accretive operators as a generalization, introduce a special operator class and provide a description of its spectral properties.

Bio: Maksim Kukushkin is a specialist in boundary problems, fractional derivatives and operator theory being author of a wide range of publications in all these areas. He has got his PhD degree in 2016 and, after the worked at  Moscow State University of Civil Engineering, Kabardino-Balkarian Scientific Center and Saint Petersburg State Transport University.

 

Lecture 2 —— Cohn-Vossen inequality on certain noncompact Kahler manifolds

Speaker: Prof. Gang Liu, East China Normal University

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract:  We generalize the Cohn-Vossen inequality to certain noncompact Kahler manifolds. This is related to a conjecture of Yau.

Bio:Gang Liu graduated from the University of Minnesota. He was a postdoctoral fellow at the University of California, Berkeley, and an assistant professor at Northwestern University. Now he is a professor at the East China Normal University.

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Lecture Series XVI — May 13, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).
 

Video: https://disk.pku.edu.cn:443/link/8A04293383593E6A308D71987895879D
Valid Until：2026-04-30 23:59

Lecture 1——Newton’s aerodynamic problem: an overview of recent results and open questions
Speaker: Alexander Plakhov University of Aveiro (Portugal) and Institute for Information Transmission Problems RAS (Moscow)
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: Newton (1687) posed the problem of finding  a convex axisymmetric bodies of the smallest aerodynamic drag. So, we are looking for the optimal curve which is the generatrix of the body. In 1993, a similar problem was formulated in a wider class of convex (not necessarily symmetric) bodies. This task proved to be much more difficult: it is about finding the optimal surface. The talk will provide an overview of recent results and methods used, and besides, we formulate some open questions. А special attention will be paid to the following statement. If all points of an open (in the relative topology) subset of the boundary of some optimal body are regular (that is, C ^ 1-smoothness holds), then this set does not contain any extreme points of the body. This statement is a strengthening of a similar result (Brock, Ferone, Kawohl, 1996), formulated for C ^ 2-smooth subsets.

 

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Lecture Series XV——April 22, 2021（15:00-17:00 Beijing time or 10:00-12:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/29E2301EB5B100B243E8F3503523C0D5
Valid Until：2026-04-30 23:59

Lecture 1—— POINT PROCESSES AND INTERPOLATION
Speaker: Alexander BUFETOV (CNRS Steklov IITP RAS)
Time: 2021-04-22 15:00-16:00 Beijing time or 10:00-11:00 St Petersburg time
Abstract: The Kotelnikov theorem recovers a Paley-Wiener function from its restriction onto an arithmetic progression. A Paley-Wiener function can also be recovered from its restriction onto a realization of the sine-process with one particle removed. If no particles are removed, then the possibility of such interpolation for the sine-process is due to Ghosh, for general determinantal point processes governed by orthogonal projections, to Qiu, Shamov and the speaker. If two particles are removed, then there exists a nonzero Paley-Wiener function vanishing at all the remaining particles.
How explicitly to interpolate a function  belonging to Hilbert space that admits a reproducing kernel, given the restriction of our function onto  a realization of the determinantal pont process governed by the kernel? In the case of the zero set of the Gaussian analytic function, or, in other words, the determinantal point process governed by the Bergman kernel, in joint work with Qiu, the Patterson-Sullivan construction is used for uniform interpolation in dense subspaces of the Bergman space. The invariance of our point process under Lobachevskian isometries plays a key rôle.
For the sine-process, the Ginibre process, the determinantal point process with the Bessel kernel and  the determinantal point process  with the Airy kernel, A.A. Borichev, A.V. Klimenko and the speaker proved that if the function decays as a sufficiently high negative power of the distance to the origin, then the answer is given by the Lagrange interpolation formula.
Bio: Alexander Bufetov is an expert in Ergodic Theory, Probability, Dynamical Systems and Statistics.
He graduated from Moscow State University being student of Acad. Ya. Sinai, one of the worldwide greatest experts in Ergodic Theory. Later on, he has got his PhD from Princeton University. In 2011 he became Doctor of Sciences. In 2015 he won the prestigious Sofia Kovalevskaya price and, thereafter, has got a honorary degree of ‘Professor of Russian Academy of Science’. He is an author of an impressive number of outstanding results https://scholar.google.com/citations?user=nAkXSowAAAAJ&hl=ru.
Prof. Bufetov had a wide range of prestigious positions: at Mathematical Institute of Russian Academy of Sciences, Higher School of Economics, Rice Univeristy, Chebyshev Laboratory at Saint Petersburg State University etc.  Now he is working at University Aix-Marseille at CNRS Director position.


Lecture 2—— Differential Network Analysis via Lasso Penalized D-Trace Loss
Speaker: Ruibin Xi (Peking University)
Time: 2021-04-22 16:00-17:00 Beijing time or 11:00-12:00 St Petersburg time
Abstract: 
Biological networks often change under different environmental and genetic conditions. In this paper, we model the network change as the difference of two precision matrices and propose a novel loss function called the D-trace loss, which allows us to directly estimate the precision matrix difference without attempting to estimate precision matrices. Under a new irrepresentability condition, we show that the D-trace loss function with the lasso penalty can give consistent estimators in high-dimensional settings if the difference network is sparse. A very efficient algorithm is developed based on the alternating direction method of multipliers to minimize the penalized loss function. Simulation studies and a real data analysis show that the proposed method outperforms other methods.
Bio: 
Dr. Ruibin Xi is an associate professor at School of Mathematical Sciences, Peking University. He obtained his PhD from Washington University in St. Louis and received post doc training at Harvard Medical School. His main research interests include statistical analysis of big biological data, cancer genomics, network and graphical models, Bayesian analysis and high-dimensional statistics. 

 

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Lecture Series XIV——April 8, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/1D59046D6638F95A152BF678ECE03FC3
Valid Until：2026-04-30 23:59

Lecture 1——Transcendence Theory over Function Fields on Quotients of Bounded Symmetric Domains
Speaker: Ngaiming Mok (The University of Hong Kong)
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: Finite-volume quotients of bounded symmetric domains Ω, which are naturally quasi-projective varieties, are objects of immense interest to Several Complex Variables, Algebraic Geometry, Arithmetic Geometry and Number Theory, and an important topic revolves around functional transcendence in relation to universal covering maps of such varieties. While a lot has already been achieved in the case of Shimura varieties by means of methods of Model Theory, Hodge Theory and Complex Differential Geometry, techniques for the general case of not necessarily arithmetic quotients Ω/Γ =: XΓ have just begun to be developed. For instance, Ax-type problems for subvarieties of products of arbitrary compact Riemann surfaces of genus ≥ 2 have hitherto been intractable by existing methods. We will explain how uniformization theorems for bi-algebraic varieties can be proven by analytic methods involving the Poincar´e-Lelong equation in the cocompact case (joint work with S.-T. Chan), generalizing in the absence of the  emisimplicity theorem of Andr´e-Deligne for monodromy groups (proven for arithmetic lattices). Klingler-Ullmo-Yafaev (2016) resolved the hyperbolic Ax-Lindemann Conjecture for Shimura varieties in the affirmative ascertaining that the Zariski closure of the image π(S) of an algebraic subset S ⊂ Ω under the universal covering map π : Ω → XΓ is totally geodesic. I will explain how the arithmeticity condition can be dropped in the cocompact case by a completely different proof using foliation theory, Chow schemes, partial Cayley transforms and K¨ahler geometry.
Bio: 莫毅明教授为香港大学明德教授与讲座教授，自1999年始兼任数学研究所所长。莫毅明1980年在斯坦福大学获得数学系哲学博士学位，旋即在普林斯顿大学开展其职业生涯，历任美国哥伦比亚大学正教授与法国巴黎大学（奥赛）正教授，1994年回香港任职香港大学数学系讲座教授。1984年莫毅明获美国斯隆研究基金，1985年获美国总统年青研究人员奖，1998年获香港裘槎优秀科研者奖，2007年获国家自然科学奖二等奖， 2009年获美国数学会伯格曼奖(Bergman Prize).莫毅明为美国数学会会士。莫毅明自1992年起担任“数学年鉴(Mathematische Annalen)”编辑委员，并于2002至2014年期间担任 “数学发明(Inventiones Mathematicae)”编辑委员。莫毅明1994年获邀在苏黎世于国际数学大会(ICM)做学术演讲，并获委任为ICM 2010(海得拉巴)的菲尔兹奖选委。2015莫毅明获选中国科学院院士与香港科学院院士。

Lecture 2 ——A New Life of the Old Sieve
Speaker: Yuri Matiyasevich
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
Abstract: Prime numbers are one of the most important objects of study in Number Theory. Greek mathematician Eratosthenes (276--194 B.C.) invented a method (known nowadays under his name) for revealing primes among all natural numbers. A more modern and powerful for tool for studying prime numbers is Riemann's zeta function. In recent years the speaker performed intensive  computer calculations in the search for new properties of this function. Unexpectedly, the Sieve of Eratosthenes naturally appeared in one calculation with the non-trivial zeros of the zeta function. This form of the sieve demonstrates a rich fractal structure lacking in the original sieve. Later another calculation revealed a different kind of a sieve which is dual to the classical Sieve of Eratosthenes. So far no theoretical explanation was found for the observed phenomena.  Calculation were not an easy computational task. They required  calculations of several thousands of initial non-trivial zeros of the zeta function with several thousands decimal digits, and solving systems consisting of several thousands linear equations. 
Bio: 马蒂亚舍维奇教授是当代俄罗斯最著名的数学家之一，圣彼得堡数学学会主席。1966年，19岁的他在逻辑学方面取得了一些突破性的成果，应邀在当年莫斯科举行的国际数学家大会上作邀请报告。1970年，尤里-马蒂亚舍维奇解决了希尔伯特第十问题。到目前为止，他在其他经典领域，如四种颜色问题和黎曼问题上取得了广泛的突破性成果。 他获得了许多著名的奖项，包括洪堡奖、苏联科学院的Markov奖等。他曾获得奥弗涅大学克莱蒙费朗分校和皮埃尔和玛丽居里大学的荣誉学位。Matiyasevich教授是AMS、巴伐利亚科学院和许多其他科学团体的成员。Yuri Vladimirivich Matiyasevich自1970年起在圣彼得堡的斯捷科洛夫研究所工作，1995年成为圣彼得堡国立大学教授。 2002年起，他担任圣彼得堡市数学奥林匹克竞赛负责人。2008年，Matiyasevich教授当选为俄罗斯科学院正式院士。Matiyasevich院士培养了一大批优秀的学生，其中有多位教授和院士。

 

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Lecture Series XIII——March 25, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).
To Join Zoom Meeting: 

 

Video: https://disk.pku.edu.cn:443/link/4459C670911CEF7FBFC326AC056FDDC5
Valid Until：2026-04-30 23:59

Lecture 1—— Polynomial complexity and Sarnak conjecture

Speaker: Prof. Wen Huang, University of Science and Technology of China(USTC)

Bio: Huang Wen received his Ph.D. from the Department of Mathematics, USTC in 2003. His research field is topological dynamical system and ergodic theory, related to the entropy and chaos theory, multipleergodic Theorem, Sarnak’s conjecture and so on. He and his collaborators proved the following results: 1) positive entropy implies weak horseshoes. 2) pointwise multiple ergodic theorem holds for distal measure-preserving systems. 3) Sarnak’s conjecture holds for dynamical systems with sub-polynomial measure complexity. He achieved many rewards: 2012 China National Science Funds for Distinguished Young Scientists; 2018 National Ten Thousand Talent Program Leading Scientists, P.R.China; 2018 Second Class National Natural Science Award, P.R.China（rank 2）.

 

Lecture 2 ——Dynamical models of some sociological problems.

Speaker: Sergei Yu. Pilyugin, Faculty of Mathematics and Computer Science,St. Petersburg State University.

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Bio: Sergei Yu. Pilyugin is Former vice President of Saint Petersburg Mathematical Society, he is a professor at Faculty of Mathematics and Computer Science, St. Petersburg State University, Russia. His research interests are in dynamical systems (especially theory of attractors and shadowing theory) and in applications (including sociological models).

 

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Lecture Series Ⅻ —— March 11, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).
To Join Zoom Meeting: 

 

Video: https://disk.pku.edu.cn:443/link/11FB200B91B098AB7C5E6A2D07EE6445
Valid Until：2026-04-30 23:59

 

Lecture 1—— The J-equation and the deformed Hermitian-Yang-Mills equation.

Speaker: Prof. Gao Chen, University of Science and Technology of China.

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: The deformed Hermitian-Yang-Mills (dHYM) equation is the mirror equation for the special Lagrangian equation. The "small radius limit" of the dHYM equation is the J-equation, which is closely related to the constant scalar curvature K\"ahler (cscK) metrics. In this talk, I will explain my recent result that the solvability of the J-equation is equivalent to a notion of stability. I will also explain my similar result on the supercritical dHYM equation.

Bio: Chen Gao got Bachelor's degree in Univeristy of Science and Techonology of China in 2012 and Ph.D. in Stony Brook University in 2017. Since then he has worked in IAS and University of Wisconsin-Madison. From January of 2021 he became a tenure-track professor in USTC.

 

Lecture 2 ——Various types of spectra and spectral measures on Cayley graphs of finitely generated groups and their actions.

Speaker: Tatiana Nagnibeda (University of Geneva)

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract: We will be interested in the Laplacian on graphs associated with infinite finitely generated groups: Cayley graphs and more generally, Schreier graphs corresponding to some natural group actions. The spectrum of such an operator is a compact subset of the closed interval [0,2], but not much more can be said about it in general. Little is known about the associated spectral measures either. We will discuss various spectral problems arising in this context and stemming from the famous question “Can one hear the shape of a drum?”

 

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Lecture Series Ⅺ—— January 28, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/5E58EEF73495E01118D5216AE2E12DA6
Valid Until：2026-04-30 23:59

Lecture 1—— On local combinatorial  formulas for Euler class of spherical fiber bundle. 
Speaker: Dr. Nikolai Mnev, Senior Research Fellow of Chebyshev Laboratory at Saint-Petersburg State University and Saint Petersburg Department of Steklov Mathematical Institute
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: We will discuss the classical problem on local combinatorial formulas of characteristic classes on example of Euler class. Suppose we have a PL spherical fiber bundle with a fiber S^n   triangulated over the base simplicial complex.  The  bundle determines  n+1 dimensional Euler characteristic class in the base. Local combinatorial formula for the Euler class is a universal combinatorial  function of elementary triangulated  S^n-bundles over n+1 simplices universally representing Euler cocycle of the bundle in simplicial cohomology of the base.   Such  functions exist for rational coefficients in cohomology.   They can be constructed  as   "twisting cochains" --  explicit local chain-level formulas for Gysin homomorphism  in the Gysin sequence of the bundle.  To get an access  to local chain combinatorics of spectral sequence of the bundle we may use Guy Hirsh  homology model of the bundle as a local system and then applying homology perturbation theory obtain local formulas as certain measure of twisting in combinatorial Hodge  structure of the elementary bundle.   The answer can be interpreted and evaluated statistically as certain combinatorial counting using  Catanzaro-Chernyak-Klein higher  Kirchhoff theorems.   The formulas are resulting in a combinatorial form of Gauss-Bonne theorem. For example  we easily obtain otherwise difficult to access statement: One can triangulate only trivial and Hopf circle bundles over a 2-dimensional sphere if the base sphere is triangulated as the boundary of 3-simplex.
Bio: Dr. Nikiolay Mnev graduated from the faculty of Mathematics and Mechanics of Saint Petersburg State University in 1980. In 1986 he defended his PhD thesis under supervision of Prof. Anatoly Vershik. Since that time he works at Steklov Institute and, besides, he has got a position at Chebyshev Laboratory starting from its foundation in 2011. Additionally, Dr. Mnev curates the so-called Fizmatklub, the organization intended to boost the level of teaching maths in Saint Petersburg Universities by organizing additional lecture courses, delivered by leading specialists.
    Dr. Nikolai Mnev’s research interests cover Algebraic Topology, Geometric Topology and Combinatorial Geometry. In 1991, he received Delbert Ray Fulkerson prize for outstanding papers in the area of discrete mathematics.

Lecture 2 ——  Recent developments in exact Lagrangian fillings.
Speaker: Honghao Gao, Michigan State University 
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
Abstract: Legendrian knots and their exact Lagrangian fillings are important geometric objects to study in low dimensional contact and symplectic topology. It was not known whether there exists a Legendrian knot that admits infinitely many exact Lagrangian fillings. In 2020, this statement was proven affirmatively, and infinitely many Lagrangian fillings have been constructed for all torus links of infinite type (with Casals), a family of positive braid links (Casals-Zaslow), all positive braid links of infinite type (with Shen-Weng), two examples that are not positive braid links (Casals-Ng). In this talk, I will review these results, and explain the construction for the torus (3,6) link appeared in the work with R. Casals.
Bio: Honghao Gao received his PhD degree from Northwestern University in 2017, under the supervision of Eric Zaslow. He was previously a postdoc at Institut Fourier, and is currently a postdoc at Michigan State University. His research interest is in contact and symplectic topology.

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Lecture Series Ⅹ—— January 14, 2021（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/0CA255AFF20FD43771B84685ECA5EEC9
Valid Until：2026-04-30 23:59

Speaker:Dr. Petr. Shpilev 

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: The lecture is based on a joint talk with Prof. Vyacheslav Melas. Within the framework of the report, a brief overview of the history of the development of the theory of optimal experiment designs will be given, the basic concepts, definitions, and some key results of this theory are considered.The problem of changing the dimension of the initial optimization task and some approaches to the solution of this problem will be considered on the examples of tasks of constructing specific optimal designs studied by the author of the report.

Bio: Dr. Shpilev graduate from the Faculty of Mathematics and Mechanics in 2004 and got his PhD degree in 2007. His research interests include: Optimal Experimental Design Theory, Regression Analysis, Statistics, Mathematical Simulation, Data Analysis, Computer Science, and Approximation Theory. 

 

Lecture 2 —— Exploring Stochastic Methods For Deep Learning and Reinforcement Learning

Speaker: Zaiwen Wen, Beijing International Center for Mathematical Research.

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract: Stochastic methods are widely used in machine learning. In this talk, we present a structured stochastic quasi-Newton method and a sketchy empirical natural gradient method for deep learning. We also introduce a stochastic quadratic penalty algorithm for reinforcement learning.

Bio: Wen's research interests include large-scale computational optimization and their applications in data sciences. Together with his coauthors, he has developed both deterministic and stochastic semi-smooth Newton algorithms for composite convex program and Newton type algorithms for Riemannian optimization, as well as academic software packages such as SSNSDP, ARNT, Arrabit, LMSVD and LMAFIT, etc. He was awarded the Science and Technology Award for Chinese Youth in 2016, and the Beijing Science and Technology Prize-Outstanding Youth Scholar Zhongguan Village Prize in 2020. He is an associate editor of Journal of the Operations Research Society of China, Journal of Computational Mathematics and a technical editor of Mathematical Programming Computation.

 

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Video: https://disk.pku.edu.cn:443/link/A59A44F4FDF41825DCBF8AE9578C8D2B

Valid Until: 2025-01-01

 

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Lecture Series Ⅷ ——December 3rd, 2020（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).
 

Video: https://disk.pku.edu.cn:443/link/51D4B1FC28EA321B4C4BC25FEF15C28F

Valid Until: 2025-01-01

 

Lecture 1——Graph-walking automata.

Speaker:Prof.  Alexander Okhotin.

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time) .

Abstract: Graph-walking automata are a model studied in theoretical computer science: they traverse an undirected graph by following its edges, and use a memory of constant size to plan their movements. Graph-walking automata can be regarded both as a model of a robot navigating an unknown environment, and as a generic model of computation, with the graph modelling its memory. This paper presents the known results on these automata, ranging from their limitations in traversing graphs, studied already in the 1970s, to the later work on the logical reversibility of their computations, including the most recent lower bounds on their size.

Bio:Alexander Okhotin (Ph.D. 2004, Queen's University) is a professor of theoretical computer science at St. Petersburg State University. His main research subjects are formal grammars, finite automata and their complexity.

 

Lecture 2 ——Modeling and Verification of Concurrent and Distributed Systems: From Reo to Mediator.

Speaker: Prof. Meng Sun.

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time) .

Abstract: In this talk I will introduce the channel-based coordination language Reo and the component-based modeling language Mediator, and show how to formalize and verify component-based concurrent and distributed system models in them. Reo provides a channel-based model which focuses on complex interactions among system components. Mediator supports a two-step hierarchical modeling approach: Automata, which provide an interface of ports, are the basic behavior units; Systems declare components or connectors through automata, and glue them together. With the help of Reo and Mediator, both components and systems can be modeled separately and precisely. 

Bio:Meng Sun received his BSc and PhD degrees in applied mathematics from Peking University, in 1999 and 2005, respectively. He then spent one year as a postdoctoral researcher in National University of Singapore. From 2006 to 2010, he worked as a scientific staff member at CWI, the Netherlands. He has been a faculty member at Peking University since 2010 and became a full professor in 2017. Currently, his research interests mainly lie in software theory and formal methods. His recent work includes coordination models and languages, coalgebra theory, model checking, theorem proving, software testing, cyber-physical systems, service-oriented and cloud computing, modeling and verification of blockchain and smart contracts, big data analysis, theoretical foundations of machine learning, deep learning and their application in formal verification.

 

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Lecture Series Ⅶ ——November 19th, 2020（20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/B06B1459AA07B80DD51E17F8406655C2

Valid Until: 2025-01-01

 

Lecture 1——Deep CT Imaging by Unrolled Dynamics

Speaker: Bin Dong, Beijing International Center for Mathematical Research, Peking University

Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

Abstract: In this talk, I will start with a brief review of the dynamics and optimal control perspective on deep learning (including supervised learning, reinforcement learning, and meta-learning), especially the so-called unrolled dynamics approach and its applications in medical imaging. Then, I will present some of our recent studies on how this new approach may help us to advance CT imaging. Specifically, I will focus on our thoughts on how to combine the wisdom from mathematical modeling with ideas from deep learning. Such combination leads to new data-driven image reconstruction models and new data-driven scanning strategies for CT imaging, and with a potential to be generalized to other imaging modalities.

Bio:Bin Dong received his B.S. from Peking University in 2003, M.Sc from the National University of Singapore in 2005, and Ph.D from the University of California Los Angeles (UCLA) in 2009. Then he spent 2 years in the University of California San Diego (UCSD) as a visiting assistant professor. He was a tenure-track assistant professor at the University of Arizona since 2011 and joined Peking University as an associate professor in 2014. His research interest is in mathematical modeling and computations in imaging and data science. A special feature of his research is blending different branches in mathematics which include: bridging wavelet frame theory, variational techniques, and nonlinear PDEs; bridging differential equations and optimal control with deep learning.

 

Lecture 2 —— Gaussian random fields in machine learning

Speaker: Viacheslav Borovitskiy, Department of Mathematics and Mechanics，Saint Petersburg State University.

Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)

Abstract: I will introduce the Gaussian process regression algorithm, a widely used approach to probabilistic modeling in machine learning, and talk about its applications and challenges associated with its use. In the end, I will mention our own recent research in this topic that was presented on International Conference on Machine Learning and will be presented on this year's conference on Neural Information Processing Systems.

Bio: He has graduated from Saint-Petersburg State University, Faculty of Mathematics and Mechanics. His main interests cover PDEs, Banach spaces, Satistics and Informatics.

 

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Lecture Series VI - November 5th, 2020 （20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

 

Video: https://disk.pku.edu.cn:443/link/E68335CAFDAD6A71A943A348EF8FC42A

Valid Until: 2025-01-01

 

Speaker: Prof. Yanjun Liu, Jiangxi Normal University

Abstract: The question of which prime powers can occur as divisors of irreducible character degrees of finite groups has a long history. One related conjecture is given by Geoffrey Robinson in 1996, who conjectured that the p-part of character degrees in a p-block of a finite group can be bounded in terms of the center of a defect group of the block. I will mention recent progress on Robinson's conjecture for odd primes,and then turn to the question of when a p-block of a finite group G is also a q-block of G. A series related work have been done by Navarro-Willems,Bessenrodt-Mall-Olsson, Navarro-Turull-Wolf and etc. The block separation property is studied by Bessenrodt-Zhang and they proved that the nilpotency, p-nilpotency of a finite group can be characterized by intersections of principal blocks of some (quotient) groups. Thus it is natural to ask if the solvability or p-solvability of a finite group can also be characterized in this way. By introducing the so-called block graph of a finite group this problem was solved affirmatively. Finally, I will talk about a conjecture relating the trivial intersection of principal blocks to the existence of nilpotent Hall subgroups.

Bio: Dr. Yanjun Liu got Ph. D. from Peking University and is now working in Jiangxi Normal University. Recently He got Humboldt Research Fellowship based on his excellent work in some canonical conjecture of representation theory.

 

Speaker: Prof. Mikhail Gavrilovich, Saint Petersburg Department of Higher School of Economics

Abstract: We consider simplicial sets equipped with a notion of smallness, and observe that this slight “topological” extension of  the “algebraic” simplicial language allows a concise reformulation  of a number of classical notions in topology, e.g. continuity, limit of a map or a sequence along a filter, various notions of equicontinuity and uniformconvergence of a sequence of functions; completeness and compactness; in algebraic topology, locally trivial bundles as a direct product after base-change and geometric  realisation as a space of discontinuous paths. These reformulations are elementary and can perhaps be used in teaching to give motivated examples of elementary concepts in category theory. Surprisingly, this category is not well-studied and thus these observations raise many  easy but open problems, which we like to think are in line with goals of tame topology put by Grothendieck. In the talk, we will work through of a couple of example, briefly mention some others, and indicate a number of open problems, who we like to think are in line with the goals of tame topology put by Grothendieck.

    We will preceed the main part of the talk by explaning a category-theoretic characterisaiton of finite solvable and nilpotent groups in terms of the Quillen lifting property, which is also used in reformulations of the notions of limit, compactness, and completeness, and others.

 

 

http://mishap.sdf.org/by:gavrilovich/treplo-groups.pdf.

 

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Lecture Series V - October 22th, 2020 （20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time).

Video：https://disk.pku.edu.cn:443/link/FD9BF2C2F871B7FE56EFD891777A6E7E

Valid Until：2025-01-01 00：00 

 

Lecture 1—— Global existence and decay of solutions to Prandtl system with small analytic data

Speaker: Prof. Ping Zhang, Mathematics Institute of Academy of Mathematics and Systems Science of Chinese Academy of Sciences, Beijing

Time：2020-10-22 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)

 

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Lecture Series IV - July 14th, 2020 （20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time）

Video： Part I：https://disk.pku.edu.cn:443/link/ADEA1AC5CB6C898F8809E6FFBC93B54C

            Part II：https://disk.pku.edu.cn:443/link/8395E85B327FAC1E80993F79F2CACCF2

Valid Until：2025-01-01 00：00

 

Lecture 1 - WORD MAPS ON SIMPLE ALGEBRAIC GROUPS AND RELATED TOPICS
Speaker: Prof. Nikolai Gordeev, Saint Petersburg State Pedagogical University
Time：2020-07-14 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time) 
Abstract:(/upload/editor/file/20200711/11112603683.pdf)

 

Lecture 2 -  Structure of Commutator Subgroups
Speaker: Prof. Zuhong Zhang， Beijing Institute of Technology
Time：2020-07-14 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time) 
Abstract: 
    This talk is based on the joint works with R. Hazrat, A. Stepanov and N. Vavilov in the past decade. In his seminal paper, more than half a century ago, Hyman Bass initialed the study of commutator subgroups and commutator formulas over rings. Since then, it attracted great attend of many leading experts including A. Bak, A.A. Suslin, L.N. Vaserstein, etc.. Various commutator formulas have been obtained in stable and non-stable settings and for a range of classical and algebraic like-groups.
   In this talk, we will describe some recent results on the study (higher/birelative) commutators in general linear groups $GL(n,A)$ as well as their elementary generators. we will also discuss some further related research and applications. 

 

Lecture Series III - June 30th, 2020 （20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time）

 

Download Slides:

   On the way to do so, we will address the parallels between topological dynamics and ergodic theory, and their applications to combinatoric number theory.

Bio: Prof. Ye got his Ph. D. in Mechanics and Mathematics Department of Moscow State University in 1991, and then did postdoc work in ICTP during 1991-1993. He was a faculty of Mathematics School in USTC since 1993. He was selected as a member of the Chinese Academy Sinica in 2019. His research interests include topological dynamics, ergodic theory and combinatoric number theory.

 

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Lecture Series II - June 16th, 2020 （20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time）

Video：Part I：https://disk.pku.edu.cn:443/link/F3034E87D1FC25E824BBDB14302AB24E

           Part II：https://disk.pku.edu.cn:443/link/E55DFDEE3CA697F5C15F978B04ABC727

Valid Until：2025-01-01 00：00

Lecture 1 - Multiple structures for quasilinear equations by the variational method
Speaker: Alexander Nazarov, PDMI RAS and Math&Mech Faculty, St. Petersburg State University
Time：2020-06-16 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time) 
Abstract: 
We study entire bounded solutions to the equations of variational nature. The model example here is $\Delta u - u + u^3 = 0$ in $\mathbb R^2$. Our approach is purely variational and is based on concentration arguments and symmetry considerations. This method allows us to construct in an unified way several types of solutions with various symmetries (radial, breather type, rectangular, triangular, hexagonal, etc.),both positive and sign-changing. It is also applicable for more general equations in any dimension.
The talk is based on the joint paper Lerman L.M., Naryshkin P.E., Nazarov A.I., Abundance of entire solutions to nonlinear elliptic equations by the variational method, Nonlinear Analysis -- TMA. 190 (2020), DOI 10.1016/j.na.2019.111590, 1-21.
 

Lecture 2 -  Periodic and quasi-periodic solutions of 1-d Q-curvature equation. 
Speaker: Jiang Meiyue, School of Mathematical Sciences, Peking University
Time：2020-06-16 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time) 
Abstract（/upload/editor/file/20200609/09145940157.pdf）: 

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Lecture Series I - June 2nd, 2020 （20:00-22:00 Beijing time or 15:00-17:00 St Petersburg time）

 

Lecture 1 - Spectral synthesis for systems of exponentials and reproducing kernels  

Speaker：Anton Baranov (Saint Petersburg State University) 

Time：2020-06-02 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time) 

Abstract: Let $x_n$ be a complete and minimal system of vectors in a Hilbert space $H$. We say that this system is hereditarily complete or admits spectral synthesis if any vector in $H$ can be approximated in the norm by linear combinations of partial sums of the Fourier series with respect to $x_n$. It was a long-standing problem whether any complete and minimal system of exponentials in $L^2(-a,a)$ admits spectral synthesis. Several years ago Yu. Belov, A. Borichev and myself gave a negative answer to this question which implies, in particular, that there exist non-harmonic Fourier series which do not admit a linear summation method. At the same time we showed that any exponential system admits the synthesis up to a one-dimensional defect. In the talk we will also discuss related problems for systems of reproducing kernels in Hilbert spaces of entire functions (such as Paley-Wiener or Fock).

 

Lecture 2 - On gauged linear sigma model and related problems  

Speaker: Prof. Huijun Fan (Peking University) 

Time：2020-06-02 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time) 

Abstract: Gauged linear sigma model was proposed by Witten in the early of 90's to explain the mirror symmetry phenomenon and the CY/LG correspondence conjecture. In this lecture, I will firstly formulate the mathematical framework of the GLSM, and then describe an algebraic  way to construct the quantum invariants of GLSM in narrow case (for general gauge group) via quasimaps. 
This was a joint work with Jarvis and Ruan. Finally I will report the recent progress in this field and related problems.