Organizing committee of Beijing-Saint Petersburg Mathematics Colloquium
(1) Huijun Fan (SMS PKU, symplectic geometry and mathematical physics, geometric analysis)
(2) Feimin Huang (CAS, institute of applied mathematics, partial differential Equation, fluid mechanics)
(3) Sergey Kryzhevich (SPBU, differential and difference equations, dynamical systems, chaotic dynamics, structural stability, hyperbolic theory)
(4) Xiaonan Ma (Université de Paris, geometry, index theory)
(5) Maxim Vsemirnov (PDMI RAS, SPBU, number theory, algebra, combinatorics)
(6) Wenyuan Yang (BICMR, geometric group theory and Kleinian groups)
(7) Dmitry Zaporozhets (PDMI RAS, SPBU, Poisson-Voronoi tessellation zeros of random analytic functions and polynomials mixed volumes)
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Lecture Series 32 —— June 16, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).
Recording: https://disk.pku.edu.cn:443/link/003A36414D9928A3A199EFE5BE0DF5E0
Valid Until: 2026-07-31 23:59
Lecture 1——Bounded elementary generation of Chevalley groups
Speaker: Prof. Nikolai Vavilov
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: We discuss several results on bounded elementary generation and bounded commutator width for Chevalley groups over Dedekind rings of arithmetic type in positive characteristics. In particular, Chevalley groups of rank \ge 2 over polynomial rings F_q[t] and Chevalley groups of rank \ge 1 over Laurent polynomial F_q[t,t^{-1}] rings, where F_q is a finite field of q elements, are boundedly elementarily generated. We sketch several proofs, using reciprocity laws, symbols in algebraic K-theory, and surjective stability for K-functors. As a result, we establish rather plausible explicit bounds, that do not depend on q and are better than the known ones even in the number case. Using these bounds we can also produce sharp bounds of the commutator width of these groups. We also mention several applications (Kac---Moody groups, first order rigidity, etc.) and possible generalisations. This is joint work with Boris Kunyavskii and Eugene Plotkin.
Bio: Professor Nikolai Alexandrovich Vavilov works at Saint-Petersburg State University, Department of Mathematics and Computer Sciences (he was one of the co-founders of the Department) and at Saint Petersburg Department of Steklov Mathematical Institute. He is one of the best Russian algebraists having a big number of brilliant results in Structure theory and representations of algebraic groups, algebraic K-theory, overgroups of semisimple groups and tori. Prof. Vavilov graduated from Leningrad State University (now Saint Petersburg State University) and got his Doctor Degree (habilitation) in 1988. He has got a big number of prestigious awards and prizes and grew up dozens of students.
Besides, Nikolai Alexandrovich intensively cooperates with Chinese colleagues. He is one of those people who launched the current program of Russian - Chinese collaboration.
Lecture 2——Arakelov geometry over adelic curves
Speaker: Prof. Huayi Chen
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
Abstract: Arakelov geometry is a theory of arithmetic geometry which combines algebraic geometry over an algebraic integer ring and complex analytic geometry to study the arithmetic properties of projective varieties over a number field. In a joint work with Atsushi Moriwaki, by using the adelic point of view of Chevalley and Weil, we extend Arakelov geometry to the setting of projective varieties over an arbitrary countable field. In this talk, I will explain the main ideas behind this theory, and the similarity and differences compared to the classical approach.
Bio: Huayi Chen is currently a Professor at Paris Diderot University and the Mathematics Institute of Jussieu–Paris Rive Gauche. He graduated from Peking University in 2000. In 2003, he got his Master's degree at Pierre and Marie Curie University. Then he got his PhD at Laurent Schwartz Mathematics Center, Ecole Polytechnique in 2006. His research interests include algebraic geometry, Arakelov geometry and Diophantine problems.
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Lecture Series 31 —— June 2, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).
Recording: https://disk.pku.edu.cn:443/link/F98451EB7316CD31517990FA148AC092
Valid Until: 2026-07-31 23:59
Lecture 1——On a geometric realization of the center of the small quantum group
Speaker: Prof. Peng Shan (Yau Mathematical Sciences Center)
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: In Lie theory, the center of many important representation categories admits geometrical interpretations as singular cohomology of certain algebraic varieties. We will explain a new realization of this type, relating the center of the small quantum group to the cohomology of certain affine Springer fibres. As an application, we obtain a conjectural formula for the dimension of the center of the small quantum group. This is based on a joint work with R. Bezrukavnikov, P. Boixeda-Alvarez, and E. Vasserot.
Bio: Peng Shan is currently a Professor at Yau Mathematical Sciences Center, Tsinghua University. Her research interests lie in Geometric Representation Theory. In 2011, she received her Ph.D. from Paris Diderot University. After graduation, Peng Shan worked at MIT as C. L. E. Moore instructor. From 2011 to 2017, she was an associate researcher at the French National Center for Scientific Research. Also, she carried out research at the University of Caen-Normandie and Paris-Sud University. She is also the invited speaker at the ICM (2022). Prof. Shan Peng is on the editorial board of "J. Algebra" and has published many papers in top mathematics journals such as J. Amer. Math. Soc., Invent. Math., Duke Math. J. and Adv. Math.
Lecture 2——Chevalley groups over rings of polynomials
Speaker: Dr. Anastasia Stavrova (Saint Petersburg State University)
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
Abstract: Let D be a Dedekind domain. In 1977, A. Suslin established that for any N>=3, and any n>=1, one has SL_N(D[x_1,...,x_n])=SL_N(D)E_N(D[x_1,...,x_n]), where E_N(D[x_1,...,x_n]) is the elementary subgroup of SL_N(D[x_1,...,x_n]), i.e. the subgroup generated by the unipotent elementary transformation matrices E+tE_ij, where E is the unit matrix, E_ij is the matrix with 1 at the position i,j and 0 everywhere else, and t is an arbitrary element of the polynomial ring D[x_1,...,x_n]. In particular, this implies that SL_N(Z[x_1,...,x_n])=E_N(Z[x_1,...,x_n]), where Z is the ring of integers. We discuss an extension of this result to all split simple linear algebraic groups (also called Chevalley groups) and to regular rings D of higher dimension.
Bio: Dr. Anastasia Stavrova is an expert in algebraic groups, non-associative algebra, and algebraic K-theory. She is a researcher in the Chebyshev Laboratory and Department of Mathematics and Computer Science at Saint Petersburg State University. Dr. Stavrova earned a specialist degree in mathematics at Saint Petersburg State University in 2005 and got her PhD in 2009 supervised by Nikolai Vavilov. She has got a great experience of working overseas (the University of Leiden, University of Padua, Ludwig Maximilian University of Munich, and the University of Duisburg-Essen). Also, she was Jerrold E. Marsden Postdoctoral Fellow at the Fields Institute in Canada. Anastasia Stavrova obtained a great number of brilliant results in Algebra and related areas. She won the Young Mathematician Prize of the Saint Petersburg Mathematical Society in 2009, the Young Russian Mathematics Scholarship in 2016. In 2018, she has got the G. de B. Robinson Award from the Canadian Mathematical Society.
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Lecture Series 30 —— May 26, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).
Recording: https://disk.pku.edu.cn:443/link/BC2A84C65A65A46B5303EFAE1C4212AA
Valid Until: 2026-06-30 23:59
Lecture 1——The non-positive curvature geometry of some fundamental groups of complex hyperplane arrangement complements
Speaker: Jingyin Huang (Ohio State University)
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: A complex hyperplane complement is a topological space obtained by removing a collection of complex codimension one affine hyperplanes from C^n (or a convex cone of C^n). Despite the simple definition, these spaces have highly non-trivial topology. They naturally emerge from the study of real and complex reflection groups, braid groups and configuration spaces, and Artin groups. More recently, the fundamental groups of some of these spaces start to play important roles in geometric group theory, though most of these groups remain rather mysterious. We introduce a geometric way to understand classes of fundamental groups of some of these spaces, by equivariantly “thickening” these groups to metric spaces which satisfy a specific geometric property that is closely related to convexity and non-positive curvature. We also discuss several algorithmic, geometric and topological consequences of such a non-positive curvature condition. This is joint work with D. Osajda.
Bio: Jingyin Huang is an assistant professor and the Alice Louise Ridenour Wood Chair in Mathematics at Ohio State University. He completed his PhD at New York University in 2015. He is an expert in geometric group theory, which studies the deep connections between the algebraic properties of groups and the geometry of spaces they act on. His research focus on certain rigidity properties of discrete groups (quasi-isometric rigidity, measure equivalence and orbit equivalence rigidity), and the geometry of non-positively curved spaces and groups. He has been awarded a 2022 Sloan Research Fellowship.
Lecture 2——Combinatorics of Lipschitz polytope and beyond
Speaker: Prof. Fedor Petrov
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
Abstract: Let $(X, \rho)$ be a finite metric space. Consider the space of real functions on $X$ with zero mean. Equip it with Lipschitz norm $\|f(x)\|=\max |f(x)-f(y)|/\rho(x, y)$ and consider the unit ball in this norm, which is a certain convex polytope. The question on classifying metrics depending on the combinatorics of this polytope have been posed by Vershik in 2015. In a joint work with J. Gordon (2017), we proved that for generic metric space the number of faces of a given dimension is always the same. This fact is intimately related to regular triangulations of the root polytope (convex hull of the roots of root system $A_n$). In this survey-style talk, we discuss both this phenomenon and further relations of the subject, observed recently by several groups of mathematicians.
Bio: Prof. Fedor Petrov is an expert in Combinatorics, Convex Geometry, Functional Analysis and Geometry of Numbers. Being a former student of Prof. A.M. Vershik, now he plays a leading role in his research group. Prof. Petrov graduated from Saint Petersburg State University in 2004, got his PhD in 2007 and habilitation (Doctor of Sciences degree) in 2018. He is a Professor and a director of one of the educational programs at the Department of Mathematics and Computer Sciences of Saint Petersburg State University combining this with a research position at the Saint Petersburg Department of Steklov Mathematical Institute. Not only Prof. Petrov is an author of a big number of impressive results in the aforementioned areas, but also a jury member of several top mathematical contests for high school and university students. Besides, he is a member of the Council of the St. Petersburg Mathematical Society (since 2018).
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Lecture Series 29 —— May 19, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).
Recording: https://disk.pku.edu.cn:443/link/872A119E054BC012A4A81977B8AA410E
Valid Until: 2026-06-30 23:59
Lecture 1——A violation of the uncertainty principle: indicator functions with thin spectrum and uniformly bounded partial Fourier integrals
Speaker: Sergey Kislyakov (St.Petersburg Department of Steklov Mathematical Institute)
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: Given a set $a$ of finite measure on the real line, it is possible to find a set $b$ with the properties mentioned in the title and differing from $a$ as little as we want in the sense of measure. There is an analog of this claim for more or less general LCA groups. The discussion will be prefaced with a short survey of various results about conditions that may or may not be fulfilled simultaneously for a function and its Fourier transform. This is a joint work with P.Perstneva.
Bio: Sergey Vitalievich Kislyakov is one of the best Russian experts in Harmonic Analysis, Functional Analysis, Interpolation theory, Fourier Analysis and many other related fields, having obtained a great deal of outstanding results in these areas. Besides, he is the author of several books that are extremely popular both among students and mature researchers. Prof. Kislyakov is a Doctor of Mathematics, an Academician of the Russian Academy of Sciences (since 2016), and the Chief Editor of the "Algebra and Analysis" journal. He was Director of the Saint Petersburg Department of Steklov Mathematical Institute.
Lecture 2——Critical Point Sets of Solutions in Elliptic Homogenization
Speaker: Fanghua Lin (Courant Institute, NYU)
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
Abstract: In this talk, I shall outline a proof for bounds on H^(n-2)–Hausdorff measure of critical point sets of solutions in elliptic homogenization. The method works for solutions of elliptic equations with Lipschitz coefficients also. This is a joint work with Zhongwei Shen.
Bio: Professor Fanghua Lin is a Silver Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University. He received his Ph.D. in 1985 from the University of Minnesota. His research interests are in nonlinear partial differential equations, geometric measure theory and applied & geometric analysis. Professor Lin has made significant contributions to the theory of liquid crystals, harmonic maps, Ginzburg-Landau equations and the theory of homogenization. He has also made important contributions to the studies of topological defects, vortices, quantitative unique continuation, nodal and critical sets of solutions of partial differential equations.
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Lecture Series 28 —— May 5, 2022（20:00-22:00 Beijing time / 15:00-17:00 St Petersburg time).
Recording: https://disk.pku.edu.cn:443/link/BBD59D040E4E91A35EFFC9E42CEF593A
Valid Until: 2026-06-30 23:59
Lecture 1——Analysis on compressible Navier-Stokes equations with strong boundary layer
Speaker: Tong Yang (City University of Hong Kong)
Time: 20:00-21:00 Beijing time (15:00-16:00 St Petersburg time)
Abstract: It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with the boundary layer. However, there are very few mathematical results on the compressible fluid despite the extensive studies when the fluid is governed by the incompressible Navier-Stokes equations. In this talk, we will present a new approach to studying the compressible Navier-Stokes equations in the subsonic and high Reynolds number regime where a subtle quasi-compressible and Stokes iteration is developed. As a byproduct, we show the spectral instability of the subsonic boundary layer. This is a joint project with Zhu Zhang.
Bio: Tong Yang is a Chair Professor of Mathematics at the City University of Hong Kong. He was President of the Hong Kong Mathematical Society from 2016 to 2020. He has been working in the fields of partial differential equations and kinetic theory. He served as an Editor-in-Chief of Analysis and Applications from 2013 to 2017 and is one of the founding Editors-in-Chief of Kinetic and Related Models launched in 2008. He also serves on several international journals, including the Editorial Advisory Board of London Mathematical Society: Bulletin and Journal, and SIAM Journal on Mathematical Analysis. He is a member of the European Academy of Sciences, The World Academy of Sciences and the Hong Kong Academy of Sciences. The awards and distinctions that he has received include the 2nd class State Natural Science Award of China in 2012 and the Croucher Senior Research Fellowship in 2011.
Lecture 2——Large bifurcation supports
Speaker: Prof. Yulij Ilyashenko
Time: 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
Abstract: The talk deals with a general problem of the bifurcation theory on the two-sphere. Consider a vector field with arbitrary degeneracies: complex singular points, multiple limit cycles and polycycles. What part of the phase portrait will bifurcate under a perturbation of this field, and what part will remain unchanged? Not only the degenerated parts of the phase portrait mentioned above will bifurcate; but some generic parts will also. A highly nontrivial question arises: WHO BIFURCATES? The answer will be given in the talk based on joint work with Natalya Goncharuk.
Bio: Prof. Yulij Ilyashenko is one of the most renowned Russian scientists working in Differential Equations, Dynamical Systems and Geometry. He obtained a big number of brilliant results in bifurcation theory and dynamics beyond uniform hyperbolicity. In particular, he proved the finiteness of the number of limit cycles for polynomial vector fields, thus giving a partial solution to Hilbert's 16th problem (the previous proof provided by Dulac contained a serious gap).
Yulij Sergeevich Ilyashenko is the Rector of the Independent University of Moscow, vice-president of Moscow Mathematical Society, and Professor at Moscow State University, Cornell University, Higher School of Economics, and Steklov Mathematical Institute. Besides, Prof. Ilyuashenko is a member of the editorial boards of several prestigious journals including Ergodic Theory and Dynamical Systems, Journal of Dynamics and control systems and Main Editor of Moscow Mathematical Journal.
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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
Prof. Zaporozhets is one of strongest researchers in Probability theory and Geometry, having major interests in Geometry of numbers, Stochastic Geometry, Convex Geometry, Poisson - Voronoi tessellation, zeros of random polynomials and random analytic functions.
Being a student of Acad. Il'dar Ibragimov, one of the most renowned experts in Probability and Statistics, Dmitry graduated from Saint Petersburg State University, defended his PhD thesis in 2005 and Doctoral thesis in 2015 (both thesis were devoted to Random Polynoms).
Later on, Prof. Zaporozhets has got the honorary degree of Professor of Russian Academy of Sciences.
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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 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 Invited Speaker of the International Congress of Mathematics 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
VIDEO： https://disk.pku.edu.cn:443/link/62236134E8043AD5871A88D2BA3F2868
Expiration Time：2025-07-31 23:59
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
VIDEO：https://disk.pku.edu.cn:443/link/5034D664212B1B1DD783D05CA07B343D
Expiration Time：2025-07-31 23:59
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.
