BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ruochuan Liu (Peking University) DTSTART:20201023T101500Z DTEND:20201023T111500Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/1 DESCRIPTION:Title: Topological cyclic homology for p-adic local fields \nby Ruochuan Liu (Peking University) as part of Beijing Moscow Mathem atics Colloquium\n\n\nAbstract\nWe introduce a new approach to compute top ological cyclic homology using the descent spectral sequence and the algeb raic Tate spectral sequence. We carry out computations in the case of a $p $-adic local field with coefficient ${\\mathbb F}_p$. Joint work with Guoz hen Wang.\n\nMeeting ID: 648 6454 8936 Password: 899678\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Frolenkov (Steklov Mathematical Institute of RAS) DTSTART:20201023T111500Z DTEND:20201023T121500Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/2 DESCRIPTION:Title: Additive divisor problem and Applications\nby D mitry Frolenkov (Steklov Mathematical Institute of RAS) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nAdditive Divisor Problem (AD P) is concerned with finding an asymptotic formula for the sum $\\sum_{n< X}d(n)d(n+a)$\, where $d(n)=\\sum_{d|n}1$ is the divisor function. Surpris ingly\, the ADP arises naturally in quite different problems of number the ory. For example\, it is related to the investigation of the 4th moment of the Riemann zeta-function\, the second moment of automorphic L-functions and the mean values of the length of continued fractions. In the talk\, I will describe the ADP and its applications.\n\nMeeting ID：648 6454 8936 Password：899678\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Yi Shi (Peking University) DTSTART:20201106T080000Z DTEND:20201106T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/3 DESCRIPTION:Title: Spectrum rigidity and integrability for Anosov diff eomorphisms\nby Yi Shi (Peking University) as part of Beijing Moscow M athematics Colloquium\n\n\nAbstract\nLet $f$ be a partially hyperbolic der ived-from-Anosov diffeomorphism on 3-torus $\\mathbb{T}^3$. We show that t he stable and unstable bundle of $f$ is jointly integrable if and only if $f$ is Anosov and admits spectrum rigidity in the center bundle. This prov es the Ergodic Conjecture on $\\mathbb{T}^3$.\n\nIn higher dimensions\, le t $A\\in{\\rm SL}(n\,\\mathbb{Z})$ be an irreducible hyperbolic matrix adm itting complex simple spectrum with different moduli\, then $A$ induces a diffeomorphism on $\\mathbb{T}^n$. We will also discuss the equivalence of integrability and spectrum rigidity for $f\\in{\\rm Diff}^2(\\mathbb{T}^n )$ which is $C^1$-close to $A$.\n\nZoom Meeting ID: 674 4141 7410\nPasswor d: 905198\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Lev Lokutsievskiy (Steklov Mathematical Institute of RAS) DTSTART:20201106T090000Z DTEND:20201106T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/4 DESCRIPTION:Title: Аn application of algebraic topology and graph the ory in microeconomics\nby Lev Lokutsievskiy (Steklov Mathematical Inst itute of RAS) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstra ct\nOne of the important questions in mechanism design is the implementabi lity of allocation rules. An allocation rule is called implementable if fo r any agent\, benefit from revealing its true type is better than benefit from lying. I’ll show some illustrative examples. Obviously\, some alloc ation rules are not implementable. Rochet’s theorem states that an alloc ation rule is implementable iff it is cyclically monotone. During the talk \, I’ll present a new convenient topological condition that guarantees t hat cyclic monotonicity is equivalent to ordinary monotonicity. The last o ne is easy to check (in contrary to cyclic one). Graph theory and algebrai c topology appear to be very useful here.\n\nZoom Meeting ID: 674 4141 741 0 \nPassword: 905198\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Taras Panov (Moscow State University) DTSTART:20201120T080000Z DTEND:20201120T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/5 DESCRIPTION:Title: Right-angled polytopes\, hyperbolic manifolds and t orus actions\nby Taras Panov (Moscow State University) as part of Beij ing Moscow Mathematics Colloquium\n\n\nAbstract\nA combinatorial 3-dimensi onal polytope $P$ can be realized in Lobachevsky 3-space with right dihedr al angles if and only if it is simple\, flag and does not have 4-belts of facets. This criterion was proved in the works of A. Pogorelov and E. Andr eev of the 1960s. We refer to combinatorial 3 polytopes admitting a right- angled realisation in Lobachevsky 3-space as Pogorelov polytopes. The Pogo relov class contains all fullerenes\, i.e. simple 3-polytopes with only 5- gonal and 6-gonal facets. There are two families of smooth manifolds assoc iated with Pogorelov polytopes. The first family consists of 3-dimensional small covers (in the sense of M. Davis and T. Januszkiewicz) of Pogorelov polytopes $P$\, also known as hyperbolic 3-manifolds of Loebell type. The se are aspherical 3-manifolds whose fundamental groups are certain extensi ons of abelian 2-groups by hyperbolic right-angled reflection groups in th e facets of $P$. The second family consists of 6-dimensional quasi toric m anifolds over Pogorelov polytopes. These are simply connected 6-manifolds with a 3-dimensional torus action and orbit space $P$. Our main result is that both families are cohomologically rigid\, i.e. two manifolds $M$ and $M'$ from either family are diffeomorphic if and only if their cohomology rings are isomorphic. We also prove that a cohomology ring isomorphism imp lies an equivalence of characteristic pairs\; in particular\, the correspo nding polytopes $P$ and $P'$ are combinatorially equivalent. This leads to a positive solution of a problem of A. Vesnin (1991) on hyperbolic Loebel l manifolds\, and implies their full classification. Our results are inter twined with classical subjects of geometry and topology such as combinator ics of 3-polytopes\, the Four Colour Theorem\, aspherical manifolds\, a di ffeomorphism classification of 6-manifolds and invariance of Pontryagin cl asses. The proofs use techniques of toric topology. This is a joint work w ith V. Buchstaber\, N. Erokhovets\, M. Masuda and S. Park.\n\nZoom Meeting ID: 626 6992 6224 Password: 363601\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 5/ END:VEVENT BEGIN:VEVENT SUMMARY:Yi Liu (Beijing International Center for Mathematical Research) DTSTART:20201120T090000Z DTEND:20201120T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/6 DESCRIPTION:Title: Finite covers of 3-manifolds\nby Yi Liu (Beijin g International Center for Mathematical Research) as part of Beijing Mosco w Mathematics Colloquium\n\n\nAbstract\nIn this talk\, I will discuss some developments in 3-manifold topology of this century regarding finite cove ring spaces. These developments led to the resolution of Thurston's virtua l Haken conjecture and other related conjectures around 2012. Since then\, people have been seeking for new applications of those techniques and the ir combination with other branches of mathematics.\n\nZoom Meeting ID: 626 6992 6224 Password: 363601\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Gaifullin (Steklov Mathematical Institute of RAS) DTSTART:20201204T080000Z DTEND:20201204T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/7 DESCRIPTION:Title: On homology of Torelli groups\nby Alexander Gai fullin (Steklov Mathematical Institute of RAS) as part of Beijing Moscow M athematics Colloquium\n\n\nAbstract\nThe mapping class groups of oriented surfaces are important examples of groups whose properties are closely rel ated to geometry and topology of moduli spaces\, topology of 3-manifolds\, automorphisms of free groups. The mapping class group of a closed oriente d surface contains two important subgroups\, the Torelli group\, which con sists of all mapping classes that act trivially on the homology of the sur face\, and the Johnson kernel\, which is the subgroup generated by all Deh n twists about separating curves. The talk will be devoted to results on h omology of these two subgroups. Namely\, we will show that the $k$-dimensi onal homology group of the genus g Torelli group is not finitely generated \, provided that k is in range from $2g-3$ and $3g-5$ (the case $3g-5$ was previously known by a result of Bestvina\, Bux\, and Margalit)\, and the $(2g-3)$-dimensional homology group the genus g Johnson kernel is also not finitely generated. The proof is based on a detailed study of the spectra l sequences associated with the actions of these groups on the complex of cycles constructed by Bestvina\, Bux\, and Margalit.\n\nZoom Meeting ID: 6 68 8175 3105\nPassword: 348558\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 7/ END:VEVENT BEGIN:VEVENT SUMMARY:Guozhen Wang (Shanghai Center for Mathematical Sciences\, Fudan Un iversity) DTSTART:20201204T090000Z DTEND:20201204T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/8 DESCRIPTION:Title: Stable homotopy groups of spheres\nby Guozhen W ang (Shanghai Center for Mathematical Sciences\, Fudan University) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nWe will discuss t he current state of knowledge of stable homotopy groups of spheres. We des cribe a computational method using motivic homotopy theory\, viewed as a d eformation of classical homotopy theory. This yields a streamlined computa tion of the first 61 stable homotopy groups and gives information about th e stable homotopy groups in dimensions 62 through 90. As an application\, we determine the groups of homotopy spheres that classify smooth structure s on spheres through dimension 90\, except for dimension 4. The method rel ies more heavily on machine computations than previous methods and is ther efore less prone to error. The main mathematical tool is the Adams spectra l sequence.\n\nZoom Meeting ID: 668 8175 3105 Password: 348558\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 8/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhifei Zhang (School of Mathematical Sciences\, Peking University) DTSTART:20210115T080000Z DTEND:20210115T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/9 DESCRIPTION:Title: Linear stability of pipe Poiseuille flow at high Re ynolds number regime\nby Zhifei Zhang (School of Mathematical Sciences \, Peking University) as part of Beijing Moscow Mathematics Colloquium\n\n \nAbstract\nThe linear stability of pipe Poiseuille flow is a long standin g problem since Reynolds experiment in 1883. Joint with Qi Chen and Dongyi Wei\, we solve this problem at high Reynolds regime. We first introduce a new formulation for the linearized 3-D Navier-Stokes equations around thi s flow. Then we establish the resolvent estimates of this new system under favorable artificial boundary conditions. Finally\, we solve the original system by constructing a boundary layer corrector.\n\nMeeting ID：645 23 63 5960\nPassword：714716\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 9/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir E. Nazaikinskii (Ishlinsky Institute for Problems in Mech anics RAS) DTSTART:20210115T090000Z DTEND:20210115T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/10 DESCRIPTION:Title: Partial spectral flow and the Aharonov-Bohm effect in graphene\nby Vladimir E. Nazaikinskii (Ishlinsky Institute for Pro blems in Mechanics RAS) as part of Beijing Moscow Mathematics Colloquium\n \n\nAbstract\nWe study the Aharonov-Bohm effect in an open-ended tube made of a graphene sheet whose dimensions are much larger than the interatomic distance in graphene. An external magnetic field vanishes on and in the v icinity of the graphene sheet\, and its flux through the tube is adiabatic ally switched on. It is shown that\, in the process\, the energy levels of the tight-binding Hamiltonian of $\\pi$-electrons unavoidably cross the F ermi level\, which results in the creation of electron-hole pairs. The num ber of pairs is proven to be equal to the number of magnetic flux quanta o f the external field. The proof is based on the new notion of partial spec tral flow\, which generalizes the ordinary spectral flow introduced by Ati yah\, Patodi\, and Singer and already having well-known applications (such as the Kopnin forces in superconductors and superfluids) in condensed mat ter physics.\n\nMeeting ID：645 2363 5960\nPassword：714716\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 10/ END:VEVENT BEGIN:VEVENT SUMMARY:Armen Sergeev (Steklov Mathematical Institute of RAS) DTSTART:20210312T080000Z DTEND:20210312T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/11 DESCRIPTION:Title: Mathematical problems in the theory of topological insulators\nby Armen Sergeev (Steklov Mathematical Institute of RAS) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nThe talk i s devoted to the theory of topological insulators - a new and actively dev eloping direction in solid state physics. To find a new topological object one have to look for the appropiate topological invariants and systems fo r which these invariants are non-trivial. The topological insulators are c haracterized by having wide energy gap stable for small deformations. A ni ce example is given by the quantum Hall spin insulator. It is a two-dimens ional insulator invariant under the time reversal. It is characterized by the non-trivial topological $\\mathbb Z_2$-invariant introduced by Kane an d Mele.\nIn our talk we consider the topological insulators invariant unde r time reversal. In the first part we present the physical basics of their theory while the second part deals with the mathematical aspects. These a spects are closely related to K-theory and non-commutative geometry.\n\nZo om Meeting ID: 646 2331 6558\nPassword：574262\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 11/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg German (Moscow State University) DTSTART:20210326T080000Z DTEND:20210326T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/12 DESCRIPTION:Title: Transference principle in Diophantine approximatio n\nby Oleg German (Moscow State University) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nThe talk will be devoted to one of t he fundamental principles in Diophantine approximation called transference principle. It reflects the relation of duality between certain problems. This principle is usually formulated in terms of Diophantine exponents - t hey generalise to the multidimensional case the measure of irrationality o f a real number. We plan to give an account on the existing relations Diop hantine exponents satisfy and try to reveal the geometric nature of those relations. After having described some basic geometric constructions\, we shall look from this perspective at the famous linear independence criteri on that belongs to Nesterenko. It appears that our approach provides an al ternative proof of this criterion\, which bases on rather simple geometric considerations.\n\nZoom Meeting ID: 673 7981 0561\nPassword：263867\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 12/ END:VEVENT BEGIN:VEVENT SUMMARY:Hu Yongquan (Morningside Center of Mathematics\, Academy of Mathem atics and Systems Science) DTSTART:20210326T090000Z DTEND:20210326T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/13 DESCRIPTION:Title: Introduction to p-adic Langlands program for GL_2< /a>\nby Hu Yongquan (Morningside Center of Mathematics\, Academy of Mathem atics and Systems Science) as part of Beijing Moscow Mathematics Colloquiu m\n\n\nAbstract\nThe $p$-adic and mod $p$ Langlands program is an avatar o f the classical Langlands program and has been first initiated by C. Breui l. In this colloquium talk\, I will give a brief introduction to the progr am and survey some recent progress in the case of $GL_2$.\n\nMeeting ID: 6 73 7981 0561\nPassword：263867\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 13/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Trushechkin (Steklov Mathematical Institute of RAS) DTSTART:20210409T080000Z DTEND:20210409T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/14 DESCRIPTION:Title: Mathematical methods of quantum key distribution\nby Anton Trushechkin (Steklov Mathematical Institute of RAS) as part o f Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nQuantum key distrib ution and\, more generally\, quantum cryptography is a modern branch of sc ience where methods of secure communication based on principles of quantum mechanics are studied. The rigorous proof of the security of quantum key distribution gave rise to a complex and beautiful mathematical theory\, w hich is based on methods of quantum information theory\, namely\, quantum entropic measures and entropic uncertainty relations. In particular\, to e stimate secret key rate\, one needs to minimize the quantum relative entro py (a convex function) subject to linear constraints. The problem is\, in general\, infinite-dimensional\, but symmetry properties of the problem re duces the dimensionality and allows one to solve this problem analytically . However\, currently\, an important task is to prove the security of quan tum key distribution with imperfect (i.e.\, practical) devices. Imperfecti ons introduce asymmetries and thus make the problem more complicated. In t he talk\, estimations for the secret key rate in the case of detection-eff iciency mismatch will be presented. Using entropic uncertainty relations\, an infinite-dimensional problem is reduced to a one-dimensional one.\n\nM eeting ID:633 6361 1209\nPassword: 127853\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 14/ END:VEVENT BEGIN:VEVENT SUMMARY:Feihu Xu (University of Science and Technology of China) DTSTART:20210409T090000Z DTEND:20210409T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/15 DESCRIPTION:Title: A quantum leap in security\nby Feihu Xu (Unive rsity of Science and Technology of China) as part of Beijing Moscow Mathem atics Colloquium\n\n\nAbstract\nQuantum cryptography or quantum key distri bution (QKD) offers information-theoretic security based on the laws of ph ysics. This is the technology at the basis of the quantum satellite "Mozi" \, put in orbit by the Chinese Academy of Sciences in 2016. In practice\, however\, the imperfections of realistic devices might introduce deviation s from the idealized models used in the security proofs of QKD. Can quantu m code breakers successfully hack real systems by exploiting the side chan nels? Can quantum code makers design innovative countermeasures to foil qu antum code breakers? In this talk\, I will talk about the theoretical and experimental progress in the practical security aspects of quantum code ma king and quantum code breaking. After numerous attempts over the past deca des\, researchers now thoroughly understand and are able to manage the pra ctical imperfections. Recent advances\, such as the decoy-state\, measurem ent-device-independent (MDI) and twin-field (TF) protocols\, have closed c ritical side channels in the physical implementations in a rigorous and pr actical manner. Further readings in [Xu et al.\, Rev. Mod. Phys. 92\, 0250 02 (2020)].\n\nMeeting ID: 633 6361 1209\nPassword: 127853\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 15/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Guterman (Moscow State University) DTSTART:20210423T080000Z DTEND:20210423T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/16 DESCRIPTION:Title: Values of permanent and positive solution of Wang- Krauter problem\nby Alexander Guterman (Moscow State University) as pa rt of Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nThe talk is bas ed on the joint work with M.V. Budrevich.\n\nThe class of $(-1\,1)$-matric es is very important in algebra and combinatorics and in various their app lications. For example\, well-known\n Hadamard matrices are of this type.\ n\nAn important matrix function is the permanent:\n$$\n{\\rm per}\\\, A= \\sum_{\\sigma\\in { S}_n} a_{1\\sigma(1)}\\cdots a_{n\\sigma(n)}\, $$\n here $A=(a_{ij})\\in M_n({\\mathbb F})$ is an $n\\times n$ matrix over a f ield ${\\mathbb F}$ and $S_n$ denotes the set of all permutations of the s et $\\{1\,\\ldots\, n\\}$.\n\nWhile the computation of the determinant can be done in a polynomial time\, it is still an open question\, if there ar e such algorithms to compute the permanent.\n\nIn this talk we discuss the permanents of $\\pm 1$-matrices.\n\n\nIn 1974 Wang posed a problem to fin d a decent upper bound for $|{\\rm per}(A)|$ if $A$ is a square $\\pm 1$-m atrix of rank $k$. In 1985 Krauter conjectured some concrete upper bound.\ n\nWe prove the Krauter's conjecture and thus obtain the complete answer t o the Wang's question. In particular\, we characterized matrices with the maximal possible permanent for each value of $k$.\n\nMeeting ID: 645 6321 1865\nPassword：341825\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 16/ END:VEVENT BEGIN:VEVENT SUMMARY:Chuanming Zong (Tianjin University) DTSTART:20210423T090000Z DTEND:20210423T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/17 DESCRIPTION:Title: From Sphere Packings to Post-Quantum Cryptography< /a>\nby Chuanming Zong (Tianjin University) as part of Beijing Moscow Math ematics Colloquium\n\n\nAbstract\nIn 1611\, Kepler made the following conj ecture: In three dimensions\, the density of the densest sphere packing is $\\pi/\\sqrt{18}$. Through the works of Newton\, Gauss\, Hilbert\, Minkow ski and others\, sphere packings has been developed into an important math ematical discipline between number theory and geometry. In 1940s\, the met hods and results of sphere packings had been applied into information theo ry by Shannon\, Hamming and others. Around 2000\, lattice sphere packings surprisingly found applications in modern cryptography. In particular\, Sh or\, Ajtai\, Pipher and others applied it into post-quantum cryptography. In this talk\, we will briefly introduce this dramatic development.\n\nMee ting ID: 645 6321 1865\nPassword：341825\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 17/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Nemirovski (Steklov Mathematical Institute of RAS) DTSTART:20210514T080000Z DTEND:20210514T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/18 DESCRIPTION:Title: Lorentz geometry and contact topology\nby Stef an Nemirovski (Steklov Mathematical Institute of RAS) as part of Beijing M oscow Mathematics Colloquium\n\n\nAbstract\nRoger Penrose observed four de cades ago that the space of light rays of a reasonable spacetime carries a natural contact structure and raised the problem of describing the causal ity relation of the spacetime in its terms. The talk will survey the progr ess made in this direction from the seminal work of Robert Low to the more recent applications of global contact rigidity.\n\nZoom meeting ID: 649 3 888 8630\nPassword：774874\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 18/ END:VEVENT BEGIN:VEVENT SUMMARY:Wenshuai Jiang (Zhejiang University) DTSTART:20210514T090000Z DTEND:20210514T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/19 DESCRIPTION:Title: Gromov-Hausdorff limit of manifolds and some appli cations\nby Wenshuai Jiang (Zhejiang University) as part of Beijing Mo scow Mathematics Colloquium\n\n\nAbstract\nGromov-Hausdorff distance is a distance between two metric spaces\, which was introduced by Gromov 1981. From Gromov's compactness theorem\, we knew that any sequence of manifolds with uniform lower Ricci curvature bounds has a converging subsequence in Gromov-Hausdorff topology to a limit metric space. The limit metric spac e in general may not be a manifold. The structure of such limit metric spa ce has been studied by Cheeger\, Colding\, Tian\, Naber and many others si nce 1990. It turns out that such theory has powerful application in geomet ry. In fact\, the resolution of Yau-Tian-Donaldson conjecture was largely relied on the development of the study of the limit metric space.\n\nIn th e first part of the talk\, we will discuss some recent progress of the Gro mov-Hausdorff limit of a sequence of manifolds with Ricci curvature bounds . In the second part\, we will discuss some applications based on the stud y of Gromov-Hausdorff limits.\n\nZoom Meeting ID: 649 3888 8630\nPassword ：774874\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 19/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Polekhin (Steklov Mathematical Institute of RAS) DTSTART:20210521T080000Z DTEND:20210521T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/20 DESCRIPTION:Title: On the application of the Ważewski method to the problem of global stabilization\nby Ivan Polekhin (Steklov Mathematica l Institute of RAS) as part of Beijing Moscow Mathematics Colloquium\n\n\n Abstract\nIn 2000\, S.P. Bhat and D.S. Bernstein proved that if the confi guration space of an autonomous control mechanical system is closed (compa ct without boundary)\, then the system cannot have a globally asymptotical ly stable equilibrium [1]. We will present a similar result for non-autono mous control systems defined on manifolds with non-empty boundaries. The t alk is based on the paper [2].\n\n[1] Bhat S.P.\, Bernstein D.S. A topolog ical obstruction to continuous global stabilization of rotational motion a nd the unwinding phenomenon Systems Control Lett.\, 39 (1) (2000)\, pp. 63 -70\n\n[2] I. Polekhin\, "On the application of the Ważewski method to t he problem of global \nstabilization"\, Systems & Control Letters\, 153 (2 021) Share Link: https://authors.elsevier.com/a/1d2Qoc8EXim67\n\nMeeting I D: 854 8688 3613 \nPassword: 303680\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 20/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaomin Zhao (College of Engineering\, Peking University) DTSTART:20210521T090000Z DTEND:20210521T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/21 DESCRIPTION:Title: High Fidelity Simulations of High-Pressure Turbine s Cascades for Data-Driven Model Development\nby Yaomin Zhao (College of Engineering\, Peking University) as part of Beijing Moscow Mathematics Colloquium\n\n\nAbstract\nGas turbines (GT) are\, and will continue to be\ , the backbone of aircraft propulsion\, as well as power generation and me chanical drive. A small GT performance improvement is expected to have a f uel-spend advantage of the billion-dollar order\, together with a signific ant CO2 emission benefit. Part of the possible performance improvements ca n be enabled by continuously advancing the understanding of the GT flow ph ysics and thus further reducing the inaccuracy of current design tools bas ed on computational fluid dynamics (CFD). By exploiting the capability of our high-fidelity CFD solver on leadership GPU-accelerated supercomputers\ , we have been able to perform state-of-the-art high fidelity simulations of turbomachinery flows. The generated data\, therefore\, can shed light o n the detailed fundamental flow physics\, in particularly the behavior of transitional and turbulent boundary layers affected by large-scale violent freestream turbulence\, under strong pressure gradient and curvature. Fur thermore\, machine learning methods are applied to the high-fidelity data to develop low order models readily applicable to GT designs.\n\nMeeting I D: 854 8688 3613 \nPassword: 303680\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 21/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrei Zotov (Steklov Mathematical Institute of Russian Academy of Sciences) DTSTART:20210604T080000Z DTEND:20210604T090000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/22 DESCRIPTION:Title: Integrable systems with elliptic dependence on mom enta and related topics\nby Andrei Zotov (Steklov Mathematical Institu te of Russian Academy of Sciences) as part of Beijing Moscow Mathematics C olloquium\n\n\nAbstract\nWe discuss a family of integrable many-body syste ms of classical (and quantum) mechanics. Some interrelations (dualities) p redict existence of integrable many-body systems with elliptic dependence on particles momenta – the most general representative of this family. W e describe some recent results on this topic. Next\, we discuss relations of the many-body systems to other families of integrable models including integrable tops and spin chains. Finally\, some interesting open problems are formulated.\n\nMeeting ID: 831 2285 8822\nPassword: 338416\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 22/ END:VEVENT BEGIN:VEVENT SUMMARY:Wenli Yang DTSTART:20210604T090000Z DTEND:20210604T100000Z DTSTAMP:20260404T095030Z UID:BeijingMoscowColloquium/23 DESCRIPTION:Title: Off-diagonal Bethe ansatz approach to quantum inte grable models\nby Wenli Yang as part of Beijing Moscow Mathematics Col loquium\n\n\nAbstract\nApplying the recent developed method-the off-diagon al Bethe ansatz method\, we construct the exact solutions of the Heisenber g spin chain with various boundary conditions. The results allows us to ca lculate the boundary energy of the system in the thermo dynamic limit. The method used here can be generalized to study the thermodynamic properties and boundary energy of other high rank models with non-diagonal boundary fields.\n\nMeeting ID: 831 2285 8822\nPassword: 338416\n LOCATION:https://stable.researchseminars.org/talk/BeijingMoscowColloquium/ 23/ END:VEVENT END:VCALENDAR