Lecture Series V - July 10th, 2020
Valid Until: 2025-08-31 23:59
Lecture 1 - Limits of the Boltzmann equation.
Speaker: Feimin Huang, Academy of Mathematics and Systems Science, CAS, China
Time: 2020-07-10 20:00-21:00 Beijing time (15:00-16:00 Moscow time)
Abstract: In this talk, I will present recent works on the hydrodynamic limits to the generic Riemann solutions to the compressible Euler system from the Boltzmann equation.
Bio: Prof. Huang, Feimin got Ph. D in Chinese Academy Sinica in 1997，and then did postdoc in ICTP, Italy and Osaka University. His research field is hyperbolic equations and conservative laws, including fluid dynamical systems, Navier-Stokes equations, and other various Partial Differential Equations. He was awarded the SIAM Outstanding Paper Prize by Society of American Industrial and Applied Mathematics in 2004. He won the Second Prize of National Natural Science Award in 2013.
Lecture 2 - On the geometric solutions of the Riemann problem for one class of systems of conservation laws.
Speaker: Vladimir Palin, Moscow State University
Time: 2020-07-10 21:00-22:00 Beijing time (16:00-17:00 Moscow time)
Abstract: We consider the Riemann problem for a system of conservation laws. For non-strictly hyperbolic in the sense of Petrovskii step-like systems, a new method of constructing a solution is described. The proposed method allows us to construct a unique solution to the Riemann problem, which for each $t$ is a picewise smooth function of $x$ with discontinuities of the first kind. Moreover, for the scalar conservation law, the solution constructed by the proposed method coincides with the known admissible solution.
Bio: Vladimir Palin recieved higher education degree from Moscow State University in 2005, PhD degree from Moscow State University in 2009. He is
now a senior lecturer in the Faculty of Mathematics and Mechanics, Moscow State University. His research interests include hyperbolic equations and systems, conservation laws and matrix equations.
Lecture Series IV - June 26th, 2020
Lecture 1 - Tying Knots in Fluids
Speaker: Prof. Yue Yang, Department of Mechanics and Engineering Science, College of Engineering, Peking University,Beijing
Time: 2020-06-26 20:00-21:00 Beijing time (15:00-16:00 Moscow time)
We develop a general method for constructing knotted vortex/magnetic tubes with the finite thickness, arbitrary shape, and tunable twist. The central axis of the knotted tubes is determined by a given smooth and non-degenerated parametric equation. The helicity of the knotted tubes can be explicitly decomposed into the writhe, localized torsion, and intrinsic twist. We construct several knotted vortex/magnetic tubes with various geometry and topology, and investigate the effect of twist on their evolution in hydrodynamic or magnetohydrodynamic flows using direct numerical simulation. In addition, we illustrate a knot cascade of magnetic field lines through the stepwise reconnection of a pair of orthogonal helical flux tubes with opposite chirality.
Yue Yang received BE degree from Zhejiang University in 2004, MS degree from the Institute of Mechanics, Chinese Academy of Sciences in 2007, and PhD degree from California Institute of Technology in 2011, then he was sponsored by the CEFRC Fellowship for postdoc research at Princeton University and Cornell University. Yang joined the Department of Mechanics and Engineering Science in College of Engineering, Peking University in 2013, and was promoted to full professor in 2020. He received the “National Distinguished Young Researcher” award and “Qiu Shi Outstanding Young Scholar Award”. His research interests include turbulence, transition, and combustion.
Lecture 2 - Supercomputer simulations of aerodynamics and aeroacoustics problems using high-accuracy schemes on unstructured meshes.
Speaker: Prof. Andrey Gorobets, Keldysh Institute of Applied Mathematics of RAS, Moscow
Time: 2020-06-26 21:00-22:00 Beijing time (16:00-17:00 Moscow time)
This talk is devoted to scale-resolving simulations of compressible turbulent flows using edge-based high-accuracy methods on unstructured mixed-element meshes. The focus is on parallel computing. Firstly, the family of edge-based schemes that we are developing will be outlined. Then our simulation code NOISEtte will be presented. It has multilevel MPI+OpenMP+OpenCL parallelization for a wide range of hybrid supercomputer architectures. A description of the parallel algorithm will be provided. Finally, our supercomputer simulations of aerodynamics and aeroacoustics problems will be demonstrated.
Andrey Gorobets graduated from Moscow State University in 2003. He then outlived three thesis defenses: 2007, Candidate of Sciences (к. ф.-м. н., equivalent to Ph.D.) at IMM RAS; 2008, European Ph.D. degree at UPC, Barcelona, Spain; 2015, Doktor nauk (д. ф.-м. н., higher doctoral degree) at the Keldysh Institute of Applied Mathematics of RAS (KIAM), Moscow, Russia. He is now a leading researcher at KIAM. His work is focused on algorithms and software for large-scale supercomputer simulations of turbulent flows.
Lecture Series III - June 12th, 2020
Lecture 1 - Slopes of modular forms and ghost conjecture of Bergdall and Pollack
Speaker：Prof. Xiao Liang （Beijing International Center for Math. Research ）
Time: 2020-06-12 20:00-21:00 Beijing time (15:00-16:00 Moscow time)
Abstract: In classical theory, slopes of modular forms are p-adic valuations of the eigenvalues of the Up-operator. On the Galois side, they correspond to the p-adic valuations of eigenvalues of the crystalline Frobenius on the Kisin's crystabelian deformations space. I will report on a joint work in progress in which we seems to have proved a version of the ghost conjecture of Bergdall and Pollack. This has many consequences in the classical theory, such as some cases of Gouvea-Mazur conjecture, and some hope towards understanding irreducible components of eigencurves. On the Galois side, our theorem can be used to prove certain integrality statement on slopes of crystalline Frobenius on Kisin's deformation space, as conjectured by Breuil-Buzzard-Emerton. This is a joint work with Ruochuan Liu, Nha Truong, and Bin Zhao.
Lecture 2 - Higher-dimensional Contou-Carrere symbols
Speaker：Prof. RAS Denis V. Osipov (Steklov Mathematical Institute of Russian Academy of Sciences)
Time: 2020-06-12 21:00-22:00 Beijing time (16:00-17:00 Moscow time)
Abstract: The classical Contou-Carrere symbol is the deformation of the tame symbol, so that residues and higher Witt symbols naturally appear from the Contou-Carrere symbol. This symbol was introduced by C. Contou-Carrere itself and by P. Deligne. It satisfies the reciprocity laws. In my talk I will survey on the higher-dimensional generalization of the Contou-Carrere symbol. The n-dimensional Contou-Carrere symbol naturally appears from the deformation of a full flag of subvarieties on an n-dimensional algebraic variety and it is also related with the Milnor K-theory of iterated Laurent series over a ring. The talk is based on joint papers with Xinwen Zhu (when n=2) and with Sergey Gorchinskiy (when n>2).
Lecture Series II - May 29th 2020
Lecture 1 - Geometry of Landau--Ginzburg models.
Speaker：Prof. Victor V. Przyjalkowski (Steklov Mathematical Institute of Russian Academy of Sciences)
Time：2020-05-29 20:00-21:00 Beijing time (15:00-16:00 Moscow time)
Abstract: We discuss geometric and numerical properties of Landau--Ginzburg models of Fano varieties that reflect geometric and numerical properties of the initial Fano varieties. The main example is the threefold case.
Lecture 2 - Deformation theory of Schroedinger equation arising from singularity theory
Speaker: Prof. Huijun Fan (Peking University)
Time：2020-05-29 21:00-22:00 Beijing time (16:00-17:00 Moscow time)
Abstract: Mirror symmetry phenomenon relates many mathematical branches in a mysterious way. For example, it is conjectured that the quantum geometry of a Calabi-Yau hypersurface is equivalent to the quantum singularity theory of the corresponding defining function. When we consider the complex structure deformation of the two sides, we get the B model mirror conjecture, where the exciting structures of deformation moduli space, Gauss Manin connection, period mapping and etc.will appear. In this lecture, I will report another way to study the deformation theory of singularity via Schroedinger equation. By study the spectral theory of Schroedinger equation, we can build the variation of Hodge theory, Gauss-Manin connection by wave function, Frobenius manifold for some cases and even BCOV type torsion invariants for singularity.
Lecture Series I - May 15th 2020
Lecture 1 - Representation volumes and dominations of 3-manifolds
Speaker：Shicheng Wang (Peking University)
Time：2020-05-15 20:00-21:00 Beijing time (15:00-16:00 Moscow time)
Abstract: We will discuss recent results on virtual representation volumes and finiteness of the mapping degree set on 3-manifolds.
Lecture 2 - Topology of integrable systems on 4-manifolds
Speaker：Elena Kudryavtseva (Moscow State University)
Time：2020-05-15 21:00-22:00 Beijing time (16:00-17:00 Moscow time)
Abstract: We will give a survey on the topology of integrable Hamiltonian systems on 4-manifolds. Open questions and problems will be also discussed. Recall that, from a topological point of view, an integrable Hamiltonian system can be treated as a singular Lagrangian fibration on a smooth symplectic 2n-manifold whose generic fibres are n-dimensional tori. By a singularity, we mean either a singular point or a singular fibre of the fibration. The topological structure of such singularities is very important for understanding the dynamics of integrable systems both globally and locally. Our goal is to describe topological invariants of such singularities and obtain their classification up to fibrewise homeomorphism (for time being we forget about symplectic structure). The next step is to combine these singularities together to study the global structure of the fibration. For many integrable systems, this structure is completely determined by topological properties of singularities.
◆ Mechanical and Mathematical Faculty of Lomonosov Moscow State University and Moscow Center for Fundamental and Applied Mathematics.
◆ Steklov International Mathematical Center, Steklov Mathematical Institute of Russian Academy of Sciences.
◆ School of Mathematical Sciences, Peking University.
◆Department of Mechanics and Engeering Science in College of Engineering, Peking University.