##### Description

The lecture announcements will be continually updated. The arrangement of the upcoming lectures is as follows:

******

**Lecture Series Ⅷ ——October 23th, 2020**

Time: 18:15-20:15 Beijing time (13:15-15:15 Moscow time), Oct. 23th.** Attention, please! The time of colloquium is different from previous ones.**

**To Join Zoom Meeting**:

https://zoom.com.cn/j/64864548936?pwd=aFg2UE1JTUpGVFY0NTRVa0R3a2FJUT09

**Meeting ID**：648 6454 8936

**Password**：899678

**Lecture 1 - Topological cyclic homology for p-adic local fields.**

**Speaker:** Prof. Ruochuan Liu, School of Mathematical Sciences, Peking University

**Time:** 18:15-19:15 Beijing time (13:15-14:15 Moscow time)

**Abstract:** We introduce a new approach to compute topological cyclic homology using the descent spectral sequence and the algebraic Tate spectral sequence. We carry out computations in the case of a p-adic local field with coefficient Fp. Joint work with Guozhen Wang.

**Bio: **Ruochuan Liu is working on p-adic aspects of arithmetic geometry and number theory, especially p-adic Hodge theory, p-adic automophic forms and p-adic Langlands program. He got his PhD from MIT at 2008. After several postdoc experience at Paris 7, McGill, IAS and Michigan, he joined the Beijing International Center for Mathematical Research at 2012. Starting from this year, he holds professorship at the School of Mathematical Sciences of Peking University.

**Lecture 2 — Additive divisor problem and Applications**

**Speaker: **Dimitry Frolenkov, Steklov Mathematical Institute (Moscow)

**Time:** 19:15-20:15 Beijing time (14:15-15:15 Moscow time)

**Abstract:** Additive Divisor Problem (ADP) 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. Surprisingly, the ADP arises naturally in quite different problems of number theory. 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.

**Bio: **Dmitry Frolenkov received his PhD degree from Steklov Mathematical Institute in 2013. Starting from 2014 he works at Steklov Mathematical Institute as a senior researcher. Besides he got the RAS award for young scientists of Russia. His research interests are centered around an analytic number theory with a special emphasis on the theory of L-functions associated to automorphic forms.

**************************************

**Second activity: Online conference Algebraic geometry and arithmetic **

The conference is on the occassion of the 70-th anniversary of our friend and colleague Vyacheslav Valentinovich Nikulin, to celebrate his huge contributions to the theory of K3 surfaces and other areas of geometry and arithmetic including reflections groups, automorphic forms and infinite-dimensional Lie algebras. The topics covered at the conference reflect the mathematical interests of V.V. Nikulin.

**Zoom meeting** ：948 1049 3176, **password ：**HWEG2Q

******

**Lecture Series Ⅶ - October 16th, 2020**

**To Join Zoom Meeting**

https://zoom.com.cn/j/61567007575?pwd=b1lJQlRZWmxKWnpCMkJQNGY3SEpCdz09

Meeting ID：615 6700 7575

Password：742316

**Time**: 2020-10-16 17:30-19:30 Beijing time (12:30-14:30 Moscow time) **（****The time is special and different from the usual time) **

**Lecture 1**** - Restriction of unitary representations of Spin(N,1) to parabolic subgroups**

**Speaker**: Prof. Yu Jun, Beijing International Center for Mathematical Research

**Time**：17：30-18：30 Beijing time （12：30-13：30 Moscow time）

**Abstract:** The orbit method predicts a relation between restrictions of irreducible unitary representations and projections of corresponding coadjoint orbits. In this talk we will discuss branching laws for unitary representations of Spin(N,1) restricted to parabolic subgroups and the corresponding orbit geometry. In particular, we confirm Duflo's conjecture in this setting. This is a joint work with Gang Liu (Lorraine) and Yoshiki Oshima (Osaka).

**Bio:** Jun Yu obtained PhD from ETH Zurich in 2012, and then did postdoc in IAS Princeton and MIT. He is now an assistant professor in Beijing international center for mathematical research at Peking University. His research field is representation theory and Langlands program, including the branching rule problem, the orbit method philosophy, and the beyond endoscopy program.

**Lecture 2: Characterizing homogeneous rational projective varieties with Picard number 1 by their varieties of minimal rational tangents.**

**Speaker:** Prof. Dmitry Timashev, Moscow State University

**Time**：18：30-19：30 Beijing time （13：30-14:30 Moscow Time)

**Abstract:** It is well known that rational algebraic curves play a key role in the geometry of complex projective varieties, especially of Fano manifolds. In particular, on Fano manifolds of Picard number (= the 2nd Betti number) one, which are sometimes called "unipolar", one may consider rational curves of minimal degree passing through general points. Tangent directions of minimal rational curves through a general point $x$ in a unipolar Fano manifold $X$ form a projective subvariety $\mathcal{C}_{x,X}$ in the projectivized tangent space $\mathbb{P}(T_xX)$, called the variety of minimal rational tangents (VMRT).

In 90-s J.-M. Hwang and N. Mok developed a philosophy declaring that the geometry of a unipolar Fano manifold is governed by the geometry of its VMRT at a general point, as an embedded projective variety. In support of this thesis, they proposed a program of characterizing unipolar flag manifolds in the class of all unipolar Fano manifolds by their VMRT. In the following decades a number of partial results were obtained by Mok, Hwang, and their collaborators.

Recently the program was successfully completed (J.-M. Hwang, Q. Li, and the speaker). The main result states that a unipolar Fano manifold $X$ whose VMRT at a general point is isomorphic to the one of a unipolar flag manifold $Y$ is itself isomorphic to $Y$. Interestingly, the proof of the main result involves a bunch of ideas and techniques from "pure" algebraic geometry, differential geometry, structure and representation theory of simple Lie groups and algebras, and theory of spherical varieties (which extends the theory of toric varieties).

**Bio**: Dmitry Timashev recieved PhD degree from Moscow State University in 1997. From 1997, he is working at the Department of Higher Algebra in the Faculty of Mathematics and Mechanics, Moscow State University, currently at the position of associate professor. His research interests include Lie groups and Lie algebras, algebraic transformation groups and equivariant algebraic geometry, representation theory and invariant theory.

******

**Lecture Series VI - September 25th, 2020**

**Time:** 2020-09-25 16:00-18:00 Beijing time (11:00-13:00 Moscow time)

**To Join Zoom Meeting**

https://zoom.com.cn/j/65021617081?pwd=RU1nU01mMkdKTnN4eHIySkFXL1VrZz09

**Meeting ID：**650 2161 7081

**Password：**489842

**Lecture 1** - ** Geometric description of the Hochschild cohomology of Group Algebras**

**Speaker**: A. S. Mishchenko (Lomonosov Moscow State University)

**Time**: 2020-09-25 16:00-17:00 Beijing time (11:00-12:00 Moscow time)

**Abstract**: /upload/editor/file/20200921/21143204927.pdf

**Bio**:

Professor A.S. Mischenko graduated from Moscow State University in 1965. He became a Professor of the Department of Higher Geometry and Topology, Faculty of Mechanics and Mathematics of this University in 1979. He also holds a position of Leading researcher at the Mathematical Steklov Institute. He is a Honored Professor of Moscow University since 2006. _{}^{}

His research interests include geometry and topology and their applications. The main direction of his work is related to the study and application of algebraic and functional methods in the theory of smooth manifolds.

**Lecture 2 - Unipotent representations and quantization of classical nilpotent varieties**

**Speaker**: Prof. Daniel Wong (黄家裕）, Chinese University of Hongkong at Shenzhen.

**Time**: 2020-09-25 17:00-18:00 Beijing time (12:00-13:00 Moscow time)

**Bio**: Graduated at Cornell University in 2013. Research area is on Representation theory of real reductive Lie groups.

******

**Previous Lectures:**

__Lecture Series V - July 10th, 2020__

**Video:**

https://disk.pku.edu.cn:443/link/55C58180540241608743998D28941762

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)

Abstract:

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.

Bio:

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)

Abstract:

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.

Bio:

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.

**Recording: **

https://disk.pku.edu.cn:443/link/36F474E90952433E4B75BED76283A758

ExpirationTime：2021-07-31 23:59

**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.

**Recording: **
https://disk.pku.edu.cn:443/link/17D6C8D96B3F620DFAC11DA76F40288D

ExpirationTime：2021-07-31 23:59

__Lecture Series I - May 15th 2020__

**Recording: **

**https://disk.pku.edu.cn:443/link/0B14E32445D33A9394769538904C939A**

ExpirationTime：2021-08-01 23:59

**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.

**For more information, please click on the following link：**

https://disk.pku.edu.cn:443/link/3FFA6A7EF0B27A568A9C20B99FA076F6

**************

**Organized by:**

◆ 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.