The lecture announcements will be continually updated. The arrangement of the upcoming lectures is as follows:
Lecture Series II - May 29th 2020
To join the meeting:
Time：2020-05-29 20:00-22:00 Beijing time (15:00-17:00 Moscow time)
Meeting ID: 619 0173 2085
Meeting Password: 311334
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 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.