The Skoltech Geometry & Topology Seminar (in Russian)

Here is a webpage of ongoing seminar at the Skoltech Center for Advanced Studies lead by Prof. Alexander Gaifullin. The main goal of this seminar is to analyze and discuss either some general topics or specific papers devoted to interactions between geometry, topology, and algebra. Each semester usually consists of a few (or just one) mini-courses given in Russian by young or senior participants/researchers.

Seminars 2020–2021

1. Nikita Klemyatin (PhD student; Skoltech & HSE). Topological characterization of the complex projective space.

   • Proof of the Hirzebruch – Kodaira theorem (CP^n).
   • Proof of the Yau theorem (CP^2).
     • Lec1.pdf. General plan.
     • Lec2.pdf. Preliminaries on Kahler manifolds.
     • Lec3.pdf. The Bogomolov-Miyaoki-Yau inequality and sectional curvature.
     • Lec4.pdf. Kahler-Einstein metricsa and Monge-Ampere equations.
     • Lec5.pdf. Bounds for Monge-Ampere.
     • Lec6.pdf. The Riemann-Roch Theorem and final of the proof.

2. Dr. Nikolay Bogachev (Postdoc/Assistant prof; Skoltech & MIPT). The dynamical proof of the Mostow Rigidity Theorem for compact hyperbolic manifolds.

   • Lecture 1. 29.01.2021.
     • Video1
     • Lec1.pdf
   • Lecture 2. 05.02.2021.
     • Video2
     • Lec2.pdf
   • Lecture 3. 19.02.2021.
     • Video3
     • Lec3.pdf
   • Lecture 4. 26.02.2021.
     • Video4
     • Lec4.pdf
   • Lecture 5. 05.03.2021.
     • Video5
     • Lec5.pdf
   • Discussion meeting. 12.03.2021.
     • Notes.pdf

3. Prof. Alexander Gaifullin (Full Prof.; Steklov Inst & MSU & Skoltech). Intro to mapping class groups and their topological aspects.

   • Lecture 1. 26.03.2021.
     • Video1
   • Lecture 2. 02.04.2021.
     • Video2
   • Lecture 3. 09.04.2021.
     • Video3
   • Notes

4. Alexey Rukhovich (PhD student; Skoltech & HSE). On the paper “Arithmetic groups symmetry and finiteness properties of Torelli groups”.

   • Lecture 1. 16.04.2021.
     • Video1
     • Lec1.pdf
   • Lecture 2. 23.04.2021.
     • Video2
     • Lec2.pdf
       
       

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