Research Group and Activities
Members
Nikolay Bogachev (team leader)
Khusrav Yorov (PhD student, 2019 – present)
- Master’s Thesis: “Quasi-arithmetic compact hyperbolic Coxeter prisms in H^3”, 2018–2019.
Mohammad Mualla (PhD student, 2019 – present)
- Current project 1: Reflective Lorentzian lattices over Z
- Current project 2: Isomorphism and Jordan decomposition of lattices over quadratic rings of integers, software implementation
Stepan Alexandrov (Bachelor’s Student, 2019 – present)
- Current project: Gale diagrams and combinatorial properties of compact hyperbolic Coxeter polytopes
Dmitry Guschin (Bachelor’s Student, 2020 – present)
- Current project: Reflective Lorentzian lattices and the Vinberg algorithm
Igor Novikov (Bachelor’s Student, 2020 – present)
- Current project: Fuchsian groups and Cartan involutions
Alexey Glazkin (Bachelor’s Student, 2021)
- Current project: discrete surfaces, hole detecting and filling algorithms, triangular meshes
Possible Research Topics and Description of My Research Interest
Possible topics
Arithmetic & quasi-arithmetic hyperbolic Coxeter groups and orbifolds/manifolds
Classification of reflective Lorentzian lattices
Crystallographic sphere packings
My research interests (some notes for students)
Description of my research interests
Current activities for team members (Fall 2020)
Advanced course [“Reflection groups”] at the IUM
Skoltech Geometry and Topology seminar lead by Prof. A.A. Gaifullin
Novosibirsk Online Seminar “Invariants of 3-manifolds”, lead by Prof. A.Yu. Vesnin
Online mini-course (at the HSE) on volumes of hyperbolic manifolds by Prof. A.Yu. Vesnin
Some other online-talks related to our research interests.