The concept of transformation groups is a mathematical formalization of the general philosophical idea of symmetry in the world. One might even say the world is cognizable inasmuch as it is symmetric. That principle is vividly reflected in Emmy Noether’s famous theorem, which drew a connection between the symmetries of a physical system and conservation laws for physical quantities.
In mathematics, the theory of transformation groups is a broad area covering different branches of algebra, geometry, topology, dynamical systems, and mathematical physics. It gives rise to the origins of group theory and the Erlangen program published by Felix Klein, who proposed the idea of considering various geometries from the viewpoint of their symmetry groups. Although transformation groups do not fit in a unified mathematical theory in a strict sense, some fields in this area extending well away from each other, there are general consolidating principles and concepts that make interosculation and mutual enrichment possible. That allows for relevant and fruitful interaction and collaboration between research being done in the various fields related to transformation groups.
The Moscow school of transformation groups was established at Moscow State University by Ernest Vinberg (1937-2020) and Arkadiy Onishchik (1933-2019).
The scope of the conference includes:
- Lie groups and Lie algebras,
- Lie, holomorphic, and algebraic transformation groups,
- Algebraic groups and invariant theory,
- The geometry and topology of homogeneous spaces,
- Discrete subgroups of Lie groups and discrete transformation groups,
- Quantum groups and universal enveloping algebras,
- Kac-Moody groups and algebras, conformal and vertex algebras,
- Lie supergroups and superalgebras,
- Representation theory,
- Integrable Hamiltonian systems.
The tentative list of keynote speakers includes: Michel Brion, Stephanie Cupit-Foutou, Corrado de Concini, Anna Feliskon, Anatoly Fomenko, Victor Ginzburg, Valery Gritsenko, Megumi Harada, Jürgen Hausen, Joel Kamnitzer, Yael Karshon, Toshiyuki Kobayashi, Hanspeter Kraft, Bernhard Krötz, Shrawan Kumar, Frank Kutzschebauch, Ivan Losev, Alexander Lubotzky, Taras Panov, Dmitri Panyushev, Vladimir Popov, Siddhartha Sahi, Nikolai Vavilov, Michèle Vergne, and Oksana Yakimova.