Speaker: Efim Zelmanov (University of California, San Diego)
Date and time: December 10, 2020, 20:00 Novosibirsk time (UTC +7)

Abstract:

We will discuss growth types and complexity of groups, algebras and monoids.

Chair: Pavel Kolesnikov
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Video

Speaker: Alexei Miasnikov (Stevens Institute of Technology)
Date and time: November 26, 2020, 19:00 Novosibirsk time (UTC +7)

Abstract:

I will talk about asymptotic group theory, which concerns with group properties that hold asymptotically almost surely. These include random groups (finitely presented, nilpotent, solvable, periodic, finite, etc.), random subgroups, generic properties, and 0-1 laws.

Chair: Evgeny Vdovin
Slides
Video

Speaker: Sergey Shpectorov (University of Birmingham)
Date and time: November 12, 2020, 19:00 Novosibirsk time (UTC +7)

Abstract:

Axial algebras were introduced as a broad generalisation of Majorana algebras of Ivanov, which in turn generalise the properties of the Griess algebra whose automorphism group is the Monster sporadic simple group. Axial algebras with graded fusion laws have inherent symmetry and hence they always have nontrivial automorphism groups.

In the talk we survey a number of recent results concerning axial algebras of Jordan and Monster type and mention several interesting open problems.

Chair: Andrey Vasil'ev
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Video

Speaker: Evgeny Khukhro (University of Lincoln & Sobolev Institute of Mathematics)
Date and time: October 29, 2020, 16:00 Novosibirsk time (UTC +7)

Abstract:

Bounding the p-length or/and nilpotent length (Fitting height) of finite groups became a classical area of research since the seminal works of P. Hall and G. Higman of 1956 on Restricted Burnside Problem and of J. Thompson of 1964 on automorphisms. Various generalizations and improvements followed in a torrent of subsequent papers, mainly in the 1960s and 1970s. This area of research became somewhat less fashionable later, and a certain perception was even formed that nothing interesting remains to be discovered, that all the methods are already known. The purpose of my talk is to dispel this perception, to highlight several important open problems results about bounding the Fitting height and p-length of finite soluble groups, as well as other length parameters applicable to not necessarily soluble groups. Among examples, there are problems about finite groups with
fixed-point-free and almost fixed-point-free automorphisms, about generalizations of the Restricted Burnside Problem, about coset identities, which have applications in the study of profinite groups, etc.

Chair: Evgeny Vdovin
Slides
Video