Speaker: Eilidh McKemmie Title: The probability of generating invariably a finite simple group Abstract: We say a group is invariably generated by a subset if every tuple in the product of conjugacy classes of elements in that subset is a generating tuple. We discuss the history of computational Galois theory and probabilistic generation problems to motivate some results about the probability of generating invariably a finite simple group. We also highlight some methods for studying probabilistic invariable generation.
Seminar room 209, Manchester Building, Jerusalem, Israel.
How do algebras grow?
The question of `how do algebras grow?', or, which functions can be realized as growth functions of algebras (associative/Lie, or algebras having certain additional algebraic properties) is a major problem in the meeting point of several mathematical fields including algebra, combinatorics, symbolic dynamics and more.
January 16, 12:00-13:00, Seminar room 209, Manchester building.
Abstract: I plan to show a proof of the statement "residually-finite-by-residually-finite extensions are weakly sofic". The proof is based on characterization of weakly sofic groups by solvability of equations over groups. It looks different from other proofs of soficity and weak soficity. I plan to discuss relations of equations on and over groups with soficity in some details.
Abstract: The profinite completion of a free profinite group on an infinite set of generators is a profinite group of greater rank. However, it is still unknown whether it is a free profinite group as well. I am going to present some partial results regarding this question.
The Teichmuller space with the Thurston metric and Outer Space with the Lipschitz metric are two examples of spaces with an asymmetric metric i.e. d(x,y)
eq d(y,x). The latter case is also incomplete: There exist Cauchy sequences that do not have a limit. We develop the theory of the completion of an asymmetric space and give lots of examples. Time permitting we will describe the case of Outer Space.
We establish topological local rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to irreducible uniform lattices in Isom(X) where X is a proper CAT(0) space with no Euclidian factors, not isometric to the hyperbolic plane. We deduce an analog of Wang’s finiteness theorem for certain non-positively curved metric spaces.
This is a joint work with Arie Levit.