Date:
Thu, 05/06/202510:00-11:00
Location:
Ross 70
Groups and dynamics seminar
Time: Thursday, May 22, 10:00
Place: Ross 70
Speaker: Zlil Sela (HUJI)
Title: A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples.
Abstract:
The JSJ decomposition and the Makanin-Razborov diagram were proved to be essential in studying varieties over free groups, semigroups and associative algebras. We suggest a unified conceptual approach to the applicability of these structures over all these algebraic categories.
With a variety over each of these algebraic categories we naturally associate a set of tuples in a free group. Then we show how to associate a Makanin-Razborov diagram with any
set of tuples in a free group.
Under a further condition on the diagram we construct a canonical one, and use it to define
a (pseudo) topology on sets of tuples that refines the Zariski toplogy. If time permits we will discuss some applications of the topology and the canonical diagram.
Time: Thursday, May 22, 10:00
Place: Ross 70
Speaker: Zlil Sela (HUJI)
Title: A canonical Makanin-Razborov diagram and a pseudo topology for sets of tuples.
Abstract:
The JSJ decomposition and the Makanin-Razborov diagram were proved to be essential in studying varieties over free groups, semigroups and associative algebras. We suggest a unified conceptual approach to the applicability of these structures over all these algebraic categories.
With a variety over each of these algebraic categories we naturally associate a set of tuples in a free group. Then we show how to associate a Makanin-Razborov diagram with any
set of tuples in a free group.
Under a further condition on the diagram we construct a canonical one, and use it to define
a (pseudo) topology on sets of tuples that refines the Zariski toplogy. If time permits we will discuss some applications of the topology and the canonical diagram.