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Thursday, November 9, 2017

4:20 PM - 5:20 PM (ET)

Exley Science Center Tower ESC 121

Event Type

Seminar/Colloquium

Contact

Canalia, Caryn

2182

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=79080

Speaker: Nadja Hempel, UCLA

*Mekler constructions in generalized stability*

** Abstract:
**Given a so called nice graph (no triangles, no squares, for any choice
of two distinct vertices there is a third vertex which is connected to one and
not the other), Mekler considered the 2-nilpotent subgroup generated by
the vertices of the graph in which two elements given by vertices commute if
and only if there is an edge between them. These groups form an interesting
collection of examples from a model theoretic point of view. It was shown that
such a group is stable if and only if the corresponding graph is stable and
Baudisch generalized this fact to the simple theory context. In a joint work
with Chernikov, we were able to verify this result for k-dependent and NTP_2
theories. This leads to the existence of groups which are
(k+1)-dependent but not k-dependent, providing the first algebraic objects
witnessing the strictness of these hierarchy.

This
is joint work with Artem Chernikov.* *