Abstract: When are two elements in a given group conjugate? We solve this problem for the group of tree almost-automorphisms. These are homeomorphisms of the tree boundary which locally look like tree automorphisms. The solution is tied with the dynamics of the group action on the tree boundary. This work is joint with W. Lederle.
I will define the notions described in the title, and ask if they are equivalent. I will present a proof showing that they are in case the theory is NIP. The proof is essentially the proof of the fact that the lack of distality is witnessed by a sequence of singletons by Pierre Simon’s.
Repeats every week every Monday until Sun Feb 02 2020 .
1:00pm to 2:00pm
Mathematics, Faculty Lounge
This semester will be devoted to resolution of singularities -- a process that modifies varieties at the singular locus so that the resulting variety becomes smooth. For many years this topic had the reputation of very technical and complicated, though rather elementary.
In fact, the same resolution algorithm can be described in various settings, including schemes, algebraic varieties or complex analytic spaces.
I will survey recent progress in defining and computing categorical enumerative invariants, analogues of Gromov-Witten invariants defined directly from a cyclic A_infinity category and a choice of splitting of the Hodge filtration on its periodic cyclic homology. A proposed definition of such invariants appeared in 2005 in work of Costello, but the original approach had technical problems that made computations impossible.