Current seminars
October 13, 2013
– October 17, 2013
The Conference
Homogeneous Dynamics, Unipotent Flows, and Applications
in honor of Marina Ratner and her work
will be held at the IAS in Jerusalem. The schedule of the conference
can be found at
Combinatorics seminar
Time and Place: Monday October 14, 11:00-13:00, Math 209
Speaker: Avraham Morgenstern, HUJI
Title: On high-dimensional acyclic tournaments
Abstract:
I will describe a high-dimensional analog for the notion of
acyclic (aka transitive) tournament. As it turns out, many standard facts about
tournaments have non-trivial high-dimensional analogs. I will prove upper and
lower bounds on the number of $d$-dimensional $n$-vertex acyclic tournaments.
From this one can deduce a high-dimensional analog of the Erd\H{o}s-Moser theorem (Every
$n$-vertex tournament contains an acyclic subtournament
on $\log n$ vertices and this is tight up to a factor of $2$). I will describe
the inter-relations among various other notions of acyclicity
in high-dimensional tournaments and present an application to Ramsey
theory.
Joint work with Nati Linial.
Mathematical
Logic seminar
Time and Place: Wednesday, October 16, 15:00, Mathematics
Building, Room 209
Speaker: Itay Kaplan
Title: Maximal permutation groups
Abstract:
(Joint work with Pierre Simon)
We prove that for all n<omega, AGL_n(Q) is a closed maximal subgroup of S(Q^n)
--- the permutation group of Q^n. The proof
generalizes to AGL_omega(Q) and to PGL_n(Q) for
n<=omega. This shows that maximal closed countable permutation subgroups
exist, and thus answers a question of Dugald
Macpherson, and as a corollary answers a question of Junker and Ziegler about reducts of non-omega categorical structures