Event № 163
ACTION NOW WANDERING SEMINAR
First meeting, Technion, 1.12.15,Butler Auditorium (near Forscheimer Faculty club)
• 9:30 cookies, small pastries and fruit from Israel's northern foothills, and refreshing drinks
• 10:00 Uri Bader, Weizmann
Ozawa's proof of Gromov's polynomial growth theorem.
Gromov's polynomial growth theorem from the early 1980's, stating that every group of polynomial growth is virtually nilpotent, is a milestone in Geometric Group Theory. In this talk I will present the entropy based, two pages proof given recently by Narutaka Ozawa.
• 11:15 Uri Shapira, Technion
Stationary measures on homogeneous spaces.
Let mu be a compactly supported measure on SL_3(R) generating a group whose Zariski closure is semi-simple. Let X be the space of all rank-2 discrete subgroups of R^3 (identified up to dilation). We describe a classification of the mu-stationary measures on X. This is part of an ongoing project with Oliver Sargent in which we classify stationary measures in situations similar to the above. The proof is an adaptation of the Benoist-Quint approach for classifying stationary measures on homogeneous spaces obtained by quotienting by a discrete subgroup. As an application we show that if v in Z^3 varies along a the quadratic surface x^2 + y^2 - z^2 then the the shapes of the 2-lattices obtained by intersecting Z^3 with the orthocomplement of v is dense in the space of shapes.
• 12:15 Lunch and informal discussions
• 14:00 Tom Meyerovich, Ben Gurion University
Sofic groups, sofic entropy, stabilizers and invariant random subgroups
Sofic groups where introduced by Gromov (under a different name), and Weiss towards the end of the millennium. This is a class of groups retaining some finiteness properties, a common generalization of amenable and residually finite groups. Entropy theory for sofic groups, initiated by L. Bowen, is developing rapidly. After recalling the concepts of soficity and entropy, I will explain some results relating them to invariant random subgroups, or equivalently stabilizer groups for measure preserving actions.
• 15:15 Brandon Seward, Hebrew University
Positive entropy actions of countable groups factor onto Bernoulli shifts
I will prove that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well-known Sinai factor theorem from classical entropy theory. As an application, I will show that for a large class of non-amenable groups, every positive entropy free ergodic action satisfies the measurable von Neumann conjecture.