The seminar meets on Thursdays, 11:10-12:00, in -101

2019–20–B meetings

Mon, Jan 27 On the relation between topological entropy and asymptotic pairs Sebastián Barbieri (Université de Bordeaux)

I will present some results that state that under certain topological conditions, any action of a countable amenable group with positive topological entropy admits off-diagonal asymptotic pairs. I shall explain the latest results on this topic and present a new approach, inspired from thermodynamical formalism and developed in collaboration with Felipe García-Ramos and Hanfeng Li, which unifies all previous results and yields new classes of algebraic actions for which positive entropy yields non-triviality of their associated homoclinic group.

Feb 6 A subshift of finite type with two different positive sofic entropies Yuqing (Frank) Lin (The University of Texas at Austin)

Dynamical entropy is an important tool in classifying measure-preserving or topological dynamical systems up to measure or topological conjugacy. Classical dynamical entropy theory, of an action of a single transformation, has been studied since the 50s and 60s. Recently L. Bowen and Kerr-Li have introduced entropy theory for actions of sofic groups. Although a conjugacy invariant, sofic entropy in general appears to be less well-behaved than classical entropy. In particular, sofic entropy may depend on the choice of sofic approximation, although only degenerate examples have been known until now.

We present an example, inspired by hypergraph 2-colorings from statistical physics literature, of a mixing subshift of finite type with two different positive topological sofic entropies corresponding to different sofic approximations. The measure-theoretic case remains open. This is joint work with Lewis Bowen and Dylan Airey.

Feb 20 Sarnak’s Möbius disjointness conjecture for dendrites and Veech systems Houcein Elabdalaoui (Université de Rouen)
Mar 12 Seminar is canceled Seminar is canceled
Mar 19 Generalized cusps on convex projective manifolds Arielle Leitner (Weizmann Institute)

Convex projective manifolds are a generalization of hyperbolic manifolds. Koszul showed that the set of holonomies of convex projective structures on a compact manifold is open in the representation variety. We will describe an extension of this result to convex projective manifolds whose ends are generalized cusps, due to Cooper-Long-Tillmann. Generalized cusps are certain ends of convex projective manifolds. They may contain both hyperbolic and parabolic elements. We will describe their classification (due to Ballas-Cooper-Leitner), and explain how generalized cusps turn out to be deformations of cusps of hyperbolic manifolds. If time permits we will discuss current work on the moduli space of generalized cusps (current joint work with Ballas and Cooper).

Mar 26 TBA Erez Nesharim (The Hebrew University)
Apr 2 TBA Zemer Kosloff (The Hebrew University)
Apr 9 Passover Passover
Apr 16 Passover Passover
Apr 23 TBA
Apr 30 TBA Daniel Ingebretson (Ben-Gurion University)
May 7 TBA Zohar Reizis (Ben-Gurion University)
May 14 TBA Kevin Boucher (Weizmann Institute)
May 21 TBA Maria Gerasimova (Bar-Ilan University)
May 28 Shavuot Shavuot
Jun 4 Open day in BGU (talk may be cancelled)
Jun 11 TBA
Jun 18 TBA Yotam Smilansky
Jun 25 TBA
Sep 3, In online Extracting an invariant of conjugacy from independence entropy Bashir Abu Khalil (BGU)

In this talk Bashir Abu Khalil will present results from his MSc. Thesis about the notion of “independence entropy” for shifts of finite type, sofic shifts and general shift spaces.