Oct 22, In Online

Homomorphic operations over secret shares

Dor Bitan (BenGurion University)


Oct 29, In Online

Random walks on dense subgroups

Yair Hartman (BenGurion University)

Imagine you have a group, with a discrete subgroup. Wouldn’t that be nice to relate random walks, and Poisson boundaries of the group and of the subgroup, in a meaningful way?
This was done by Furstenberg for lattices in semisimple Lie groups as an essential tool in an important rigidity result. We are concerned with dense subgroups. We develop a technique for doing it that allows us to exhibit some new interesting phenomena in Poisson boundary theory. I’ll explain the setting in which we work, and will focus mainly on our construction (leaving the applications as “further reading”).
Joint work with Michael Björklund and Hanna Oppelmayer

Nov 5, In Online

Deformations of 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 CooperLongTillmann. Generalized cusps are certain ends of convex projective manifolds. They may contain both hyperbolic and parabolic elements. We will describe their classification (due to BallasCooperLeitner), and explain how generalized cusps turn out to be deformations of cusps of hyperbolic manifolds. We will also explore the moduli space of generalized cusps, it is a semialgebraic set of dimension n^2n, contractible, and may be studied using several different invariants. For the case of three manifolds, the moduli space is homeomorphic to R^2 times a cone on a solid torus.

Nov 12, In Online

TBA



Nov 19, In Online

Nontrivial phase transition in percolation

Ariel Yadin (BenGurion University)

In 1920 Ising showed that the infinite line Z does not admit a phase transition for percolation. In fact, no “onedimensional” graph does. However, it has been asked if this is the only obstruction. Specifically, Benjamini & Schramm conjectured in 1996 that any graph with isoperimetric dimension greater than 1 will have a nontrivial phase transition.
We prove this conjecture for all dimensions greater than 4. When the graph is transitive this solves the question completely, since lowdimensional transitive graphs are quasiisometric to Cayley graphs, which we can classify thanks to Gromov’s theorem.
This is joint work with H. DuminilCopin, S. Goswami, A. Raufi, F. Severo.

Nov 26, In Online

Is invariable generation hereditary?Online

Gil Goffer (Weizmann Institute)

I will discuss the notion of invariably generated groups and present a construction of an invariably generated group that admits an index two subgroup that is not invariably generated. The construction answers questions of Wiegold and of KantorLubotzkyShalev. This is a joint work with Nir Lazarovich.

Dec 3, 16:00–17:00, In Online

TBA

Yaar Solomon


Dec 10, In Online

Approximation by algebraic numbers and homogeneous dynamics

Erez Nesharim (The Hebrew University)

Diophantine approximation quantifies the density of the rational numbers in the real line. The extension of this theory to algebraic numbers raises many natural questions. I will focus on a dynamical resolution to Davenport’s problem and show that there are uncountably many badly approximable pairs on the parabola. The proof uses the Kleinbock–Margulis uniform estimate for nondivergence of nondegenerate curves in the space of lattices and a variant of Schmidt’s game. The same ideas applied to Ahlforsregular measures show the existence of real numbers which are badly approximable by algebraic numbers. This talk is based on joint works with Victor Beresnevich and Lei Yang.

Dec 17, 15:30–16:30, In Online

Multiscale substitution tilings

Yotam Smilansky (Rutgers University)

Multiscale substitution tilings are a new family of tilings of Euclidean space that are generated by multiscale substitution rules. Unlike the standard setup of substitution tilings, which is a basic object of study within the aperiodic order community and includes examples such as the Penrose and the pinwheel tilings, multiple distinct scaling constants are allowed, and the defining process of inflation and subdivision is a continuous one. Under a certain irrationality assumption on the scaling constants, this construction gives rise to a new class of tilings, tiling spaces, and tiling dynamical systems, which are intrinsically different from those that arise in the standard setup. In the talk, I will describe these new objects and discuss various structural, geometrical, statistical, and dynamical results. Based on joint work with Yaar Solomon.

Dec 24, In Online

On the local limit theorem in dynamical systems

Zemer Kosloff (The Hebrew University)

In 1987, Burton and Denker proved the remarkable result that in every aperiodic dynamical system (including irrational rotations for example) there is a square integrable, zero mean function such that its corresponding time series satisfies a CLT. Subsequently, Volny showed that one can find a function which satisfies the strong (almost sure) invariance principle. All these constructions resulted in a nonlattice distribution.
In a joint work with Dalibor Volny we show that there exists an integer valued cocycle which satisfies the local limit theorem.

Dec 31, 15:30–16:30, In Online

On the decay of the Fourier transform of selfconformal measures

Amir Algom (Penn State University)

Let P be a selfconformal measure with respect to an IFS consisting of finitely many smooth contractions of [0,1]. Assuming a mild and natural condition on the derivative cocycle, we prove that the Fourier transform of P decays to zero at infinity. This is related to the highly active study of the properties of the Fourier transform of dynamically defined measures, dating back to the important work of Erdos about Bernoulli convolutions in the late 1930’s.
This is joint work with Federico Rodriguez Hertz and Zhiren Wang.

Jan 7, In Online

Amenability, proximality, and higher order syndeticityOnline

Guy Salomon (Weizmann Institute)

An action of a discrete group G on a compact Hausdorff space X is called proximal if for every two points x and y of X there is a net g_i in G such that lim(g_i x)=lim(g_i y), and strongly proximal if the action of G on the space Prob(X) of probability measures on X is proximal. The group G is called strongly amenable if all of its proximal actions have a fixed point and amenable if all of its strongly proximal actions have a fixed point.
In this talk, I will present a correspondence between (strongly) proximal actions of G and Boolean algebras of subsets of G consisting of certain kinds of “large” subsets. I will use these Boolean algebras to establish new characterizations of amenability and strong amenability. Furthermore, I will show how this machinery helps to characterize “dense orbit sets” answering a question of Glasner, Tsankov, Weiss, and Zucker.
This is joint work with Matthew Kennedy and Sven Raum.

Jan 14, In Online

Conjugacy of free automorphisms of finite order of subshifts of finite typeOnline

Jeremias Epperlein (University of Passau)

An old question in symbolic dynamics asks if every two involutions
without fixed points in the automorphism group of the 2shift are
conjugate.
Based on work of Fiebig, Boyle and Schmieding we show that they are at
least conjugate in the stabilized automorphism group.

Feb 11, 16:25–17:30, In Online

Substitution on infinite alphabets and generalized BratteliVershik models.Online

Shrey Sanadhya (The University of Iowa)

We consider substitutions on countably infinite alphabets as Borel dynamical system and build their BratteliVershik models. We prove two versions of Rokhlin’s lemma for such substitution dynamical systems. Using the BratteliVershik model we give an explicit formula for a shiftinvariant measure (finite and infinite) and provide a criterion for this measure to be ergodic. This is joint work with Sergii Bezuglyi and Palle Jorgensen.
