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

This Week

Time: 16:00–17:00

Place: Online

Yaar Solomon

2020–21–A meetings

Upcoming Meetings

Dec 3, 16:00–17:00, In Online TBAOnline Yaar Solomon
Dec 10, In Online Approximation by algebraic numbers and homogeneous dynamicsOnline 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 Ahlfors-regular 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 TBAOnline Yotam Smilansky (Rutgers University)
Dec 24, In Online TBAOnline Zemer Kosloff‏ (The Hebrew University)
Dec 31, 15:30–16:30, In Online TBAOnline Amir Algom (Penn State University)
Jan 7, In Online TBAOnline Guy Salomon (Weizmann Institute)
Jan 14, In Online TBAOnline

Past Meetings

Oct 22, In Online Homomorphic operations over secret sharesOnline Dor Bitan (Ben-Gurion University)
Oct 29, In Online Random walks on dense subgroupsOnline Yair Hartman (Ben-Gurion 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 manifoldsOnline 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. We will also explore the moduli space of generalized cusps, it is a semi-algebraic set of dimension n^2-n, 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 TBAOnline
Nov 19, In Online Non-trivial phase transition in percolationOnline Ariel Yadin (Ben-Gurion University)

In 1920 Ising showed that the infinite line Z does not admit a phase transition for percolation. In fact, no “one-dimensional” 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 non-trivial phase transition.
We prove this conjecture for all dimensions greater than 4. When the graph is transitive this solves the question completely, since low-dimensional transitive graphs are quasi-isometric to Cayley graphs, which we can classify thanks to Gromov’s theorem. This is joint work with H. Duminil-Copin, 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 Kantor-Lubotzky-Shalev. This is a joint work with Nir Lazarovich.