[Recent Entries][Archive][Friends][User Info]
July 5th, 2024
| July 5th, 2024 | |
|---|---|
| 01:44 pm [Link] |
вещаю в tau.ac.il Вещаю походу в Тель-Авиве Math Colloquium: Misha Verbitsky (IMPA / HSE) Hyperbolic groups are not Ulam stable Mon, July 8, 12:15pm – 1:15pm Let G be a Lie group equipped with a left-invariant Riemannian metric d, and Γ any group. An ε-homomorphism is a map ρ:Γ→G which is "not far" from a homomorphism. More formally, an ε-homomorphism is a map ρ:Γ→G satisfying d(ρ(xy),ρ(x)ρ(y)) < ε for all x,y ϵ Γ. A group Γ is called Ulam stable if any ε-homomorphism Γ→ U(n) can be approximated by homomorphisms. Ulam stability was originally treated by D. Kazhdan (1982), following a question of V. Milman. Kazhdan has proven that all amenable groups are Ulam stable. Then he constructed an ε-homomorphism ρ:Γ→U(n), for any given ε >0,which cannot be 1/10-approximated by a homomorphism, where Γ is the fundamental group of a genus 2 Riemann surface. I would give a geometric version of his construction, and construct an ε-homomorphism ρ:Γ→G which cannot be 1/10-approximated for any Lie group G, where Γ is the fundamental group of a compact Riemannian manifold of strictly negative sectional curvature. This is a joint work with Michael Brandenbursky. Math Colloquium meetings take place on Mondays 12:15-13:15 in Schreiber building, room 006 * * * Thursday, July 11, 2024, 16:15-17:45, Schreiber 309 Mikhail Verbitsky (IMPA, Rio de Janeiro, and HSE, Moscow) Complex geometry and the isometries of the hyperbolic space The isometries of a hyperbolic space are classified into three classes - elliptic, parabolic, and loxodromic; this classification plays the major role in homogeneous dynamics of hyperbolic manifolds. Since the work of Serge Cantat in the early 2000-ies it is known that a similar classification exists for complex surfaces, that is, compact complex manifolds of dimension 2. These results were recently generalized to holomorphically symplectic manifolds of arbitrary dimension. I would explain the ergodic properties of the parabolic automorphisms, and prove the ergodicity of the automorphism group action for an appropriate deformation of any compact holomorphically symplectic manifold. This is a joint work with Ekaterina Amerik. * * * ну и до кучи, 14-го в HUJI. Привет Current Mood: |
sick| Previous Day | 2024/07/05 [Archive] |
Next Day |