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Пишет Misha Verbitsky (![[info]](http://lj.rossia.org/img/userinfo.gif){kind=small} tiphareth)@ 2024-07-05 13:44:00 |
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| Настроение: |  sick |
| Музыка: | План ПланЫч + АГНИЯR - A.D.Тел (1990-2000) |
| Entry tags: | .il, math, travel |
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
