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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.

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