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Пишет Misha Verbitsky (![[info]](http://lj.rossia.org/img/userinfo.gif){kind=small} tiphareth)@ 2014-07-10 23:15:00 |
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| Настроение: |  tired |
| Музыка: | О. Болдырев - КОШКА |
| Entry tags: | .il, math, travel |
В Хайфе
В Хайфе до 21-го июля.
Вещаю в Тель-Авиве (13 и 15 июля, 13:00-14:30,
Schreiber 008), доклады:
"Symplectic packing on simple Kahler manifolds,
hyperkahler manifolds and tori",
"Hypercomplex manifolds of quaternionic
dimension 2 and HKT-structures,"
в Вейцманне 17-го, 14:00,
"Kahler threefolds without subvarieties."
Абстракты выступлений:
"Symplectic packing on simple Kahler manifolds,
hyperkahler manifolds and tori",
Let $M$ be a compact symplectic manifold
of volume $V$. We say that $M$ admits a full
symplectic packing if for any collection $S$
of symplectic balls of total volume less than
$V$, $S$ admits a symplectic embedding to $M$.
In 1994, McDuff and Polterovich proved that
symplectic packings of Kahler manifolds can
be characterized in terms of Kahler cones of
their blow-ups. When $M$ is a Kahler manifold
which is not a union of its proper subvarieties
(such a manifold is called simple) these Kahler
cones can be described explicitly using Demailly
and Paun structure theorem for Kahler cones.
It follows that any simple Kahler manifold admits
a full symplectic packing. This is used to show
that compact tori and hyperkahler manifolds
with irrational symplectic form admit a
full symplectic packing. This is work in
progress, joint with Michael Entov.
* * *
"Hypercomplex manifolds of quaternionic
dimension 2 and HKT-structures,"
Hypercomplex manifold is a manifold with three
complex structures generating a quaternion algebra.
Hypercomplex geometry is a quaternionic counterpart of
complex geometry; however, compact hypercomplex manifolds
almost never admit a Kahler structure (if they
do, they are automatically hyperkahler, quite rare
but much better understood).
Kahler metric is a metric which is locally a
complex Hessian of a function, called "a Kahler potential".
HKT metric on a hypercomplex manifold is a natural
analogue of a Kahler metric on a complex manifold.
HKT metric is a metric which is locally defined as a
quaternionic Hessian of a function, called "HKT potential".
We push this analogy further, proving a quaternionic
analogue of Buchdahl-Lamari's theorem for complex surfaces.
Buchdahl and Lamari have shown that a complex surface M
admits a Kahler structure iff $b_1(M)$ is even. We show that
a hypercomplex manifold M with trivial canonical bundle
(more precisely, with Obata holonomy SL(2, H))
admits an HKT structure iff $H^{0,1}(M)$ is even.
Its proof is suprisingly easier than the proof of
Buchdahl and Lamari, which involves regularization of
positive currents; no regularization is necessarily
(or possible) in quaternionic situation. This is a
joint work with Geo Grantcharov and Mehdi Lejmi.
I will try to explain all terms to make the lecture
accessible for anybody with basic knowledge of
differential and algebraic geometry.
* * *
Kahler threefolds without subvarieties.
Let $M$ be a compact Kahler 3-fold without
non-trivial subvarieties. We prove that $M$ is a
complex torus.
The proof is based on Brunella's
fundamental theorem about structure of 1-dimensional
holomorphic foliations and Demailly's regularization
of positive currents. This is a joint work with
F. Campana and J.-P. Demailly. I will try to
explain all notions to make the lecture accessible
for anybody with basic knowledge of differential
and algebraic geometry.
Израильская мобила, если что, 0549484954
но я не очень умею ей пользоваться.
Поселились в Бат-Галиме, потому как дешево и у моря.
Не русскоязычных тут, по-моему, просто нет,
всюду дикая грязь, русские магазины, кошки, помойки,
хрущобы, кошки. Конотоп, натурально. В квартире два
зомбоящика, русских каналов больше, чем нерусских.
Отключили оба, с отвращением, сколько можно.
Со дня на день жду восстания зомби, по всему Конотопу, с
требованиями прекратить геноцид преследования
русскоязычных и #ПутинВведиВойска.
На юге война, но досюда не долетает.
Привет
