[Turkmath:6136] Feza Gursey Merkezinde "Dual Perspectives" konusmasi (9 Haziran Cuma)

[sadik.deger at boun.edu.tr]

Sayin liste uyeleri,

Bogazici Universitesi Kandilli kampusunde yer alan Feza Gursey Fizik ve
Matematik Arastirma Merkezinde matematikciler ile kuramsal fizikcileri
bulusturmayi hedefledigimiz "Dual Perspectives" konusma dizisine 9 Haziran
Cuma gunu detaylari asagida ve ekteki posterde yer alan konusmayla devam
ediyoruz.

Butun ilgilenenleri bekleriz,

Nihat Sadik Deger, Umut Varolgunes

------------------------------------------------------

Konusma dizisinin web sayfasi: https://umutvg.github.io/dp.html

Tarih: 9 Haziran 2023, Cuma (Sabah bolumu 10:30-12:00, Oglen bolumu    
13:30-15:00)

Konusmaci: Felix Schlenk, University of Neuchatel

Baslik: Symplectic Almost Squeezings of Large 4-balls

Ozet: In this first general talk I will explain what "symplectic" means, and
sketch a proof of Gromov's non-squeezing theorem and of Gromov's   
2-ball theorem.
These basic symplectic rigidity results already have applications to   
problems in
dynamics, such as short-time super-recurrence and the non-existence of local
attractors of certain Hamiltonian PDEs. For the second part, write   
$B^4(a)$ for
the ball of capacity $a=\pi r^2$, and $Z^4$ for the symplectic   
cylinder $D^2(1)
\times \RR^2$ where $D^2(1)$ is the disc of area 1. Going beyond Gromov's non-
squeezing theorem, Sackel, Song, Varolgunes, and Zhu recently showed that for
$a>1$ the complement $B^4(a) - S$ of a subset $S$ in the ball cannot   
be embedded
symplectically into $Z^4$ if the Minkowski dimension of $S$ is $<2$. They also
found that this result is sharp provided that $a<2$, and then Brendel extended
this to $a<3$. In joint work with Emmanuel Opshtein, we find in any ball
$B^4(a)$ a finite union of planar Lagrangian discs $S$ such that $B^4(a)
\setminus S$ symplectically embeds into $Z^4$. Among the applications are:
capacity killing; non-displaceability of the Clifford torus $T(1/d,1/d)$ from
$S$ in $B^4(d)$; and the existence of very short Reeb chords from a Legendrian
knot back to itself or to $S$.


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