Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 30, 2017.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2017          October 2017          November 2017
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1  2    1  2  3  4  5  6  7             1  2  3  4
3  4  5  6  7  8  9    8  9 10 11 12 13 14    5  6  7  8  9 10 11
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24 25 26 27 28 29 30   29 30 31               26 27 28 29 30



Monday, October 30, 2017

4:00 pm in 245 Altgeld Hall,Monday, October 30, 2017

#### Symplectic non-squeezing and Beltrami equation

###### Alexander Tumanov   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Gromov's Non-Squeezing Theorem is a remarkable result in symplectic geometry. It says that the ball $B^{2n}(r)$ of radius $r$ in ${\mathbb R}^{2n}$ can be symplectically embedded in the "cylinder" $B^2(R)\times {\mathbb R}^{2n-2}$ of radius $R$ only if $r\le R$. The proof uses so called J-complex (pseudoholomorphic) curves. We will describe a construction of J-complex disks based on the classical scheme for solving the Beltrami equation in complex analysis. We will discuss related results and open problems.

5:00 pm in 445 Altgeld Hall,Monday, October 30, 2017