David Lehavi

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TITLE:  
Mikhalkin's Classification of M-Curves in Maximal Position with Respect
to Three Lines

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ABSTRACT: 

One of the classical problems in real algebraic geometry is to describe
all the possible topological configurations of real plane curves;
sadly, little advancement has been made towards this goal. One of the
most beautiful results achieved in attempting this problem is
Mikhalkin's classification of smooth real plane curves with the maximal
possible number of components, which have a certain intersection
pattern with 3 lines called ``maximal position''. We will review the
background, and the main ideas in Mikhalkin's proof.

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Manfred Einsiedler

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TITLE: Amoebas and algebraic dynamics


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ABSTRACT:  I will describe how amoebas help to describe the dynamical properties of
$\mathbb Z^d$-actions by automorphisms of compact abelian groups, and give
concrete examples for that connection. One property, that is best
characterized by the amoeba, is expansiveness of subactions.  A $\mathbb
Z^k$-subaction is expansive if there exists an $\epsilon>0$ such that there
are not two points $x\neq y$ that stay $\epsilon$-close forever (for the
$\mathbb Z^k$-action).