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UID:news1938@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20251116T165201
DTSTART;TZID=Europe/Zurich:20251120T141500
SUMMARY:Number Theory Seminar: Marc Abboud (University of Neuchâtel)
DESCRIPTION:Title: On the rigidity of periodic points for automorphisms of 
 affine surfaces \\r\\nAbstract: I will discuss the following results. Let
  S be a complex affine surface and f\,g be two automorphisms of positive e
 ntropy. If f and g have a Zariski dense set of periodic points in common t
 hen they have the same set of periodic points. The proof uses the dynamics
  at infinity of such automorphisms and the construction of their canonical
  Green functions and equilibrium measures both for archimedean places and 
 non-archimedean ones. One of the main ingredients is the theorem of arithm
 etic equidistribution on adelic line bundles over quasiprojective varietie
 s from Yuan and Zhang. I will also discuss examples of affine surfaces whe
 re I manage to show a stronger rigidity: having the same periodic points i
 mply that the automorphisms share a common iterate. The examples are the a
 ffine plane and Markov surfaces which are related to the character variety
  of the punctured torus. 
X-ALT-DESC:<h2>Title: On the rigidity of periodic points for automorphisms 
 of affine surfaces<br />&nbsp\;</h2>\n<p>Abstract: I will discuss the foll
 owing results. Let S be a complex affine surface and f\,g be two automorph
 isms of positive entropy. If f and g have a Zariski dense set of periodic 
 points in common then they have the same set of periodic points. The proof
  uses the dynamics at infinity of such automorphisms and the construction 
 of their canonical Green functions and equilibrium measures both for archi
 medean places and non-archimedean ones. One of the main ingredients is the
  theorem of arithmetic equidistribution on adelic line bundles over quasip
 rojective varieties from Yuan and Zhang. I will also discuss examples of a
 ffine surfaces where I manage to show a stronger rigidity: having the same
  periodic points imply that the automorphisms share a common iterate. The 
 examples are the affine plane and Markov surfaces which are related to the
  character variety of the punctured torus.&nbsp\;</p>
DTEND;TZID=Europe/Zurich:20251120T151500
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