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UID:8733@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20251017T160000
DTEND;TZID=Europe/Paris:20251017T170000
DTSTAMP:20251015T082553Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-249/
SUMMARY:Jing Tao (University of Oklahoma): From 2×2 matrices to infinite-t
 ype surfaces
DESCRIPTION:Jing Tao: To every topological surface one can associate a grou
 p called the mapping class group (sometimes called the modular group)\, co
 nsisting of homeomorphisms of the surface up to isotopy. In the case of th
 e torus\, this group is SL(2\,Z)\, whose elements fall into three dynamica
 l types detected by the trace: elliptic (|tr A| &lt\; 2)\, parabolic (|tr 
 A|=2)\, and hyperbolic (|tr A| &gt\; 2).\n\nRemarkably\, Thurston showed t
 hat an analogous classification exists for maps of finite-type surfaces: a
 fter cutting along a canonical multicurve\, each component carries a map 
 that is either periodic or pseudo-Anosov\, and the map is reducible preci
 sely when the reducing multicurve is nonempty. This mirrors the role of Jo
 rdan blocks in linear algebra.\n\nIn this talk\, I will first present thes
 e classical examples—from the linear case of 2×2 matrices to the nonlin
 ear case of finite-type surfaces—before discussing joint work with Mlade
 n Bestvina and Federica Fanoni\, where we investigate how this classificat
 ion extends (or fails) for more general surfaces.
CATEGORIES:Colloquium
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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DTSTART:20250330T030000
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