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TZID:Europe/Paris
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UID:8563@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250314T160000
DTEND;TZID=Europe/Paris:20250314T170000
DTSTAMP:20250310T095301Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-206/
SUMMARY:Ivan Cheltsov (The University of Edinburgh): Which cubics admit rat
 ional parametrization?
DESCRIPTION:Ivan Cheltsov: Every day we deal with geometric objects defined
  by algebraic equations (circles\, parabolas\, hyperbolas\, splines\, sphe
 res\, hyperboloids\, etc). In many applications\, we have to parametrize t
 hem using the simplest possible functions - rational functions in several 
 variables. To find such parametrization maybe tricky. This is a very class
 ical problem - rational parametrization of a circle has been found by Pyth
 agoras when he found Pythagoras triples\, and the same approach gives expl
 icit rational parametrization of a sphere or any geometric object given by
  one quadratic equation. In more complicated cases\, the problem can be ve
 ry difficult. Moreover\, quite often rational parametrization does not exi
 st - there are many algebraic objects that do not admit rational parametri
 zation. For example\, majority of plane cubic curves cannot be parametrize
 d by rational functions (the proof for Fermat cubic curves follows from Eu
 ler's proof of Fermat's Last Theorem for exponent 3). In my talk\, I will 
 focus on the existence of a rational parametrization of cubics - geometric
  objects defined by one equation of degree 3 (cubic curves\, cubic surface
 s\, cubic 3-folds\, etc).
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:20241027T020000
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