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DTSTAMP:20250703T225322Z
DESCRIPTION:Title: Integrable systems from a Newton polygon.\n\nAbstract: L
 et $P(x\,y)in mathbb C[x\,y]$ a bivariate polynomial\, written $P(x\,y)=su
 m_{(i\,j)in N}P_{i\,j} x^i y^j$. The polytope $Nsubset mathbb Z imes mathb
 b Z$ is called the Newton's polytope and its convex envelope is the Newton
 's polygon. The locus of solutions $P(x\,y)=0$ in $mathbb C imes mathbb C$
  is a plane curve (an immersed Riemann surface). Its geometry can be produ
 ced from the combinatorics of the Newton's polygon. This allows to constru
 ct a Baker-Akhiezer function and a Lax pair associated to $P(x\,y)$\, in o
 ther words an integrable system. In fact there are several integrable syst
 ems that can be associated to P. The easiest is the isospectral system\, f
 ollowing the Krichever's reconstruction method\, and the others can be see
 n as 'quantum' deformations. In particular we can get an isomonodromic sys
 tem and other deformations. We shall illustrate on the elliptic curve $P(x
 \,y)=y^2-x^3+g_2 x+x_3$.\n\n \n\nWeb - Please fill in this form: https://f
 orms.gle/S1NcNQ8BxkzfAXcj9\n
DTSTART:20211207T203000Z
DTEND:20211207T213000Z
SUMMARY:Bertrand Eynard\, Institut de Physique Théorique\, CEA (Commissaria
 t à l'Energie Atomique et aux Energies Alternative)
URL:/mathstat/channels/event/bertrand-eynard-institut-
 de-physique-theorique-cea-commissariat-lenergie-atomique-et-aux-energies-3
 35385
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