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SUMMARY:Egor Shelukhin (University of Montreal)
DTSTART:20220501T110000Z
DTEND:20220501T115000Z
DTSTAMP:20260423T004822Z
UID:GDS/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/56/">The
  transcendental Bézout problem revisited</a>\nby Egor Shelukhin (Universi
 ty of Montreal) as part of Geometry and Dynamics seminar\n\n\nAbstract\nB
 ézout's classical theorem states that n complex polynomials of degree k o
 n C^n \nhave at most k^n isolated common zeros. The logarithm of the maxim
 al function \nof an entire function on C\, instead of the degree\, control
 s the number of zeros \nin a ball of radius r. The transcendental Bézout 
 problem seeks to extend this \nestimate to entire self-mappings f of C^n v
 ia the n-th power of the logarithm \nof the maximal function. A celebrated
  counterexample of Cornalba-Shiffman shows \nthat this is dramatically fal
 se for n>1. However\, it is true on average\, under \nlower bounds on the 
 Jacobian\, or in a weaker form for small constant perturbations \nof f. We
  explain how topological considerations of persistent homology and \nMorse
  theory shed new light on this question proving the expected bound for a \
 nrobust count of zeros. This is part of a larger joint project with Buhovs
 ky\, \nPayette\, Polterovich\, Polterovich\, and Stojisavljevic.\n
LOCATION:https://researchseminars.org/talk/GDS/56/
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