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SUMMARY:Ali Ulaş Özgür Kişisel (METU)
DTSTART:20231124T124000Z
DTEND:20231124T134000Z
DTSTAMP:20260423T035752Z
UID:OBAGS/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/36/">R
 andom Algebraic Geometry and Random Amoebas</a>\nby Ali Ulaş Özgür Kiş
 isel (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr
 act\nRandom algebraic geometry studies variable properties of typical alge
 braic varieties as opposed to invariant properties or extremal properties.
  For instance\, a complex algebraic projective plane curve is always topol
 ogically connected\, which is an invariant property\;  a real algebraic pr
 ojective plane curve of degree $d$ has\, by a classical theorem of Harnack
 \, at most $\\displaystyle{g+1=(d-1)(d-2)/2+1}$ connected components where
  $g$ denotes genus\, which is an extremal property\; whereas a random real
  algebraic projective degree $d$ plane curve in a suitable precise sense (
 to be explained in the talk) has an expected number of connected component
 s of order $d$. In this talk\, I will first present the setup and some of 
 the main known results of the field of random algebraic geometry. I will t
 hen proceed to discuss some of our results on the expected properties of a
 moebas of random complex algebraic varieties\, based on a joint work with 
 Turgay Bayraktar\, and another joint work with Jean-Yves Welschinger.\n
LOCATION:https://researchseminars.org/talk/OBAGS/36/
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