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SUMMARY:Ben Castle (University of Illinois Urbana-Champaign)
DTSTART:20260827T180000Z
DTEND:20260827T190000Z
DTSTAMP:20260914T071132Z
UID:OLS/218
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/218/">Za
 riski Topological Reconstruction Theorems via Model Theory</a>\nby Ben Cas
 tle (University of Illinois Urbana-Champaign) as part of Online logic semi
 nar\n\n\nAbstract\nA recent and quite surprising book of Kollár-Lieblich-
 Olsson-Sawin (KLOS) showed that in many cases\, the full structure of an a
 lgebraic variety is determined by its underlying Zariski topological space
 . More precisely\, this means there is a certain classification of all hom
 eomorphisms between varieties in the relevant cases. The strongest version
  of the original KLOS theorem only works for certain varieties over uncoun
 table fields of characteristic zero. Meanwhile\, in a recent work with Ron
 an O’Gorman — working over uncountable algebraically closed fields —
  we prove the natural generalization to arbitrary varieties in arbitrary c
 haracteristic. Interestingly\, the key idea in generalizing the proof come
 s from model theory. In this talk\, I will try to explain what exactly the
  KLOS theorem says and why it is interesting\; then I will give a sketch o
 f why the original proof failed to generalize and why model theory ends up
  being relevant.\n
LOCATION:https://researchseminars.org/talk/OLS/218/
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