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SUMMARY:Paul Alexander Helminck (Durham U.)
DTSTART:20220520T140000Z
DTEND:20220520T150000Z
DTSTAMP:20260423T020953Z
UID:LAGARTOS/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGARTOS/43/
 ">Generic root counts and flatness in tropical geometry</a>\nby Paul Alexa
 nder Helminck (Durham U.) as part of (LAGARTOS) Latin American Real and Tr
 opical Geometry Seminar\n\n\nAbstract\nIn this talk\, we give new generic 
 root counts of square polynomial systems using methods from tropical and n
 on-archimedean geometry. The main theoretical ingredient is a generalizati
 on of a famous theorem by Bernstein\, Kushnirenko and Khovanskii\, which n
 ow says that the behavior of a single well-behaved zero-dimensional tropic
 al fiber spreads to an open dense subset. We use this theorem on modificat
 ions of the universal polynomial system to obtain generic root counts of d
 eterminantal subvarieties of the universal parameter space.\nAn important 
 role in these generalizations is played by the notion of tropical flatness
 \, which allows us to link a single tropical fiber to fibers over an open 
 dense subset. We also prove a tropical analogue of Grothendieck's generic 
 flatness theorem\, saying that a given morphism is tropically flat over a 
 dense open subset.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/43/
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