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SUMMARY:Collinearity on cubic surfaces
DTSTART;VALUE=DATE-TIME:20221117T100000Z
DTEND;VALUE=DATE-TIME:20221117T110000Z
DTSTAMP;VALUE=DATE-TIME:20221128T175200Z
UID:indico-event-122@events.dm.unipi.it
DESCRIPTION:Speakers: Jan Dobrowolski (University of Manchester)\n\nWe stu
dy the ternary relation R of collinearity between points of a smooth cubic
surface X. Our aim is to understand sequences of triples (A\,B\,C) of fin
ite sets with |A|=|B|=|C| whose Cartesian products have asymptotically max
imal possible size of the intersection with the relation R (i.e. growing r
oughly as quickly as the square of the size of the sets A\,B\,C). This is
an instance of the so-called Elekes-Szabó problem. It is well-known that
such configurations can be built on planar cubic curves\, hence we can fi
nd them in an intersection of X with a plane. We prove that if X is smooth
and irreducible\, then actually any such configuration on X concentrates
on its intersection with a plane\, and if X is reducible the same holds in
most cases. This is a joint work with Martin Bays and Tingxiang Zou.\n\n
https://events.dm.unipi.it/event/122/
LOCATION:Aula Seminari (Dipartimento di Matematica)
URL:https://events.dm.unipi.it/event/122/
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