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SUMMARY:Myrto Mavraki (University of Toronto)
DTSTART:20241203T213000Z
DTEND:20241203T223000Z
DTSTAMP:20260419T151704Z
UID:BC-MIT/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/16/">
 Uniformity in unlikely intersections and the dynamical André--Oort conjec
 ture</a>\nby Myrto Mavraki (University of Toronto) as part of BC-MIT numbe
 r theory seminar\n\nLecture held in Maloney 560 at Boston College.\n\nAbst
 ract\nA rational map is postcritically finite (PCF) if its critical orbits
  are finite. Postcritically finite maps play an important role in dynamics
 . Further\, it was suggested by Silverman that they play a role analogous 
 to CM elliptic elliptic curves. Inspired in part by the Pink-Zilber conjec
 tures in unlikely intersections\, Baker and DeMarco formulated a conjectur
 e aiming to describe the subvarieties of $M_d$ that contain a Zariski dens
 e set of PCF points. Their conjecture\, now known as dynamical André--Oor
 t conjecture (or DAO)\, was recently resolved in the case of curves by Ji-
 -Xie\, but remains open in higher dimensions. In this talk we will describ
 e recent work with DeMarco and Ye\, providing uniform bounds on the config
 urations of PCF points in families of subvarieties in $M_d$. We also provi
 de a gap principle in the spirit of Dimitrov--Gao--Habegger's\, Kühne's\,
  and Gao--Ge--Kühne's work on the uniform Mordell--Lang conjecture.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/16/
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