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DTSTART;TZID=America/New_York:20241114T100000
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DTSTAMP:20260411T063405
CREATED:20241107T191256Z
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SUMMARY:(Un)likely intersections
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Tom Scanlon\, UC Berkeley \nTitle: (Un)likely intersections\n\nAbstract: The Zilber-Pink conjectures predicts that for an ambient special variety  (such as an abelian variety or a Shimura variety)\, if   is an irreducible algebraic subvariety which is not contained a proper special subvariety of  (e.g. a proper algebraic subgroup in the abelian variety case or a variety of Hodge type in the case of Shimura varieties)\, then the union of the unlikely intersections  as  ranges over the special subvarieties of  with  is not Zariski dense in .  While various instances of this conjecture have been proven\, it remains open in most cases of interest.  In this lecture\, I will describe some of my work with Jonathan Pila in which we prove an effective function field version of this conjecture along with a counterpart to the Zilber-Pink conjecture proven with Sebastian Eterović:  after accounting for some geometric obstructions\, the likely intersections\, i.e. the union of the intersections  with  special and \,  are dense in the Euclidean topology in .   Our techniques for both results come from o-minimal complex analysis and differential algebra.\n\n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_111424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
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