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Logic Seminar - Ben Castle | Einstein Institute of Mathematics

Logic Seminar - Ben Castle

Date: 
Wed, 26/10/202211:00-12:45
Location: 
Shprintsak Building, Room 102
Restricted Trichotomy in Characteristic Zero
Abstract:  Zilber's Restricted Trichotomy Conjecture predicts that the Zilber trichotomy should hold for all structures interpreted in algebraically closed fields. In other words, if K is algebraically closed and interprets M, and M is reasonably "rich" in a precise sense (namely not 1-based), then M interprets a copy of K. I will give a brief overview of this conjecture, including previously solved cases and the common strategy most of them use. I will then describe the recent proof that the conjecture holds in full generality when K is the field of complex numbers.