Groups and dynamics seminar

Time: Thursday, June 26, 10:00
ZOOM:







Join URL: https://huji.zoom.us/j/84347250567?pwd=iFTTpSzITDQWirF2maX9ObVSmP3Ng5.1




Meeting ID

843 4725 0567
Passcode347740
Speaker: Sobhi Massalha (HUJI)


 Title: Sentence over Random Groups
Abstract:


Around 2013, a natural conjecture by Julia Knight anticipated that given a first order sentence, its truth value over a random group in the few relators model, is equivalent to its truth value over non-abelian free groups.
Our work extends the framework of this conjecture to random groups in the Gromov Density Model, at optimal density d<1/2. 
We prove the conjecture for sentences that belong to the Boolean algebra of universal sentences, as well as for sentences of minimal rank with arbitrary number of quantifiers, for random groups of density d<1/2.
In this talk, we will present our results and, as time permits, outline the key strategies and ideas involved in the proofs.
Note: Sobhi's lecture is part of the requirements to complete his thesis. It will largely overlap with the colloquium he gave last year.