Julia Knight (Notre Dame)

April 28, 2020 @ 2:00 am – 3:00 am

Title: Limiting Density and Free Structures
by Julia Knight (Notre Dame) as part of Computability theory and applications

Gromov had asked what a random group looks like – in a limiting density sense. I conjectured that the elementary frst order theory of the random group on n >= 2 generators, and with a single relator matches
that of the non-Abelian free groups. Coulon, Ho, and Logan have proved that the theories match on universal sentences. We may ask Gromovs question for other varieties. Franklin and I looked for varieties for which
calculating the limiting densities is easier. We have examples for which the elementary frst order theory of the random structure matches that of the free structure, and other examples for which the theories differ.
(joint work with Johanna Franklin)