# When does injectivity imply surjectivity?

Monday, November 23, 2015 -

4:30pm to 5:30pm

Any injective map from a finite set to itself is surjective. Ax's Theorem extends this to algebraic varieties and regular maps. Gromov invented sofic groups as a way to extend to this result to cellular automata and other settings. We'll re-prove his results via sofic entropy theory. Similarly we use sofic mean dimension to prove non-embeddability results in topological dynamics and $l^p$ dimension to prove non-embeddability results in representation theory.

Speaker:

Lewis Bowen

University of Texas, Austin & Princeton University

Event Location:

Fine Hall 314