14 citations · 77 across the 28 of their papers we have counts for
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Around Gromov's injectivity lemma and applications to post-injunctive groups
Xuan Kien Phung
Gottschalk's surjunctivity conjecture states that for all group universes and finite alphabets, every equivariant and continuous selfmap of the full shift, known as cellular automa…
Strongly sofic monoids, sofic topological entropy, and surjunctivity
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
We introduce the class of strongly sofic monoids. This class of monoids strictly contains the class of sofic groups and is a proper subclass of the class of sofic monoids. We defin…
First-order model theory and Kaplansky's stable finiteness conjecture
Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
Using algebraic geometry methods, the third author proved that the group ring of a surjunctive group with coefficients in a field is always stably finite. In other words, every gro…
On dynamical finiteness properties of algebraic group shifts
Xuan Kien Phung
Let be a group and let be an algebraic group over an algebraically closed field. We introduce algebraic group subshifts which generalize both the class of al…