QLunch: Marta Pavelka

Speaker: Marta Pavelka

Title: How many triangulations of the 3-sphere are there?

Abstract: The question “How many triangulations of the 3-sphere with a given number of tetrahedra are there?” has been studied for several decades. It was posed by Bergfinnur Durhuus and Thordur Jonsson in 1995 in connection with models of quantum gravity and their convergence, and later highlighted by Mikhael Gromov as a fundamental problem in topology. The central open question is whether the number of such triangulations grows exponentially in the number of tetrahedra or super-exponentially. In this talk, we survey current progress and discuss approaches used to investigate this problem. We also present classes of 3-spheres, and more generally d-spheres, known to exhibit exponential growth, including the family of 2-locally constructible spheres.