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Talk "Degree of commutativity in infinite groups" (Y. Antolín, Vanderbilt University)

In a finitely generated group, we count the numbers of pairs of elements in a ball of radius n which commute, and register the proportion of these among all possible pairs. Taking the limit of these numbers provides us the degree of commutativity of the group. We conjecture that the degree of commutativity is positive if and only if the group is virtually abelian and I will present some results in this direction.