Let G be a countably infinite group and let Sub_G be the compact space of subgroups H ⩽ G. Then an invariant random subgroup (IRS) of G is a probability measure ν on Sub_G which is invariant under the conjugation action of G on Sub_G. In particular, if ν is ergodic, then ν is a notion of randomness on Sub_G with a 0-1 law for every group-theoretic property. In this talk, after a brief introduction to the theory of invariant random subgroups, I will discuss some of the many open questions in this relatively new area of group theory.
Simon Thomas is Distinguished Professor in the Department of Mathematics and member of the Graduate Faculty of Philosophy at Rutgers University. Professor Thomas is a Fellow of the American Mathematical Society and has given invited addresses at the International Congress of Mathematicians (Madrid 2006) and the 14th International Congress of Logic, Methodology and Philosophy of Science (Nancy, 2011). He has served on numerous editorial boards and was Keynote Speaker at the Jahrestagung der Deutschen Mathematiker-Vereinigung (Hamburg, 2015). In addition he served as Chair of the 2018 External Review Committee for the Stevens Department of Mathematics.
Date: Monday, October 25th
Time: 3:30pm (refreshments at 3:00pm)
Location: Peirce, Room 218
Attendance: This is a technical talk open to all. A campus map is available at https://tour.stevens.edu. Visitors to the campus are required to wear masks indoors.