Binghamton University Graduate Conference in Algebra and Topology
Abstract: Given a finitely generated group, G, what properties of G can we detect in finite group approximations of G? I will survey progress on different approaches to this broad question while touching the theories of subgroup growth, intersection growth, quantifying residual finiteness, commensurability graphs, and random walks on groups.
Abstract: We all have our doubts off and on if life is really so wonderful. But that is not what I want to address here. Watching the Jimmy Stewart movie with this title, there was one scene which captured my imagination: the Guardian Angel shows George Bailey how the world would have been without him.
Personally, I never had much need to know how the world would have looked without me. However, all other things equal, how would life have been if I had lived in a different time and place, would be something of interest to me! This is the stuff of movies and fairy tales. But at least it is possible to play this as an intelectual game.
I was born and raised in Germany before WWII. After getting my Ph.D. in 1962, I married a fellow mathematician and we immigrated to the US one year later, where we have been teaching at a university ever since. What would life have been if I stayed in Germany, did not get married, were born fifty or hundred years earlier, or were born in another country? Looking at actual and potential role models over the centuries helped me answer some of these questions. In essence, it got me back to the roots of what shaped my life.
Abstract: This talk will survey results about finitely generated groups acting on one-manifolds and their regularity. The focus will be on the differences in algebraic structure between groups of homeomorphisms which are merely continuous, which are once differentiable, and which have higher degrees of regularity. Examples will be drawn from various branches of group theory and topology and will include lattices in semi-simple Lie groups, nilpotent groups, right-angled Artin groups, and mapping class groups of surfaces.