Lynette Agcaoili’s MA presentation is scheduled for April 30, 2024. Everyone is welcome and graduate students are especially encouraged to attend.
Tuesday, April 30, 2024, 3:00 – 5:00 pm, Keller 404
Title: An Introduction to Inverse Limits
Abstract: The goal of this presentation is to give an introduction to inverse limits in a way that is (hopefully) accessible to advanced undergraduates/incoming graduate students. We will, of course, define what inverse limits are, and then construct injective resolutions for both abelian groups and inverse systems. We will then talk about flasque resolutions and some properties of flasque to construct a short exact sequence of inverse systems. Finally we will give explicit constructions of the inverse limit of a system and its first derived functor (i.e. varprojlim_{leftarrow}^(1) A_i), and show that if our indexing set is the natural numbers, then the second derived functor and higher are all 0 (i.e. varprojlim_{leftarrow}^(n) A_i = 0 for any n>1).
Calendar
Apr
26
Fri
Apr 26 @ 3:30 pm – 4:30 pm
Apr
30
Tue
Apr 30 @ 3:00 pm – 4:00 pm
May
1
Wed
May 1 all-day
May
17
Fri
May 17 @ 3:30 pm – 4:30 pm
Speaker: Rostislav Grigorchuk, Distinguished prof. of Mathematics at Texas A&M.
Title: Fractal, liftable and scale groups.
Abstract: Scale groups are closed subgroups of the group of isometries of a regular tree that fix an end of the tree and are vertex-transitive. They play an important role in the study of locally compact totally disconnected groups as was recently observed by P-E.Caprace and G.Willis. In the past they were studied in the context of abstract harmonic analysis, random walks and amenability. It is a miracle that they are closely related to fractal groups, a special subclass of self-similar groups.
In my talk I will discuss two ways of building scale groups. One is based on the use of scale-invariant groups studied by V.Nekrashevych and G.Pete, and a second is based on the use of liftable fractal groups. The examples based on both approaches will be demonstrated using such groups as Lamplighter, Basilica, Hanoi Tower Group, Group of Intermediate Growth (between polynomial and exponential) constructed by the speaker in 1980, and GGS-groups. Additionally, the group of isometries of the ring of integer p-adics and group of dilations of the field of p-adics will be mentioned in the relation with the discussed topics.
Jul
14
Sun
Jul 14 – Jul 27 all-day
Jul
20
Sat
Jul 20 – Jul 24 all-day