Abstract: 

Suppose that G is a group and I is an infinite index set. Then one can easily construct automorphisms from $\prod_{i\in I}G$ to itself by permuting indices and choosing an indexed family of automorphism from G to itself. However, the natural question then arrises: when does every automorphism of $\prod_{i\in I}G$ essentially decompose into the form described above? In general, we are interested in when classes of groups have such property with respect to all (reduced) products. Using model theoretic methods, one can show that certain natural families of groups have such property and that a total characterization is quite complicated. This is joint work with Ilijas Farah and Pierre Touchard. 

Bio-Sketch: 

Kyle Gannon received his PhD from the University of Notre Dame in 2020. He served as a Hedrick Assistant Professor at UCLA from 2020 to 2023 and became an assistant professor at BICMR in 2023. His research interests lie in mathematical logic, specifically model theory and its connections to topological dynamics, measure theory, and probability theory.