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 recieved his PhD at the Univeristy of Notre Dame in 2020. He was a Hedrick Assistant Proessor at UCLA from 2020-2023. He became an assistant professor at BICMR in 2023. His interest are in mathematical logic, more specifically model theory and its connenctions to topological dynamics, measure theory, and probability theory.