Dr. Justin Alexander Bloom

For his PhD in Mathematics at the University of Washington in Seattle, Justin Bloom researched tensor triangular geometry (tt-geometry), a rapidly developing field initiated in 2005 that connects algebra, topology, and geometry. TT geometry analyzes the global structure of tensor triangulated categories using geometric methods, assigning to each an invariant known as the spectrum. Understanding this spectrum yields deep structural insight into the category. Within this framework, Dr. Bloom studied the relationship between the representation type of a finite-dimensional algebra and its tt-geometry.

At Bar-Ilan’s Department of Mathematics, Dr. Bloom is a postdoctoral researcher working on K-rigidity, a concept he developed that arises from tt-geometry, and ultimately, from homotopy theory—a branch of mathematics used to study geometric objects up to deformation. TT geometry is used, in part, towards identifying and classifying mathematical theory aim to identify and classify mathematical “atoms,” the smallest building blocks from which more complex structures are formed. K-rigidity operates in the context of representations, objects that can be combined via tensor products. Dr. Bloom investigates these in relation to the tensor multiplication of atoms, seeking deep connections between modular representation theory and quantum algebra.

Dr. Bloom also served for three years as a judge for the University of Washington Math Hour Olympiad, a competition for students in grades 6 through 10. He founded and led the university’s graduate student representation theory seminar (StARTS), a large, well-organized, and widely attended series.