Math Union Colloquium

The idea of generative effects is best understood as the idea that "the whole is greater than the sum of its parts." This is primarily developed in Adam's thesis. Entanglement seems to be an obvious example of this, at least intuitively. By first defining the basic idea of entangled states as simply those that are not product states and then developing the intuition behind generative effects, one builds enough baseline to introduce and explain, at least at a conceptual level, the ideas of entanglement cohomology as developed by Mainiero and explained by Ferko, Iyer, Mossayebi, and Sanfey. Although neither explicitly links entanglement to generative effects, the parallels are clear and the presentation will go through this. This topic is interesting because by being able to recognize entanglement at a generative effect, the methods developed in Adam can be used to further understand entanglement. Although the more categorical approach will probably not be explored in too much depth for brevity and simplicity's sake, the possible impact of the non-abelian case will be explored with mentions of why generative effects allow us to use tools such as von-neumann algebras that tie together things such as haag duality and entanglement cohomology. They will likely not be explored in too much depth, but they will at least be explained conceptually so that attendees can understand the current interest in the field. I am one of the co-authors of the ferko et al paper and am currently working with ferko on a follow up to the paper using generative effects as described here.