For most people the word “wild” invokes an untamed wilderness or perhaps a feral animal. In mathematics and computational complexity, the term refers to a specific, thorny phenomenon that arises in problems related to classification – such as classifying matrices, differential equations, or types of symmetry.
Such problems don’t have a straightforward solution, if they have any solution at all, so wildness is sometimes regarded as the frontier at best, or as the end of the road at worst.
The phenomenon has traditionally been confined to geometry and representation theory, but it appears in other areas, too, including physics and computer science. A better understanding of wildness in its many guises might help push these fields forward.
That’s why SFI Omidyar Fellow Josh Grochow, SFI Professor Cristopher Moore, Vlatko Vedral (Oxford and the National University of Singapore), and Jerzy Weyman (University of Connecticut) are hosting a workshop at SFI this week, Wildness in Computer Science, Physics, and Mathematics. They’re inviting researchers to share wild problems from their own fields, hoping an interdisciplinary conversation will spur new ideas and avenues of investigation.
Quantum entanglement offers an example: Entangled particles, connected at the quantum level, cannot be described independently, so classifying the patterns in which particles can be entangled is a wild problem. Understanding those patterns might inspire advances in quantum computing and encryption.
Grochow organized the workshop after wildness showed up repeatedly in his research at the intersection of computer science and mathematics. “All these problems I was thinking about, in geometric complexity theory and in a few problems in computer science, had this one hard nugget of wildness,” he says. “The fact that we don’t understand wildness is a barrier standing in the way of progress in all these areas.”
More about the workshop here.