Many identities between Feynman integrals can be understood graph theoretically. We can also ask about other graph invariants with these same symmetries and ask what they look like mathematically and what they tell us back about the Feynman integrals. I will talk concretely about some such invariants and these questions.
The Koopman-von Neumann (KvN) formulation brings Hilbert space to classical mechanics, and has applications from dynamical systems to quantum-classical interaction. The formulation, however, has not been exploited to its full extent. We show that the existence of a family of extensions to the KvN equation allows for the derivation of the canonical ensemble distribution through simple...
Ultra-relativistic heavy-ions collisions performed at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC) produce a deconfined state of quarks and gluons, called the quark-gluon plasma (QGP). One of the primary goals of these collisions is to infer the properties of the QGP through the modifications it imparts on the evolution high-energy quarks and gluons (also...
As the 2024 Nobel Prizes highlight, neural networks have emerged both as an important physical paradigm, and for representing complex phenomena beyond physics. The fidelity of neural network representations of complex phenomena relies on a fundamental tension between universality and generalizability. In this talk, we will argue that, for neural network training, optimization is the enemy of...
