Talks

An ongoing program of work in statistical physics and quantum dynamics is concerned with understanding the character of systems which follow an unconventional approach towards thermal equilibrium. In this talk, I will add to this story by introducing examples of simple 1D systems---both classical and quantum---which thermalize in very unusual ways. These examples have dynamics which is strictly local and translation-invariant, but in spite of this, they: a) can have very long thermalization times, with expectation values of local operators relaxing only over times exponential in the system size; and b) can thermalize only when they are placed in extremely large baths, with the required bath size growing exponentially (or even faster) in system size. Proofs of these results will be given using techniques from geometric group theory, a beautiful area of mathematics concerned with the complexity and geometry of infinite discrete groups. This talk will be based on a paper in preparation with Shankar Balasubramanian, Sarang Golaparakrishnan, and Alexey Khudorozhkov.

---

Zoom link: https://pitp.zoom.us/j/99430001465?pwd=NENlS1M5UGc5UWM1ekQvRWFrZGYyUT09

In 2013, Cachazo, He and Yuan discovered a remarkable framework for scattering amplitudes in Quantum Field Theory (QFT) which mixes the real, complex and tropical geometry associated to the moduli space of n points on the projective line, $M_{0,n}$. By duality, this moduli space has a twin moduli space of $n$ generic points in $P^{n-3}$, leading to dual realization of scattering amplitudes, using a generalization of the CHY formalism introduced in 2019 by Cachazo, Early, Guevara and Mizera (CEGM). Any duality begs for an explanation! And, what physical phenomena lie between the twin moduli spaces? CEGM developed a framework to answer the question for moduli spaces of $n$ points in any $P^{k-1}$, leading to the discovery of rich, recursive structures and novel behaviors which portend an extension of QFT. We discuss recent joint works with Cachazo and Zhang, and with Geiger, Panizzut, Sturmfels, Yun, in which we dig deeper into some of the many mysteries which arise.

---

Zoom link: https://pitp.zoom.us/j/95706337178?pwd=cnBka3lFWDBoRlFZV1VadXdGZ1JnZz09