Integrated Calendar

Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this talk, I will describe the model from a different point of view, emphasizing the equilibrium and nonequilibrium aspects of its dynamics from a statistical physics perspective.I will discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise.

Renormalized perturbation theory for QFTs typically produces divergent series, because the series coefficients grow factorially at high order. It has been a historical challenge to understand the asymptotic nature of perturbative series, and it has been unclear in what precise sense semiclassical expansions capture the physics of even weakly-coupled QFTs. I will discuss a recent conjecture that the semiclassical expansion of path integrals for asymptotically free QFTs yields well-defined answers once the implications of resurgence theory are taken into account. Resurgence theory relates expansions around different saddle points of a path integral to each other, and has the striking practical implication that the high-order divergences of perturbative series encode precise information about the non-perturbative physics of a QFT. These ideas will be discussed in the context of several QCD-like theories, where systematic semiclassical control over the dynamics is achieved using adiabatic compactifications on a circle. Fitting a conjecture by ’t Hooft, understanding the origin of the notorious renormalon divergences of perturbation theory of asymptotically-free QFTs allows us to see the microscopic origin of the mass gap of these QFTs in the semiclassical domain.

Neural responses in many cortical regions encode information relevant to behavior—information that necessarily changes as that behavior changes with learning. While such responses are reasonably theorized to be related to behavior causation, the true nature of that relationship cannot be clarified by simple learning studies, which show primarily that responses change with experience. Neural activity that truly tracks behavior (as opposed to simply changing with experience) will not only change with learning but also change back when that learning is extinguished. By recording the activity of ensembles of gustatory cortical (GC) single neurons from rats that were put in a conditioning-extinction protocol I could test which element - single neurons or population dynamics followed the behavior pattern (and I'll leave the answer to the talk). Additional results will implicate the basolateral amygdala (BLA) as the driver of the changes observed in the cortex.

Representation theory of inner forms of GL(n) over a local non-archimedean field - old and new results - PART ONE