Talks

Neutrinos have been assumed to have no mass. If neutrinos have mass, neutrino oscillations should occur. Neutrino oscillations were discovered by studying atmospheric and solar neutrinos. I will discuss the discovery of neutrino oscillations and the status of the oscillation studies.

Large neural networks are often studied analytically through scaling limits: regimes in which some structural network parameters (e.g. depth, width, number of training datapoints, and so on) tend to infinity. Such limits are challenging to identify and study in part because the limits as these structural parameters diverge typically do not commute. I will present some recent and ongoing work with Alexander Zlokapa (MIT), in which we provide the first solvable models of learning – in this case by Bayesian inference – with neural networks where the depth, width, and number of datapoints can all be large.

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A formulation of the 2-dimensional Ising model on a triangulated Riemann sphere is proposed that converges to the exact conformal field theory (CFT) in the continuum limit. The solution is based on reconciling Regge's simplicial geometry for the Einstein Hilbert action with an Affine map to quantum correlators on the tangent plane. Numerical tests of the 2d Ising sphere and radial quantized phi4 theory on $R x S^2$ are presented.  Extending the method to more general fields theories on curved manifolds is discussed. 

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I will discuss the derivation of the Emergent Second Law recently identified in Freitas and Esposito, Nat. Commun. 13, 5084 (2022). For stochastic systems with a well defined macroscopic limit, this result provides a link between the deterministic dynamics that emerges in such a limit, and the fluctuations that are observed at steady state. I will also discuss ongoing work about the generalization of this result to evolving non-equilibrium states.