Talks

One big question in the physics of large-scale structures is how we can trace back the evolution of cosmic structures and reconstruct the initial density field. The universe we observe today is dotted with galaxy clusters separated by vast voids, in sharp contrast to its initial state, which was nearly uniform with only minor density fluctuations. The evolution from this early uniformity to today's complex structure of galaxies is a profound transformation, with many intermediate processes still unexplained. This talk focuses on this transformation, aiming to reconstruct both the initial density and the displacement fields of galaxies observed in spectroscopic surveys. I will discuss new reconstruction algorithms that depend weakly, if at all, on a cosmological model. These algorithms have paved the way for new astrophysical achievements in several directions, such as: Baryon Acoustic Oscillations (BAO) analysis, morphological analysis of proto-halos, and kinematic Sunyaev-Zel'dovich (kSZ) effect.

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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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