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The code space of a quantum error-correcting code can often be identified with the degenerate ground-space within a gapped phase of quantum matter. We argue that the stability of such a phase is directly related to a set of coherent error processes against which this quantum error-correcting code (QECC) is robust: such a quantum code can recover from adiabatic noise channels, corresponding to random adiabatic drift of code states through the phase, with asymptotically perfect fidelity in the thermodynamic limit, as long as this adiabatic evolution keeps states sufficiently "close" to the initial ground-space. We further argue that when specific decoders -- such as minimum-weight perfect matching -- are applied to recover this information, an error-correcting threshold is generically encountered within the gapped phase. In cases where the adiabatic evolution is known, we explicitly show examples in which quantum information can be recovered by using stabilizer measurements and Pauli feedback, even up to a phase boundary, though the resulting decoding transitions are in different universality classes from the optimal decoding transitions in the presence of incoherent Pauli noise. This provides examples where non-local, coherent noise effectively decoheres in the presence of syndrome measurements in a stabilizer QECC.

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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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