Quantum non-Gaussianity, i.e., the impossibility of a state being a mixture of Gaussian states, is a key resource in bosonic systems, especially in the context of continuous-variable quantum computation. Here we present a novel characterization of quantum non-Gaussianity in terms of the zeros of the Schrödinger wavefunction. Under a mild energy assumption, the wavefunction of a single mode admits a natural extension to a holomorphic function over the complex plane. This allows us to prove a Hudson-like theorem: a pure state is Gaussian if and only if its complex extension has no zeros, thereby making the presence of such zeros a faithful signature of non-Gaussianity. Exploiting the Gaussian dynamics of these complex zeros, we show that suitable phase shifts typically bring them to the real axis, where they become observable in some quadrature probability distribution. We then construct a certification protocol based on homodyne detection — a common and accessible measurement set-up — that allows us to witness quantum non-Gaussianity using data from only a single quadrature. Our work drastically simplifies the setup required to detect quantum non-Gaussianity in bosonic quantum states.

The one-dimensional Kardar-Parisi-Zhang (KPZ) universality class is a broad collection of models including one-dimensional random interface growth, directed polymers and particle systems. At its center lies the KPZ fixed point, a scaling invariant Markov process which governs the asymptotic fluctuations of all models in the class, and which contains all the rich fluctuation behavior seen in the class.

In these lectures, I will explain how one can derive explicit formulas for the transition probabilities of the KPZ fixed point, and how they reveal connections with random matrix theory and with certain classical integrable differential equations. As a starting point for the derivation, we will use the polynuclear growth model (PNG), a model for crystal growth in one dimension that is intimately connected to the classical longest increasing subsequence problem for a uniformly chosen random permutation. The solution will be obtained through a mix of probabilistic and integrable methods.

The lectures will begin with a general overview of the KPZ universality class and its conjectural scaling limits, and I will aim to keep prerequisite knowledge to a minimum.

The one-dimensional Kardar-Parisi-Zhang (KPZ) universality class is a broad collection of models including one-dimensional random interface growth, directed polymers and particle systems. At its center lies the KPZ fixed point, a scaling invariant Markov process which governs the asymptotic fluctuations of all models in the class, and which contains all the rich fluctuation behavior seen in the class.

In these lectures, I will explain how one can derive explicit formulas for the transition probabilities of the KPZ fixed point, and how they reveal connections with random matrix theory and with certain classical integrable differential equations. As a starting point for the derivation, we will use the polynuclear growth model (PNG), a model for crystal growth in one dimension that is intimately connected to the classical longest increasing subsequence problem for a uniformly chosen random permutation. The solution will be obtained through a mix of probabilistic and integrable methods.

The lectures will begin with a general overview of the KPZ universality class and its conjectural scaling limits, and I will aim to keep prerequisite knowledge to a minimum.

The one-dimensional Kardar-Parisi-Zhang (KPZ) universality class is a broad collection of models including one-dimensional random interface growth, directed polymers and particle systems. At its center lies the KPZ fixed point, a scaling invariant Markov process which governs the asymptotic fluctuations of all models in the class, and which contains all the rich fluctuation behavior seen in the class.

In these lectures, I will explain how one can derive explicit formulas for the transition probabilities of the KPZ fixed point, and how they reveal connections with random matrix theory and with certain classical integrable differential equations. As a starting point for the derivation, we will use the polynuclear growth model (PNG), a model for crystal growth in one dimension that is intimately connected to the classical longest increasing subsequence problem for a uniformly chosen random permutation. The solution will be obtained through a mix of probabilistic and integrable methods.

The lectures will begin with a general overview of the KPZ universality class and its conjectural scaling limits, and I will aim to keep prerequisite knowledge to a minimum.

The one-dimensional Kardar-Parisi-Zhang (KPZ) universality class is a broad collection of models including one-dimensional random interface growth, directed polymers and particle systems. At its center lies the KPZ fixed point, a scaling invariant Markov process which governs the asymptotic fluctuations of all models in the class, and which contains all the rich fluctuation behavior seen in the class.

In these lectures, I will explain how one can derive explicit formulas for the transition probabilities of the KPZ fixed point, and how they reveal connections with random matrix theory and with certain classical integrable differential equations. As a starting point for the derivation, we will use the polynuclear growth model (PNG), a model for crystal growth in one dimension that is intimately connected to the classical longest increasing subsequence problem for a uniformly chosen random permutation. The solution will be obtained through a mix of probabilistic and integrable methods.

The lectures will begin with a general overview of the KPZ universality class and its conjectural scaling limits, and I will aim to keep prerequisite knowledge to a minimum.