Organisation des séminaires et calendrier

The generation of primordial density inhomogeneities from inflaton quantum fluctuations is a crucial prediction of inflation. The correlation functions of these fluctuations, called cosmological correlators, can be studied in a perturbative framework where the quantum fluctuations can be described as quantum fields that propagate in a curved space-time. However, this propagation has a complex time and kinematic dependence due to broken Lorentz invariance, implying technical difficulties for analytical correlator computations.

In this talk, after reviewing the essential features of the physics of inflation and cosmological correlators, I will present a new framework to study the analytical properties of these correlators. It is based on the use of Laplace transforms to decompose the mode functions that encode the propagation of fields in curved geometry in terms of their flat-space counterpart, which are plane waves. Following simple diagrammatic rules, any cosmological correlator can then be written from integrating the corresponding flat-space one against a Laplace space kernel. As an illustration, I will show new analytical results obtained with this framework for tree-level massive correlators and for the cosmological collider at strong mixing.

Abstract: 

These lectures will provide an introduction to tensor-network methods in quantum many-body physics, with an emphasis on matrix-product states (MPS).

• Basic tensor-network language, including graphical notation, virtual indices, bond dimensions, gauge freedom, canonical forms, QR and singular-value decompositions, and the role of entanglement in controlling the efficiency of the representation.
• Main MPS algorithms, including contractions, correlation functions, matrix-product operators, DMRG, and time-evolution methods.
• Brief introduction to projected entangled-pair states (PEPS) as a higher-dimensional generalization of MPS, together with the basic ideas behind approximate PEPS contraction.
• Tensor-network representations of mixed states, quantum channels, and Lindblad dynamics, with applications to thermal states and open quantum systems.

Based on https://arxiv.org/abs/2606.24803.

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Abstract:
The Onsager algebra plays an important role in exactly solvable models. One of the most notable examples is the solution to the 2D classical Ising model using the Onsager algebra by Lars Onsager in 1944. I will explain the appearance of the Onsager algebra in various quantum lattice models, and report the recent results on the Onsager algebra as the symmetry of the 6-vertex model at root of unity values of anisotropy. The talk is based on a series of work in arXiv: 2606.25660, 2103.14569, 2012.10224 and work in progress.