Centre de Physique Théorique

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September 2018

From 2 to 8 September, Cargèse

IESC Pre-school, Analytics, Inference, and Computation in Cosmology: Advanced methods

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This is an introductory school to a thematic trimester that will held at the IHP in Paris. It is organized by the Institut Henri Poincaré (IHP) in collaboration with the Institut d’Études Scientifiques de Cargèse (IESC). The themes which are addressed are part of Mathematical Frontiers in Cosmology.

Cosmology is about understanding the origin and evolution of the universe and the formation of all structure within it — one of the most challenging intellectual projects undertaken by humanity. To make progress, we need the most powerful mathematical methods available: analytics to guide us through subtle theoretical issues, simulations to compute the detailed quantitative predictions of the theory, and statistical inference to confront these predictions with large cosmological data sets.

The IHP trimester entitled “Analytics, Inference, and Computation in Cosmology,” will be dedicated not only to the “what” and the “why” but also, and specifically, to the “how” of cosmological calculation. Is the mathematical toolset of cosmology adequate for the challenges ahead? Where do we need new ideas?

Whether it be on advances in analytical techniques, innovative computational methods or new ways to infer cosmological information from cosmological data, this trimester will be an occasion to gather the leading experts from around the world to share their expertise, spark new ideas and collaborations, and equip the next generation of cosmologists with the innovative mathematical tools we need as we enter a new era in precision cosmology.

Wednesday 12 September 14:00-15:00, Amphi 5 du CPT

Quantum proper time

Fabio Costa

The proper time of a relativistic particle depends on its trajectory: acceleration, or gravitational fields, can cause trajectories with equal starting and final points to accumulate different proper time. What happens to a particle that is in a quantum superposition of different trajectories? How does the particle decide how much proper time it should experience? I will show how such questions lead to the prediction of novel effects at the interface of quantum theory and relativity, in a low-energy regime insensitive to quantum field effects. I will further introduce an effective formalism for composite relativistic quantum particles, which can act as “clocks” measuring quantum proper time. I will finally propose that the formalism can facilitate the analysis of unexplored physical regimes, where quantum properties of gravity can lead to quantum causal structures.

Wednesday 26 September 14:00-15:00, CPT, Amphi 5

What is the optimal geometry for the lowest eigenvalue of the Laplace operator?

David Krejcirik (Department of Mathematics, Czech Technical University, Prague, République tchèque)

Résumé

We give an introductory talk on the optimisation of eigenvalues
of the Robin Laplacian as regards the geometry of the domain
under perimeter and area constraints.

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