About

Program

Date and Time:

09 April 2024 & 10 April 2024
09:00hrs - 17:00hrs

Place:

• Tuesday: Cassini room, ground floor, Bât 709 (DAp), Orme des Merisiers
• Wednesday morning: Cassini room, ground floor, Bât 709 (DAp), Orme des Merisiers
• Wednesday afternoon: Galilée seminar room, Bât 713, Orme des Merisiers

Day 1

1. GR introduction
   Time: 09:00hrs - 09:45hrs
   Contact Person: Sacha, Andreas
   

   General Relativity was published by Einstein in 1915 and has completely changed our understanding of gravity. In this presentation, we will first introduce the ground principles of GR before giving an overview of the mathematical tools used to derive Einstein equations of General Relativity. We will finally conclude by discussing motivation behind beyong-GR theories of gravity and how the latter can be constructed.

2. Introduction to Cosmology
   Time: 10:00hrs - 11:45hrs with 15 min break in between
   Contact person: Vilasini, Andreas
   

   In this presentation, we will embark on a journey through the universe's thermal history, exploring key milestones from the Cosmic Microwave Background (CMB) to the horizon problem, and the theory of cosmic inflation. We'll then delve into baryon acoustic oscillations (BAOs), and the era of the dark ages, and reionization, leading up to the formation of cosmic structures. Through understanding gravitational instability and the Jeans length, we will examine the growth of perturbation modes across different epochs, culminating in an overview of the \( \Lambda \)CDM model and alternative cosmological frameworks. The presentation will conclude by addressing the current challenges and open questions in cosmology, offering a comprehensive yet concise exploration of the universe's evolution and structure.

3. Bayesianism
   Time: 14:00hrs - 15:45hrs with 15 min break in between
   Contact Person: Lisa Goh, Andreas, Hugo
   

   Bayesianism is a formal approach for building-up knowledge and making rational decision under uncertainty. One key application of Bayesianism is that given a priori information about the possible states of the world, one is able to propagate information from observed states to unobserved (latent) states, resulting into a posteriori information. This propagation process is known as inference.

   In a cosmological context, this translates typically into an a priori \( \Lambda \)CDM model, which links latent cosmology (\( \Omega \), \( H_0 \), etc.) to observations (galaxy, lensing, clusters, etc.). From given observations, one is then able to infer cosmology. After a theoretical introduction, we will present current methodology involving sampling methods based on Monte Carlo Markov Chains (MCMC) and variational methods based on Neural Networks (NN).

4. Summary Statistics
   Time: 16:00hrs - 16:45hrs
   Contact Person: Fabian, Vilasini
   

   In the first session of our summary statistics course, we will introduce the concept of summary statistics, providing an intuitive understanding of its importance in data analysis. The discussion will then pivot to two-point statistics, laying the foundation for why and how we move beyond these traditional methods.

Day 2

1. Summary Statistics
   Time: 09:00hrs-09:45hrs
   Contact Person: Vilasini
   

   In this second session we'll explore advanced statistical measures including the bispectrum, probability distribution functions (PDFs), L1-norm, and peak and void statistics. The session aims to broaden our statistical toolkit for analyzing complex datasets, and will include hands-on material if time allows, setting the stage for a deeper dive into practical applications.

2. Observables
   Time: 10:00hrs-11:45hrs with 15 min break in between
   
   In this presentation the following observables will be covered:
   
   

   • Strong Lensing:
     Contact: Sacha
     This short presentation aims at describing the gravitational lensing effect with a focus on its strong regime. We will give the useful theoretical tools to understand this effects before discussing the potentiality of its probes to constrain cosmological parameters. If time allows, a notebook will be presented in which a full analysis of a strong lens is performed, first on simulations, and then on real data.
   • Galaxy Clustering:
     Contact: Romain, Hugo
     Galaxy clustering corresponds to a field of observational cosmology that aim to extract cosmological informations from the spatial distribution of galaxies. Indeed, the way galaxies agglomerate - the clustering - is driven by gravitational collapse (and thus the nature of gravity) and by the expansion of the Universe (and therefore the nature of Dark Energy). Looking at the spatial distribution of galaxies at different epochs is therefore a powerful tool to constrain the expansion rate of the Universe and the growth rate of structure.
   • Weak lensing:
     Contact: Fabian
     This short presentation aims at giving a brief introduction to weak lensing, starting from the historical overview of the main cosmological survey with a focus on systematics and give an overview on infering the data using 2 point correlation function.
   • Clusters and voids:
     Contact: Lucie, Nicolas
     Galaxy clusters, as the most massive collapsed objects in the Universe, occupy the nodes of the Cosmic Web. They are hence tracers of both the formation of structures and the history of expansion. We will describe the different components of galaxy clusters (dark matter, hot gas and galaxies) and present their observational aspects (in optical, Xrays and mm), with their advantages and inconvenients. We will finally review the main cosmological tests with galaxy clusters, develop their principle and the latest results.
   • CMB
     Contact: Lisa
     In this short presentation we aim to cover what the CMB is, and what the state of the art is with CMB.
3. ML, Inverse problem
   Time: 14:00hrs-15:45hrs
   Contact: Hubert, Ezequeil
   In this presentation the following topics will be covered:

   • General introduction to inverse problems
   • Optimization problems (classical vs Bayesian frameworks)
   • Applications to cosmology:
     • weak lensing mass mapping
     • radio-interferometry
   • Resolution algorithms:
     • "Classical" approaches
     • Data-driven approaches: deep learning framework
   • And Uncertainty quantification if time permits.
4. Surveys
   Time: 16:00hrs-16:45hrs
   Contact Person: Fabian
   

   In this presentation we will give a brief historical overview of the surveys, where the main characteristics will be discussed for each of them.

Resources