Schedule

I will present an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers/cosmologists seeking to analyse and interpret a wide variety of data about the Universe. The level will start from elementary notions, without assuming any previous knowledge of statistical methods, and then progresses to more advanced, research-level topics. After an introduction to the importance of statistical inference for the physical sciences, elementary notions of probability theory and inference are introduced and explained. Bayesian methods are then presented, starting from the meaning of Bayes Theorem and its use as inferential engine, including a discussion on priors and posterior distributions. Numerical methods for generating samples from arbitrary posteriors (including Markov Chain Monte Carlo and Nested Sampling) are then covered. If time allows, I will discuss the topic of Bayesian model selection.

Chapter 1 – Principles of inference: Bayesian vs Frequentist.

Chapter 2 – Basics: Priors, Likelihood, Posterior, Evidence.

Chapter 3 – IBayesian Model Building.

Chapter 4 – Numerical technique for Bayesian inference: MCMC and Nested Sampling .

Chapter 5 – Principles of Model Comparison, Interpretation and Numerical Tools.

Useful books

E.T. Jaynes, Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1, CUP (2003) D. MacKay, Information Theory, Inference and Learning Algorithms, CUP (2003), freely available from: inference

Prerequisites

A familiarity with basic data analysis (likelihood, chi-square fits, hypothesis testing) at undergraduate level will be useful.

It is a basic fact of life that Nature comes to us in many scales. Galaxies, planets, molecules, atoms and nuclei have very different sizes, and are held together by very different binding energies. However, it is another important fact of life that phenomena involving distinct scales can often be analysed by considering one relevant scale at a time. Taking advantage of these scale separations leads to so-called effective field theories. In these lectures, I will first introduce the basic concepts of effective field theories and then apply them to various examples in cosmology.

• Lecture 1 – Introduction to Effective Field Theory.

• Lecture 2 – EFT of Inflation.

• Lecture 3 – EFT of Large-Scale Structure.

Literature

• "Inflation and String Theory", Daniel Baumann, Liam McAllister, - arxiv:1404.2601

• "Effective Theory of Cosmological Perturbations", Federico Piazza, Filippo Vernizzi, - arxiv:1307.4350

• "Lectures on Inflation", Leonardo Senatore - arxiv:1609.00716

• "The Effective Field Theorist’s Approach to Gravitational Dynamics", Rafael A. Porto, - arXiv:1601.04914v2

Prerequisites

The course will mostly be self-contained, but some knowledge of basic cosmology and quantum field theory will be helpful.

I will present an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers/cosmologists seeking to analyse and interpret a wide variety of data about the Universe. The level will start from elementary notions, without assuming any previous knowledge of statistical methods, and then progresses to more advanced, research-level topics. After an introduction to the importance of statistical inference for the physical sciences, elementary notions of probability theory and inference are introduced and explained. Bayesian methods are then presented, starting from the meaning of Bayes Theorem and its use as inferential engine, including a discussion on priors and posterior distributions. Numerical methods for generating samples from arbitrary posteriors (including Markov Chain Monte Carlo and Nested Sampling) are then covered. If time allows, I will discuss the topic of Bayesian model selection.

Chapter 1 – The importance of a principled inferential framework.

Chapter 2 – Bayesian inference : Principles (prior, posterior, difference wrt frequentist interpretation of the likelihood).

Chapter 3* – Introduction to Bayesian hierarchical methods.

Chapter 4 – Bayesian technology: MCMC (Metropolis-Hastings, HMC).

Chapter 5* – Introduction to model selection and difference with hypothesis testing.

NB: Chapters labeled with the symbol "*" will be addressed if time permits and the audience wishes.

Useful books

E.T. Jaynes, Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1, CUP (2003) D. MacKay, Information Theory, Inference and Learning Algorithms, CUP (2003), freely available from: inference

Prerequisites

A familiarity with basic data analysis (likelihood, chi-square fits, hypothesis testing) at undergraduate level will be useful.

About the fascinating history of cosmological thinking and the guiding role of gravity, starting from ancient Greece, through the birth of science with Galileo and Newton, to its becoming part of science in 1917 with Einstein’s famous paper “Cosmological Considerations in the General Theory of Relativity” up to Lemaitre’s understanding of the expansion of the universe.

We study the cosmological consequences of codecaying dark matter?a recently proposed mechanism for depleting the density of dark matter through the decay of nearly degenerate particles. A generic prediction of this framework is an early dark matter dominated phase in the history of the Universe, that results in the enhanced growth of dark matter perturbations on small scales. We compute the duration of the early matter dominated phase and show that the perturbations are robust against washout from free streaming. The enhanced small-scale structure is expected to survive today in the form of compact microhalos and can lead to significant boost factors for indirect-detection experiments, such as FERMI, where dark matter would appear as point sources [1]. Following [2], we also comment on the likelihood of primordial black hole formation.

The nature of the most abundant components of the Universe, dark energy and dark matter, is still to be uncovered. What can be learned considering the 21cm radiation observed with the intensity mapping (IM) technique? This poster shortly present the 21cm IM, i.e. what kind of signal it is, then shows how it varies when competitive and realistic dark energy and dark matter scenarios are at play. The focus is on how distinctive and detectable these effects are, presenting forecasts for the bounds that a radio telescope like the Square Kilometre Array (SKA) would be able to uniquely set.

The work presented is based on [1], [2] and [3].

Massive neutrinos uniquely affect cosmic voids. We explore their impact on void clustering using both the DEMNUni and MassiveNuS simulations. For voids, neutrino effects depend on the observational tracers. As neutrino mass increases, the number of small voids traced by cold dark matter particles increases and the number of large voids decreases. Surprisingly, when massive halos are used as tracers, we see the opposite effect. How neutrinos impact the scale at which voids cluster and the void correlation is similarly sensitive to the tracers. This scale dependent bias is not due to simulation volume or halo density. The interplay of these signatures in the void abundance and clustering leaves a distinct fingerprint that could be detected with observations and potentially help break degeneracies between different cosmological parameters. This paper paves the way to exploit cosmic voids in future surveys to constrain the mass of neutrinos.

This work is based on [1]. In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial instabilities in the establishment/destruction of the steady profile. Here, through a detailed phase-space analysis based both on a spherical Vlasov solver, a shell code and a N-body code, we revisit the evolution of collisionless self-gravitating spherical systems with initial power-law density profiles $\rho(r) \propto r^n$, $0 \le n \le -1.5$, and Gaussian velocity dispersion. Two sub-classes of models are considered, with initial virial ratios $\eta = 0.5$ (“warm”) and $\eta = 0.1$ (“cool”). Thanks to the numerical techniques used and the high resolution of the simulations, our numerical analyses are able, for the first time, to show the clear separation between two or three well known dynamical phases: (i) the establishment of a spherical quasi-steady state through a violent relaxation phase during which the phase-space density displays a smooth spiral structure presenting a morphology consistent with predictions from self-similar dynamics, (ii) a quasi-steady state phase during which radial instabilities can take place at small scales and destroy the spiral structure but do not change quantitatively the properties of the phase-space distribution at the coarse grained level and (iii) relaxation to non spherical state due to radial orbit instabilities for $n \le -1$ in the cool case.

Hybrid metric-Palatini gravity theory is a newly proposed theory, whose action depend linearly on the metric scalar curvature and nonlinearly on the arbitrary function of Palatine scalar curvature. The fascinating property of this theory is to maintain all the positive results of GR at solar system and compact object scale as well as to add explanation to the recent cosmological observations. Looking at the recent popularity of this theory, we study the issue of cosmic inflation in this theory. For this purpose, we calculate the slow-roll parameter, scalar-to-tensor ratio and spectral index and then investigate their behavior graphically to check the growth of the universe. We also check our findings with the recent observational data.

We present an extension of the excursion-set theory presented in [1] and originally formulated by [2] by taking into account the large-scale perturbations induced by nearby protofilaments defined as saddle point in the potential field. The mass, accretion rate and formation time of dark matter haloes are analytically predicted. The model predicts that at fixed mass, mass accretion rate and formation vary with orientation and distance from the saddle, demonstrating the indeed assembly bias is influenced by the large-scale tides. Our results are in agreement with recent observations of [3] and provide a new framework to compute the effects of the large scale anisotropy on halo populations.

It is a basic fact of life that Nature comes to us in many scales. Galaxies, planets, molecules, atoms and nuclei have very different sizes, and are held together by very different binding energies. However, it is another important fact of life that phenomena involving distinct scales can often be analysed by considering one relevant scale at a time. Taking advantage of these scale separations leads to so-called effective field theories. In these lectures, I will first introduce the basic concepts of effective field theories and then apply them to various examples in cosmology.

• Lecture 1 – Introduction to Effective Field Theory.

• Lecture 2 – EFT of Inflation.

• Lecture 3 – EFT of Large-Scale Structure.

Literature

• "Inflation and String Theory", Daniel Baumann, Liam McAllister, - arxiv:1404.2601

• "Effective Theory of Cosmological Perturbations", Federico Piazza, Filippo Vernizzi, - arxiv:1307.4350

• "Lectures on Inflation", Leonardo Senatore - arxiv:1609.00716

• "The Effective Field Theorist’s Approach to Gravitational Dynamics", Rafael A. Porto, - arXiv:1601.04914v2

Prerequisites

The course will mostly be self-contained, but some knowledge of basic cosmology and quantum field theory will be helpful.

I will present an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers/cosmologists seeking to analyse and interpret a wide variety of data about the Universe. The level will start from elementary notions, without assuming any previous knowledge of statistical methods, and then progresses to more advanced, research-level topics. After an introduction to the importance of statistical inference for the physical sciences, elementary notions of probability theory and inference are introduced and explained. Bayesian methods are then presented, starting from the meaning of Bayes Theorem and its use as inferential engine, including a discussion on priors and posterior distributions. Numerical methods for generating samples from arbitrary posteriors (including Markov Chain Monte Carlo and Nested Sampling) are then covered. If time allows, I will discuss the topic of Bayesian model selection.

Chapter 1 – Principles of inference: Bayesian vs Frequentist.

Chapter 2 – Basics: Priors, Likelihood, Posterior, Evidence.

Chapter 3 – IBayesian Model Building.

Chapter 4 – Numerical technique for Bayesian inference: MCMC and Nested Sampling .

Chapter 5 – Principles of Model Comparison, Interpretation and Numerical Tools.

Useful books

E.T. Jaynes, Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1, CUP (2003) D. MacKay, Information Theory, Inference and Learning Algorithms, CUP (2003), freely available from: inference

Prerequisites

A familiarity with basic data analysis (likelihood, chi-square fits, hypothesis testing) at undergraduate level will be useful.

It is a basic fact of life that Nature comes to us in many scales. Galaxies, planets, molecules, atoms and nuclei have very different sizes, and are held together by very different binding energies. However, it is another important fact of life that phenomena involving distinct scales can often be analysed by considering one relevant scale at a time. Taking advantage of these scale separations leads to so-called effective field theories. In these lectures, I will first introduce the basic concepts of effective field theories and then apply them to various examples in cosmology.

• Lecture 1 – Introduction to Effective Field Theory.

• Lecture 2 – EFT of Inflation.

• Lecture 3 – EFT of Large-Scale Structure.

Literature

• "Inflation and String Theory", Daniel Baumann, Liam McAllister, - arxiv:1404.2601

• "Effective Theory of Cosmological Perturbations", Federico Piazza, Filippo Vernizzi, - arxiv:1307.4350

• "Lectures on Inflation", Leonardo Senatore - arxiv:1609.00716

• "The Effective Field Theorist’s Approach to Gravitational Dynamics", Rafael A. Porto, - arXiv:1601.04914v2

Prerequisites

The course will mostly be self-contained, but some knowledge of basic cosmology and quantum field theory will be helpful.

About the fascinating history of cosmological thinking and the guiding role of gravity, starting from ancient Greece, through the birth of science with Galileo and Newton, to its becoming part of science in 1917 with Einstein’s famous paper “Cosmological Considerations in the General Theory of Relativity” up to Lemaitre’s understanding of the expansion of the universe.

The Bayesian Estimation Applied to Multiple Species (BEAMS; [1]) framework employs probabilistic supernova (SN) classifications to estimate the Hubble parameter that quantifies the relationship between distance and redshift over cosmic time. However, it requires knowledge of the host galaxy spectroscopic redshifts, limiting its use in upcoming missions such as that of the Large Synoptic Survey Telescope (LSST) for which follow-up spectroscopy will be infeasible. Photometric redshifts (photo-$z$) point estimates suffer from significant bias, scatter, and outlier effects, making them unsuitable for precision SN cosmology. Photo-$z$ probability density functions (PDFs) appropriately encapsulate the nontrivial uncertainties, but there are few mathematically motivated methodologies that make use of the information. We build on one such mathematically motivated approach, the Cosmological Hierarchical Inference with Probabilistic Photometric Redshfts (CHIPPR; [2]) probabilistic graphical model and present Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR), a Bayesian hierarchical model that naturally melds the BEAMS and CHIPPR approaches to use both posterior PDFs of SN type, redshift, and distance modulus based on photometric lightcurve fits and posterior PDFs of redshift based on host galaxy photometry. By combining probabilistic data products in a fully self-consistent way, we infer a posterior PDF over the cosmological parameters in the absence of spectroscopic observations.

The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational field, which is subject to dynamics. The lack of time does not imply the lack of evolution but rather brings to the forefront the role of internal clocks which are some largely arbitrary internal degrees of freedom with respect to which the evolution of timeless systems can be described. We take this idea seriously and try to understand what it implies for quantum mechanics when the fixed external time is replaced by an arbitrary internal clock.

With the advent of powerful telescopes such as the Square Kilometre Array (SKA), the Large Synoptic Survey Telescope (LSST) and the Laser Interferometer Gravitational-Wave Observatory (LIGO), we are entering a golden era of multimessenger transient astronomy. In order to cope with the dramatic increase in data volume, as well as successfully prioritise spectroscopic follow-up resources, we propose a new machine learning approach for the classification of radio transients. In this talk I will outline the algorithm's three main steps: (1) augmentation and interpolation of the data using Gaussian processes; (2) feature extraction using a wavelet decomposition; (3) classification with the popular machine learning algorithm random forests. I will present an application of our algorithm to existing radio transient data, illustrating its ability to accurately classify most radio transients after just 8 hours, and how performance is expected to increase as more training data is acquired. Finally, I will present a general approach for including multimessenger data for general transient classification, and demonstrate its effectiveness by showing the impact of incorporating a single optical data point into the analysis, which significantly reduces confusion.

Inferring the distribution of dark matter from the distribution of tracers such as galaxies and dark matter halos is one of the most important inference problem in current cosmology. It has far reaching consequences in accurate distance measurements using Baryon acoustic oscillations(BAOs), understanding the nature of dark matter, constraining modification of gravity on large-scales. However, this is a difficult task owing to our incomplete knowledge of structure formation on non-linear scales and biased formation of dark matter halos. However, with the advent of large-scale computing, clever algorithms and better understanding of structure formation, it is now possible to do a full forward-modelled Bayesian reconstruction of the large-scale structures. This has important advantages in that correlation of different measurement errors in inference are automatically incorporated in the analysis. Also, observational effects can be easily incorporated into the analytically modelled structure formation process. We are currently working to enhance the performance of these methods by using novel understanding of the biased formation of dark matter halos.

The main subject of this work is the study of a general linear boundary value problems with Drazin and right Drazin (resp. left Drazin) invertible operators and corresponding to initial boundary operators. The obtained results are then employed to solve Schrodinger equation equation.

Since the introduction of random matrices by Wishart in the study of the statistics of population characteristics, and its later use by Wigner to model heavy nuclei, random matrix theory has found applications in many field of physics, like quantum chaos, disordered systems, quantum entanglement, neural networks, gauge theory, statistical physics, cosmology, just to cite a few. I will first introduce the basic concepts of this field, that enable one to predict the distribution of eigenvalues of random matrices, and then apply them to selected problems of interest in cosmology.

• Lecture 1 – Introduction to Random Matrix Theory.

• Lecture 2 – Applications to cosmology.

Useful books

• "The Oxford Handbook of Random Matrix Theory", Ed. Gernot Akemann, Jinho Baik, and Philippe Di Francesco.

Prerequisites

The course will be self-contained, but a basic knowledge of linear algebra and probability at undergraduate level will be useful.

As our data sets grow and become ever more complex, advanced data analysis methods are becoming increasingly important to make principled statistical inferences and learn something about the physical processes in our universe. In these lectures I will build on the knowledge of Bayesian statistics gained on some of the other lectures and introduce some advanced techniques rooted in these principles. We will discuss Bayesian hierarchical models in depth and work through some case studies in astronomy and cosmology where Bayesian (hierarchical) models have been crucial to our understanding of the physics. Finally, I will discuss the increasingly important case where our data sets are too large for run-of-the-mill Bayesian posterior estimation or model comparison to be feasible, and discuss how (statistical) machine learning can help us in these situations.

Lecture 1 – Bayesian Hierarchical Inference and Probabilistic Graphical Models.

Lecture 2 – Bayesian Statistics: Case Studies from Astronomy and Cosmology.

Lecture 3 – Statistical Machine Learning.

Prerequisites

The course will be largely self-contained, but some familiarity with Bayesian statistics will be helpful.

Since the introduction of random matrices by Wishart in the study of the statistics of population characteristics, and its later use by Wigner to model heavy nuclei, random matrix theory has found applications in many field of physics, like quantum chaos, disordered systems, quantum entanglement, neural networks, gauge theory, statistical physics, cosmology, just to cite a few. I will first introduce the basic concepts of this field, that enable one to predict the distribution of eigenvalues of random matrices, and then apply them to selected problems of interest in cosmology.

• Lecture 1 – Introduction to Random Matrix Theory.

• Lecture 2 – Applications to cosmology.

Useful books

• "The Oxford Handbook of Random Matrix Theory", Ed. Gernot Akemann, Jinho Baik, and Philippe Di Francesco.

Prerequisites

The course will be self-contained, but a basic knowledge of linear algebra and probability at undergraduate level will be useful.

It is a basic fact of life that Nature comes to us in many scales. Galaxies, planets, molecules, atoms and nuclei have very different sizes, and are held together by very different binding energies. However, it is another important fact of life that phenomena involving distinct scales can often be analysed by considering one relevant scale at a time. Taking advantage of these scale separations leads to so-called effective field theories. In these lectures, I will first introduce the basic concepts of effective field theories and then apply them to various examples in cosmology.

• Lecture 1 – Introduction to Effective Field Theory.

• Lecture 2 – EFT of Inflation.

• Lecture 3 – EFT of Large-Scale Structure.

Prerequisites

The course will mostly be self-contained, but some knowledge of basic cosmology and quantum field theory will be helpful.

Although the formation of the structures in the universe is mainly driven by large scale gravitational instabilities, our understanding of the evolution of galaxies and galaxy clusters is tightly coupled to the complex galaxy formation physics, which is highly non-linear and where various aspects still are poorly understood. Therefore advanced computer simulations with large dynamical range have to be performed, following simultaneously various physical processes across different scales. This series of lectures will give insight into modern numerical simulation techniques. The hands on tutorials will provide a first hand experience in the simple numerical challenges inherited in simulation n-body systems.

• Lecture 1 – Methods for Cosmological Simulations (N-Body/Hydro/Initial-conditions).

• Lecture 2 – Numerical Treatment of Physical Processes (Star-Formation and Black-Holes, Magnetic-Fields, Transport-Processes).

• Hands on 1 – Numerical Integration (Euler and Leapfrog).

• Hands on 2 – Treating N-Bodies (Central potential and self-gravity).

Literature

• "Simulation Techniques for Cosmological Simulations", Space Science Review, Dolag et al. 2009a.

• "Non-Thermal Processes in Cosmological Simulations", Space Science Review, Dolag et al. 2009b.

• See also Volume 2 of The Encyclopedia of Cosmology., especially Chapter 3 and Chapter 9.

• The hands on tutorials are based on the Gravitational Dynamics lecture at LMU.

Hands On preparation

Before the school, please prepare the following exercises. Thereby you should learn how to use commands in a unix shell, how to compile and execute a program, how to define variables, functions and structures/classes in C++ and especially prepare a vector class with useful members functions and operator definitions. You should also know how to write out a data file from your code and how to plot the results with gnuplot.

Although the formation of the structures in the universe is mainly driven by large scale gravitational instabilities, our understanding of the evolution of galaxies and galaxy clusters is tightly coupled to the complex galaxy formation physics, which is highly non-linear and where various aspects still are poorly understood. Therefore advanced computer simulations with large dynamical range have to be performed, following simultaneously various physical processes across different scales. This series of lectures will give insight into modern numerical simulation techniques. The hands on tutorials will provide a first hand experience in the simple numerical challenges inherited in simulation n-body systems.

• Lecture 1 – Methods for Cosmological Simulations (N-Body/Hydro/Initial-conditions).

• Lecture 2 – Numerical Treatment of Physical Processes (Star-Formation and Black-Holes, Magnetic-Fields, Transport-Processes).

• Hands on 1 – Numerical Integration (Euler and Leapfrog).

• Hands on 2 – Treating N-Bodies (Central potential and self-gravity).

Literature

• "Simulation Techniques for Cosmological Simulations", Space Science Review, Dolag et al. 2009a.

• "Non-Thermal Processes in Cosmological Simulations", Space Science Review, Dolag et al. 2009b.

• See also Volume 2 of The Encyclopedia of Cosmology., especially Chapter 3 and Chapter 9.

• The hands on tutorials are based on the Gravitational Dynamics lecture at LMU.

Hands On preparation

Before the school, please prepare the following exercises. Thereby you should learn how to use commands in a unix shell, how to compile and execute a program, how to define variables, functions and structures/classes in C++ and especially prepare a vector class with useful members functions and operator definitions. You should also know how to write out a data file from your code and how to plot the results with gnuplot.

It is a basic fact of life that Nature comes to us in many scales. Galaxies, planets, molecules, atoms and nuclei have very different sizes, and are held together by very different binding energies. However, it is another important fact of life that phenomena involving distinct scales can often be analysed by considering one relevant scale at a time. Taking advantage of these scale separations leads to so-called effective field theories. In these lectures, I will first introduce the basic concepts of effective field theories and then apply them to various examples in cosmology.

• Lecture 1 – Introduction to Effective Field Theory.

• Lecture 2 – EFT of Inflation.

• Lecture 3 – EFT of Large-Scale Structure.

Prerequisites

The course will mostly be self-contained, but some knowledge of basic cosmology and quantum field theory will be helpful.

Although the formation of the structures in the universe is mainly driven by large scale gravitational instabilities, our understanding of the evolution of galaxies and galaxy clusters is tightly coupled to the complex galaxy formation physics, which is highly non-linear and where various aspects still are poorly understood. Therefore advanced computer simulations with large dynamical range have to be performed, following simultaneously various physical processes across different scales. This series of lectures will give insight into modern numerical simulation techniques. The hands on tutorials will provide a first hand experience in the simple numerical challenges inherited in simulation n-body systems.

• Lecture 1 – Methods for Cosmological Simulations (N-Body/Hydro/Initial-conditions).

• Lecture 2 – Numerical Treatment of Physical Processes (Star-Formation and Black-Holes, Magnetic-Fields, Transport-Processes).

• Hands on 1 – Numerical Integration (Euler and Leapfrog).

• Hands on 2 – Treating N-Bodies (Central potential and self-gravity).

Literature

• "Simulation Techniques for Cosmological Simulations", Space Science Review, Dolag et al. 2009a.

• "Non-Thermal Processes in Cosmological Simulations", Space Science Review, Dolag et al. 2009b.

• See also Volume 2 of The Encyclopedia of Cosmology., especially Chapter 3 and Chapter 9.

• The hands on tutorials are based on the Gravitational Dynamics lecture at LMU.

Hands On preparation

Before the school, please prepare the following exercises. Thereby you should learn how to use commands in a unix shell, how to compile and execute a program, how to define variables, functions and structures/classes in C++ and especially prepare a vector class with useful members functions and operator definitions. You should also know how to write out a data file from your code and how to plot the results with gnuplot.

Although the formation of the structures in the universe is mainly driven by large scale gravitational instabilities, our understanding of the evolution of galaxies and galaxy clusters is tightly coupled to the complex galaxy formation physics, which is highly non-linear and where various aspects still are poorly understood. Therefore advanced computer simulations with large dynamical range have to be performed, following simultaneously various physical processes across different scales. This series of lectures will give insight into modern numerical simulation techniques. The hands on tutorials will provide a first hand experience in the simple numerical challenges inherited in simulation n-body systems.

• Lecture 1 – Methods for Cosmological Simulations (N-Body/Hydro/Initial-conditions).

• Lecture 2 – Numerical Treatment of Physical Processes (Star-Formation and Black-Holes, Magnetic-Fields, Transport-Processes).

• Hands on 1 – Numerical Integration (Euler and Leapfrog).

• Hands on 2 – Treating N-Bodies (Central potential and self-gravity).

Literature

• "Simulation Techniques for Cosmological Simulations", Space Science Review, Dolag et al. 2009a.

• "Non-Thermal Processes in Cosmological Simulations", Space Science Review, Dolag et al. 2009b.

• See also Volume 2 of The Encyclopedia of Cosmology., especially Chapter 3 and Chapter 9.

• The hands on tutorials are based on the Gravitational Dynamics lecture at LMU.

Hands On preparation

Before the school, please prepare the following exercises. Thereby you should learn how to use commands in a unix shell, how to compile and execute a program, how to define variables, functions and structures/classes in C++ and especially prepare a vector class with useful members functions and operator definitions. You should also know how to write out a data file from your code and how to plot the results with gnuplot.