Overall aim: To provide a modern perspective on fundamental concepts of statistical physics and hydrodynamics and to introduce the main ideas on chaotic classical systems and tools to study them.

Main topics:
- Statistical Physics -- Module covered during the first half of the course

- Fluid Dynamics and Classical Chaos -- Module covered during the second half of the course

Teachers:
- Giuseppe Di Giulio, Researcher, Stockholm University, teaches Statistical Physics
- Yuefei Liu, Researcher, Nordita (Nordic Institute for Theoretical Physics), teaches Fluid Dynamics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

In this course, students work as mentors for participants at the upper‑secondary and university levels in the project Sprettur. Mentors play an essential role in supporting and encouraging other students in their studies and social life. Their role is to build constructive relationships with participants, act as positive role models, and take part in joint activities organised within Sprettur. Mentorship is based on relationship‑building and regular meetings and involves a commitment to the students the mentor supports. 

Sprettur is a support project for students with a foreign background who seek additional support to improve their academic performance and participation in the university community. Students in the course work as mentors and are paired with participants based on shared interests. Mentors also work together in groups and in consultation with teachers and project coordinators. 

Students may choose to enrol in the course in the autumn semester, spring semester, or distribute the workload across both semesters (the full academic year). The course structure accommodates this choice, but all academic requirements remain the same. Mentors plan regular meetings with Sprettur participants and typically spend three hours per month with participants, three hours per month in homework groups, and attend a total of five seminars. 

Students submit journal entries on Canvas and design and deliver a learning experience for the participants in Sprettur. Journal entries are based on readings and critical reflections on the mentorship role and on personal experience in the project. The course is taught in Icelandic and English. 

Upon completing the course and meeting all requirements, students receive 5 ECTS credits and an official certificate of participation and completion of the project. 

Students fill out an electronic application form, and the supervising teacher contacts applicants. 

More information about Sprettur can be found here: www.hi.is/sprettur 

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Introduction to how numerical analysis is used to explore the properties of physical systems. Programming environment and graphical representation. The application of functional bases for solving models in quantum and statistical mechanics. Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Seminar course on topics of current interest in astrophysics and cosmology.

Banach spaces and Hilbert spaces and their main properties. Dual of Banach spaces.
Principles of functional analysis: Hahn--Banach theorem, Uniform boundedness Principle and Banach--Steinhaus, open mapping and closed graph theorems.

Weak topologies. Banach--Alaoglu theorem.
Riesz's lemma. Orthogonality in Banach spaces.

Operators and their adjoints. Compact operators.
Spectrum and resolvent. Lax--Milgram. The spectral theorem for compact, self-adjoint operators.

Sobolev spaces. Sobolev spaces on the real line and immersions. Approximation and dense subspaces. Poincaré inequality. Sobolev spaces in higher dimension. Extension theorem. Sobolev embeddings. Rellich--Kondrachov. Poincaré inequality in higher dimension. Poincaré--Wirtinger.

Curves, surfaces and manifolds in Euclidean space. Differentiable manifolds, vector fields and tensor fields. Hypersurfaces in Euclidean space, first and second fundamental forms, curvature, convex hypersurfaces. Inner geometry of surfaces. Riemannian manifolds, geodesics. The Gauss-Bonnet theorem for surfaces.

Path integral formulation of quantum field theory, anomalies, Ward identities, regularization and renormalization. Yang-mills theory, spontaneous symmetry breaking and the Higgs mechanism.

This is a reading course.

Quantum information theory provides the foundation and guiding principles for the development of emerging quantum technologies. This unit introduces students to the essential tools and ideas of quantum information theory. It begins with the theoretical framework for describing open quantum systems to model the effects of environmental noise. We will then define the concept of quantum information, show how it can be quantified, and how it is processed and transmitted over noisy channels. By generalizing information theory to quantum systems, we will see how quantum effects can be used as a resource for information processing.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

Introduction to the scientific method. Ethics of science and within the university community.
The role of the student, advisors and external examiner. Effective and honest communications.
Conducting a literature review, using bibliographic databases and reference handling. Thesis structure, formulating research questions, writing and argumentation. How scientific writing differs from general purpose writing. Writing a MS study plan and proposal. Practical skills for presenting tables and figures, layout, fonts and colors. Presentation skills. Project management for a thesis, how to divide a large project into smaller tasks, setting a work plan and following a timeline. Life after graduate school and being employable.

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.

Overall aim: To provide a modern perspective on fundamental concepts of statistical physics and hydrodynamics and to introduce the main ideas on chaotic classical systems and tools to study them.

Main topics:
- Statistical Physics -- Module covered during the first half of the course

- Fluid Dynamics and Classical Chaos -- Module covered during the second half of the course

Teachers:
- Giuseppe Di Giulio, Researcher, Stockholm University, teaches Statistical Physics
- Yuefei Liu, Researcher, Nordita (Nordic Institute for Theoretical Physics), teaches Fluid Dynamics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

In this course, students work as mentors for participants at the upper‑secondary and university levels in the project Sprettur. Mentors play an essential role in supporting and encouraging other students in their studies and social life. Their role is to build constructive relationships with participants, act as positive role models, and take part in joint activities organised within Sprettur. Mentorship is based on relationship‑building and regular meetings and involves a commitment to the students the mentor supports. 

Sprettur is a support project for students with a foreign background who seek additional support to improve their academic performance and participation in the university community. Students in the course work as mentors and are paired with participants based on shared interests. Mentors also work together in groups and in consultation with teachers and project coordinators. 

Students may choose to enrol in the course in the autumn semester, spring semester, or distribute the workload across both semesters (the full academic year). The course structure accommodates this choice, but all academic requirements remain the same. Mentors plan regular meetings with Sprettur participants and typically spend three hours per month with participants, three hours per month in homework groups, and attend a total of five seminars. 

Students submit journal entries on Canvas and design and deliver a learning experience for the participants in Sprettur. Journal entries are based on readings and critical reflections on the mentorship role and on personal experience in the project. The course is taught in Icelandic and English. 

Upon completing the course and meeting all requirements, students receive 5 ECTS credits and an official certificate of participation and completion of the project. 

Students fill out an electronic application form, and the supervising teacher contacts applicants. 

More information about Sprettur can be found here: www.hi.is/sprettur 

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Introduction to how numerical analysis is used to explore the properties of physical systems. Programming environment and graphical representation. The application of functional bases for solving models in quantum and statistical mechanics. Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Seminar course on topics of current interest in astrophysics and cosmology.

Banach spaces and Hilbert spaces and their main properties. Dual of Banach spaces.
Principles of functional analysis: Hahn--Banach theorem, Uniform boundedness Principle and Banach--Steinhaus, open mapping and closed graph theorems.

Weak topologies. Banach--Alaoglu theorem.
Riesz's lemma. Orthogonality in Banach spaces.

Operators and their adjoints. Compact operators.
Spectrum and resolvent. Lax--Milgram. The spectral theorem for compact, self-adjoint operators.

Sobolev spaces. Sobolev spaces on the real line and immersions. Approximation and dense subspaces. Poincaré inequality. Sobolev spaces in higher dimension. Extension theorem. Sobolev embeddings. Rellich--Kondrachov. Poincaré inequality in higher dimension. Poincaré--Wirtinger.

Curves, surfaces and manifolds in Euclidean space. Differentiable manifolds, vector fields and tensor fields. Hypersurfaces in Euclidean space, first and second fundamental forms, curvature, convex hypersurfaces. Inner geometry of surfaces. Riemannian manifolds, geodesics. The Gauss-Bonnet theorem for surfaces.

Path integral formulation of quantum field theory, anomalies, Ward identities, regularization and renormalization. Yang-mills theory, spontaneous symmetry breaking and the Higgs mechanism.

This is a reading course.

Quantum information theory provides the foundation and guiding principles for the development of emerging quantum technologies. This unit introduces students to the essential tools and ideas of quantum information theory. It begins with the theoretical framework for describing open quantum systems to model the effects of environmental noise. We will then define the concept of quantum information, show how it can be quantified, and how it is processed and transmitted over noisy channels. By generalizing information theory to quantum systems, we will see how quantum effects can be used as a resource for information processing.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

Introduction to the scientific method. Ethics of science and within the university community.
The role of the student, advisors and external examiner. Effective and honest communications.
Conducting a literature review, using bibliographic databases and reference handling. Thesis structure, formulating research questions, writing and argumentation. How scientific writing differs from general purpose writing. Writing a MS study plan and proposal. Practical skills for presenting tables and figures, layout, fonts and colors. Presentation skills. Project management for a thesis, how to divide a large project into smaller tasks, setting a work plan and following a timeline. Life after graduate school and being employable.

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.

Overall aim: To provide a modern perspective on fundamental concepts of statistical physics and hydrodynamics and to introduce the main ideas on chaotic classical systems and tools to study them.

Main topics:
- Statistical Physics -- Module covered during the first half of the course

- Fluid Dynamics and Classical Chaos -- Module covered during the second half of the course

Teachers:
- Giuseppe Di Giulio, Researcher, Stockholm University, teaches Statistical Physics
- Yuefei Liu, Researcher, Nordita (Nordic Institute for Theoretical Physics), teaches Fluid Dynamics

This course provides a comprehensive introduction to advanced and modern topics in Electrodynamics aimed at undergraduate and master's students. The course assumes familiarity with Newtonian mechanics, but the main concepts of special relativity and vector calculus are covered initially. 

Aim: To introduce perturbative quantum field theory and some of its applications in modern physics. 

Main topics: relativistic quantum mechanics, bosonic and fermionic fields, interactions in perturbation theory, Feynman diagram methods, scattering processes and particle decay, elementary processes in quantum electrodynamics (QED).

This course provides a basic introduction to Einstein's relativity theory: Special relativity, four-vectors and tensors. General relativity, spacetime curvature, the equivalence principle, Einstein's equations, experimental tests within the solar system, gravitational waves, black holes, cosmology.

Teachers: Benjamin Knorr and Ziqi Yan, postdocs at Nordita

In this course, students work as mentors for participants at the upper‑secondary and university levels in the project Sprettur. Mentors play an essential role in supporting and encouraging other students in their studies and social life. Their role is to build constructive relationships with participants, act as positive role models, and take part in joint activities organised within Sprettur. Mentorship is based on relationship‑building and regular meetings and involves a commitment to the students the mentor supports. 

Sprettur is a support project for students with a foreign background who seek additional support to improve their academic performance and participation in the university community. Students in the course work as mentors and are paired with participants based on shared interests. Mentors also work together in groups and in consultation with teachers and project coordinators. 

Students may choose to enrol in the course in the autumn semester, spring semester, or distribute the workload across both semesters (the full academic year). The course structure accommodates this choice, but all academic requirements remain the same. Mentors plan regular meetings with Sprettur participants and typically spend three hours per month with participants, three hours per month in homework groups, and attend a total of five seminars. 

Students submit journal entries on Canvas and design and deliver a learning experience for the participants in Sprettur. Journal entries are based on readings and critical reflections on the mentorship role and on personal experience in the project. The course is taught in Icelandic and English. 

Upon completing the course and meeting all requirements, students receive 5 ECTS credits and an official certificate of participation and completion of the project. 

Students fill out an electronic application form, and the supervising teacher contacts applicants. 

More information about Sprettur can be found here: www.hi.is/sprettur 

This course provides a general overview of diverse topics in modern astrophysics. The focus of the course might vary from year to year. In this term (Fall 2021), the topic will be high-energy astrophysics.

Introduction to how numerical analysis is used to explore the properties of physical systems. Programming environment and graphical representation. The application of functional bases for solving models in quantum and statistical mechanics. Communication with Linux-clusters and remote machines. The course is taught in English or Icelandic according to the needs of the students.

Programming language: FORTRAN-2008 with OpenMP directives for parallel processing.

The course is an introduction to some basic concepts of condensed matter physics. Curriculum: Chemical bonds, crystal structure, crystal symmetry, the reciprocal lattice. Vibrational modes of crystals, phonons, specific heat, thermal conductivity. The free electron model, band structure of condensed matter, effective mass. Metals, insulators and semiconductors. The course includes three labs.

Seminar course on topics of current interest in astrophysics and cosmology.

Banach spaces and Hilbert spaces and their main properties. Dual of Banach spaces.
Principles of functional analysis: Hahn--Banach theorem, Uniform boundedness Principle and Banach--Steinhaus, open mapping and closed graph theorems.

Weak topologies. Banach--Alaoglu theorem.
Riesz's lemma. Orthogonality in Banach spaces.

Operators and their adjoints. Compact operators.
Spectrum and resolvent. Lax--Milgram. The spectral theorem for compact, self-adjoint operators.

Sobolev spaces. Sobolev spaces on the real line and immersions. Approximation and dense subspaces. Poincaré inequality. Sobolev spaces in higher dimension. Extension theorem. Sobolev embeddings. Rellich--Kondrachov. Poincaré inequality in higher dimension. Poincaré--Wirtinger.

Curves, surfaces and manifolds in Euclidean space. Differentiable manifolds, vector fields and tensor fields. Hypersurfaces in Euclidean space, first and second fundamental forms, curvature, convex hypersurfaces. Inner geometry of surfaces. Riemannian manifolds, geodesics. The Gauss-Bonnet theorem for surfaces.

Path integral formulation of quantum field theory, anomalies, Ward identities, regularization and renormalization. Yang-mills theory, spontaneous symmetry breaking and the Higgs mechanism.

This is a reading course.

Quantum information theory provides the foundation and guiding principles for the development of emerging quantum technologies. This unit introduces students to the essential tools and ideas of quantum information theory. It begins with the theoretical framework for describing open quantum systems to model the effects of environmental noise. We will then define the concept of quantum information, show how it can be quantified, and how it is processed and transmitted over noisy channels. By generalizing information theory to quantum systems, we will see how quantum effects can be used as a resource for information processing.

The primitive equations are derived and applied on atmospheric weather systems on various scales. Geostrophic wind, gradient wind, sea breeze, thermal wind, stability and wind profile of the atmospheric boundary layer. Vertical motion. Gravity waves and Rossby waves. Introduction to quasi-geostrophic theory, vorticity equation, potential vorticity, omega-equation and geopotential tendency equation. Quasi-geostrophic theory of mountain flows.

Introduction to the scientific method. Ethics of science and within the university community.
The role of the student, advisors and external examiner. Effective and honest communications.
Conducting a literature review, using bibliographic databases and reference handling. Thesis structure, formulating research questions, writing and argumentation. How scientific writing differs from general purpose writing. Writing a MS study plan and proposal. Practical skills for presenting tables and figures, layout, fonts and colors. Presentation skills. Project management for a thesis, how to divide a large project into smaller tasks, setting a work plan and following a timeline. Life after graduate school and being employable.

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Many real-world systems—such as social networks, ecosystems, brain networks, and communication infrastructures—are inherently complex. These systems exhibit emergent behaviors that cannot be predicted by studying their individual components alone. The significance of studying these complex systems was highlighted by the 2021 Nobel Prize in Physics, awarded for groundbreaking research in this area.

Network science provides powerful tools for modeling and understanding complex systems, and offers data-driven approaches to uncovering their underlying structures and dynamics. This course introduces students to fundamental statistical methods with a particular focus on their application within network science. It is designed to provide a comprehensive foundation in the principles and techniques essential for network modeling, analysis, and statistical inference in complex networks.

Students will explore:

1. Network Structure – Core concepts include random networks, such as configuration models, degree distribution, centrality measures, and community structures.
2. Network Dynamics – Key dynamic processes on networks, such as diffusion, random walks, epidemic spread modeling, percolation, and branching processes.
3. Statistical Inference on Networks – Techniques for inferring structure and dynamics from networked data, covering topics like network reconstruction, community detection, and dynamic inference.