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This is a two-week thematic program with a focus on recent developments in Teichmüller theory which promise to be fertile in the near future. These includeThe metric theory of Teichmüller spaces and other spaces, including the recent breakthroughs in the Thurston metric.Higher Teichmüller theory, and its interplay with Higgs bundles, algebraic geometry and Anosov representations.The Teichmüller theory of infinite-type surfaces, including their quasiconformal theory and what is known as the ``big" mapping class group.Relations with anti-de Sitter geometry.The techniques for these areas come from complex analysis, hyperbolic geometry, dynamics, partial differential equations, projective geometry, geometric and combinatorial group theory, algebraic geometry, Kähler geometry and other fields —  these often give several points of view on the same objects showing the richness of the theory.The workshop will consist of a series of mini-courses (with lectures typically totalling 3 hours) toget...

The workshop aims to bring together experts from two different disciplines: mathematical aspects of scattering amplitudes, and cosmology. In the last decades we have got a tremendous amount of insights in the structure of perturbative on-shell scattering amplitudes. This includes unitarity methods, recursion relations, worldsheet models, bootstrap methods and more recently also an intriguing connection to positive geometry, positive Grassmannian, Associahedron and the Amplituhedron. This all pushes us closer to a reformulation of the perturbative S-matrix using a completely new set of principles. At the same time, similar remarkable structures have been observed in cosmological correlators, which are fundamental objects capturing the physics of our Universe. This connects two seemingly different fields of theoretical physics. This workshop will help to advance these connections further.Eligibility criteria:Registrations for the PGSAC Program are open to graduate students and researcher...

The progress in parallel of high-speed electronics and low temperature technologies has revolutionized the study of quantum matter. Many of the gedanken experiments of the fathers of quantum mechanics are now realized routinely, as well as many new ones that the founders could hardly have dreamed of.  The possibility of quantum-based encryption, communication and computing is getting concrete and some real implementations are already available. This so-called second quantum revolution which is mostly yet to come will be the fruit of a close collaboration between theory (theoretical physics, but also applied mathematics) and experiment.Our aim is to address some of the central theoretical open questions in the field. The program will be centered around three main topics:(i) Quantum trajectories and Quantum control,(ii) Measurement induced phase transitions and finally,(iii) Quantum information and computation.The goal of this program is to gather researchers from the above areas, from t...

This course teaches basic numerical methods that are widely used across many fields of physics. The course is based on the Julia programming language. Topics include an introduction to Julia, linear algebra, Monte Carlo methods, differential equations, and are based on applications by researchers at Perimeter. The course will also teach principles of software engineering ensuring reproducible results Instructor: Erik Schnetter/Dustin Lang/Subhayan Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

The main objective of this course is to discuss some advanced topics in gravitational physics and its applications to high energy physics. Necessary mathematical tools will be introduced on the way. Instructor: Ruth Gregory/Aldo Riello Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will cover the basics of Quantum Foundations under three main headings. Part I – Novel effects in Quantum Theory. A number of interesting quantum effects will be considered. Interferometers: Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, The quantum-Zeno effect. The no cloning theorem. Quantum optics (single mode). Hong-Ou-Mandel dip. Part II - Conceptual and interpretational issues. Axioms for quantum theory for pure states: Von-Neumann measurement model. * The measurement (or reality) problem. EPR Einstein’s 1927 remarks, the Einstein-Podolsky-Rosen argument. Bell’s theorem, nonlocality without inequalities. The Tirolson bound. The Kochen-Specker theorem and related work by Spekkens On the reality of the wavefunction: Epistemic versus ontic interpretations of the wavefunction and the Pusey-Barrett-Rudolph theorem proving the reality of the wave function. Gleason’s theorem. Interpretations. The landscape of interpretations of quantum theory (the Harrigen Spekkens classification). The de Broglie-Bohm interpretation, the many worlds interpretation, wave- function collapse models, the Copenhagen interpretation, and QBism. Part III - Structural issues. Reformulating quantum theory: we will look at some reformulations of quantum theory and consider the light they throw on the structure of quantum theory. These may include time symmetric quantum theory and weak measurements (Aharonov et al), quantum Bayesian networks, and the operator tensor formalism. Generalised probability theories: These are more general frameworks for probabilistic theories which admit classical and quantum as special cases. Reasonable principles for quantum theory: we will review some of the recent work on reconstructing quantum theory from simple principles. Indefinite causal structure and indefinite causal order. Finally we will conclude by looking at (i) the close link between quantum foundations and quantum information and (ii) possible future directions in quantum gravity motivated by ideas from quantum foundations. Instructor: Lucien Hardy/Bindiya Arora Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will introduce you to some of the geometrical structures underlying theoretical physics. Previous knowledge of differential geometry is not required. Topics covered in the course include: Introduction to manifolds, differential forms, symplectic manifolds, symplectic version of Noether’s theorem, integration on manifolds, fiber bundles, principal bundles and applications to gauge theory. Instructor: Mykola Semenyakin/Maite Dupuis Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

The Standard Model of particle physics is introduced, and reviewed, from a modern effective field theory perspective. Instructor: Seyda Ipek/Gang Xu Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

Pedro has selected 9 papers for this mini-course.

• Infrared Photons and Gravitons by Weinberg, 1965
• Determination of an Operator Algebra for the 2D Ising Model by Kadanoff and Ceva, 1971
• Confinement of Quarks by Wilson, 1974,
• Phenomenological Lagrangians by Weinberg, 1979,
• Gravitational Effects on and of Vacuum Decay by Coleman and De Luccia, 1980
• Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions by Amati, Ciafaloni and Veneziano, 1987
• Quantum Spin Chains and The Haldane Gap by Affleck, 1988
• The Large N Limit of SFTs and Supergravity by Maldacena, 1997
• Entanglement Entropy and Quantum Field Theory by Calabrese and Cardy, 2008

The format will be: A] Pedro will give a 1h30m lecture about one of these papers on a Monday or a Friday (the Monday or Friday right after B] unless there is a holiday) B] One week later, X students give a presentation of Y minutes about important recent papers that refer/are related to that paper. At the end of this lecture we give feedback about those presentations. What is X and what is Y depends on how many students volunteer to present. Of course, people who just want to attend without presenting are also most welcome!

The establishment of the complete framework of Quantum Mechanics is one of the epochal events of not just science, but human history. In addition to giving a highly successful theoretical basis for understanding the universe of the very small, the very large and the very complex, its technological spin offs are the mainstay of modern civilization. ICTS plans to celebrate the centenary of modern quantum mechanics and look towards the emerging frontiers which will shape the next 100 years. Thus, in the QM100 meeting we plan to gather a galaxy of international scientists in areas ranging across Quantum Mechanics in all its manifestations with different themes from High Energy Physics, String Theory, Cosmology, Condensed Matter Physics, Atomic and Molecular Physics, Quantum Chaos as well as Quantum Information/Computing and Mathematics.In-person participation is by invitation only. There will, however, be an option for online participation. We may be able to accommodate a selected few youn...