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This course will introduce some advanced topics in general relativity related to describing gravity in the strong field and dynamical regime. Topics covered include properties of spinning black holes, black hole thermodynamics and energy extraction, how to define horizons in a dynamical setting, formulations of the Einstein equations as constraint and evolution equations, and gravitational waves and how they are sourced. Instructor: William East/Ghazal Geshnizjani Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

We will discuss mathematical aspects of classical and quantum field theory, including topics such as: symplectic manifolds and the phase space, symplectic reduction, geometric quantization, Chern-Simons theory, and others. Instructor: Kevin Costello/Mykola Semenyakin Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

Cooperation is seen across all biological scales ranging from cells to societies. In organisms like bacteria, the decision-making process is genetically hardwired but higher animals endowed with cognitive abilities have to make choices that can affect not only their own survival but also that of their group.Uncovering the organizing principles that lead to evolution of cooperation is an issue of fundamental importance that transcends disciplinary boundaries. Insights can be obtained from studying biological communities, through mathematical and agent-based modeling, cognitive science, social network dynamics and behavioral economics. Such investigations can also lead to the understanding of other intriguing evolutionary phenomena like opinion dynamics, evolution of fairness and spiteful behaviour. Evolutionary Game Theory  provides a powerful framework for addressing such questions in the context of both biological and cultural evolution. In this program, we will therefore be addressin...

Constructing a theory of quantum gravity, and with it a notion of quantum spacetime is one of the biggest challenges faced by modern theoretical physics. This workshop will bring together researchers from a wide range of viewpoints and give them an opportunity to exchange ideas and gain new insights.

The workshop is supported by the Simons Foundation.

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Workshop Speakers

Marcela Carena (Perimeter Institute)
Astrid Eichhorn (Universität Heidelberg)
Netta Englehardt (MIT)
Johanna Erdmenger (University of Würzburg)
Gulia Gubitosi (University of Naples Federico II)
Renate Loll (Radboud University)
Jessica Muir (Perimeter Institute)
A.W. Peet (University of Toronto)
Alessia Platania (University of Copenhagen)
Jocelyn Read (California State University, Fullerton)
Kasia Rejzner (York University)
Mairi Sakellariadou (King's College London)
Sarah Shandera (Pennsylvania State University)
Sumati Surya (Raman Research Institute)
Karen Yeats (University of Waterloo)

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Scientific Organizers
Bianca Dittrich (Perimeter Institute)
Sabrina Pasterski (Perimeter Institute)
Céline Zwikel (Perimeter Institute)
Sruthi Narayanan (Perimeter Institute)

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...

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

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