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This course introduces mathematical and numerical tools that are useful for various fields of theoretical physics. In the numerical part of the course, students will develop introductory programming skills in both Python and Mathematica. The mathematical part of the course covers three main topics: First, we will study basics of smooth manifolds, define forms on them, and then de Rham cohomology. Second, we will introduce homology theory, and explain in what sense it can be understood as dual to cohomology. Lastly, we will study homotopy theory. Throughout the course, we will emphasize many applications to physics.

Structure:

We will discuss 8 papers which had huge impact in physics. One week Instructor Pedro Vieira will discuss a paper; students should read it beforehand. One week later students discuss recent papers referring to that paper (20 min each student, ~ 3 presentations; at the end of the class Pedro will grade the presentations based on “Physics”, “Presentation”, “Question handling”; and give comments).

By the end of the course, students will have explored a vast set of topics in theoretical physics — spotting potential gaps to be fixed — sharpened their presentation skills through steady practice, and sparked cross-disciplinary conversations through our shared physics language.

The papers: The papers we will cover (can find the pdfs in this spreadsheet):

Sept 1 & 8: On the Number of Prime Numbers less than a Given Quantity, Riemann, 1859

Sept 8 & 21: Limits on Massless Particles, Weinberg and Witten, 1980

Sept 22 & 28: Neural networks and physical systems with emergent collective computational abilities, Hopfield, 1982

Sept 29 & Oct 8: Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Laughlin, 1983

Oct 9 & 19: Why there is nothing rather than something, Coleman, 1988

Oct 20 & 26: Universality and Scaling in Gravitational Collapse of a Massless Scalar Field, Choptuik, 1993

Oct 27 & Nov 2: Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Mirzakhani, 2007

Nov 3 & 9: Supersymmetry and Morse Theory, Witten, 1982

Location & Building Access: Please refer to the above spreadsheet for class location as it will vary from week to week. Perimeter Institute, 31 Caroline St N, Waterloo Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

Lean-verified Quantum Information Theory, Sep 15 - Oct 1 Instructor: Rodolfo Reis Soldati

We introduce formal theorem proving with the Lean 4 programming language, placing emphasis on developing Quantum Information Theory theorems and proofs. Formal proof writing is an increasingly important skill as Quantum Information grows more sophisticated, and as machine-verification tools gain popularity. Participants will learn core theorem-proving syntax, the basics of Lean’s own type theory, the notion and use of tactics, and will gain familiarity with the Mathlib and Physlib/QuantumInfo libraries.

Entanglement theory for quantum systems described by von Neumann algebras, Oct 6 - 29 Instructor: Lauritz van Luijk

In quantum systems with infinitely many degrees of freedom, pairs of subsystems can be infinitely entangled. But are there operationally distinct forms of infinite entanglement? This short course gives a basic mathematical introduction to von Neumann algebras and explains why, when, and how they can be used to describe finite and infinite quantum systems and their subsystems. We will formulate quantum information-theoretic properties, including examples from cryptography and entanglement theory, in this algebraic framework. We will then discuss how some of these operational properties are equivalent to structure-theoretic properties of the von Neumann algebras describing the subsystems. In particular, we answer the opening question by identifying entanglement properties, such as embezzlement of entanglement, that distinguish setups with non-isomorphic algebras. We will see how the classification of von Neumann algebras into types I, II, and III, together with their respective subtypes, can be formulated solely in terms of operational entanglement properties.

Location & Building Access: Please refer to each lecture listing on this site for class location as it will vary from week to week. Perimeter Institute, 31 Caroline St N, Waterloo Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

The aim of the first part is to present a brief overview of selected topics in quantum theory. Schrodinger, Heisenberg and Interaction picture is discussed and applied to study time evolution. Density matrices and Feynman path integrals are introduced. The second part of the course derives the Feynman rules for scalar quantum field theory and introduces renormalization.

The aim of this course is to revisit much of the undergraduate classical physics curriculum in preparation to the study of both General Relativity and Quantum Field Theory. We will focus on the notion of symmetry and Noether's theorem in both mechanical and field theoretical systems (stress energy tensor). We will discuss the Lagrangian, or "action principle", and Hamiltonian, or "phase space", perspectives on mechanics and their mutual relationship. We will then discuss selected topics in special relativity and electrodynamics, culminating with the derivation of the Lienard-Wiechart potentials.

• compact binary coalescence, continuous wave, and dark matter searches; building gravitational wave catalogs
• multi-messenger gravitational wave astronomy
• gravitational wave observatories, instrument science, and detector characterization
• structure and integrating into the collaboration

          

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Lecturers:

Patrick Brady (University of Wisconsin-Milwaukee)
Elenna Capote (LIGO Hanford Observatory)
Derek Davis (University of Rhode-Island)
Chad Hanna (Pennsylvania State University)
Jess McIver (University of British Columbia)
Lorenzo Mirasola (University of the Balearic Islands)
Barbara Patricelli (University of Pisa)
Jessica Steinlechner (Maastricht University)
Daniel Williams (The University of Glasgow)
Nicolas Arnaud (CNRS/IN2P3 & Université Claude Bernard Lyon 1)

Tutorials:
Cort Posnansky (Pennsylvania State University)
Shio Sakon (Pennsylvania State University)
Harrison Siegel (Perimeter Institute)
Atidya Vijaykumar (CITA)

Scientific Organizers:

Luis Lehner (Perimeter Institute)
Will East (Perimeter Institute)
Rob Coyne (University of Rhode Island)
Edward Porter (APC)
Lan Nguyen Quynh (Phenikaa University)

The 2026 Tri-Institute Summer School on Elementary Particles (TRISEP) will be held July 13-24 at Perimeter Institute. 

TRISEP is an international summer school organized jointly by Perimeter Institute, SNOLAB, and TRIUMF, Canada's laboratory for particle and nuclear physics. TRISEP will feature lectures by leading experts in the fields of particle physics and particle astrophysics (broadly defined) and is designed to be very interactive with ample time for questions, discussions and interaction with the speakers. The school is intended for graduate students of all levels, both theorists and experimentalists, preferably with some knowledge of quantum field theory.

Previous TRISEP Schools:

2025, 2024, 2023, 2022, 2021,2019,2018, 2017, 2016, 2015, 2014 and 2013.

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Scientific Organizers

Cliff Burgess (McMaster University, Perimeter Institute)
Mina Arvanitaki (Perimeter Institute)
Marcela Carena (Perimeter Institute, University of Chicago)
Michael Fedderke (Perimeter Institute)
Junwu Huang (Perimeter Institute)
Sergei Sibiryakov (McMaster University, Perimeter Institute)
Carlos Wagner (University of Chicago)

This course is part of the 2026 Undergraduate Summer School curriculum. We will explore some of the interesting combinatorial and algebraic structures in perturbative quantum field theory and look at how they can be helpful for quantum field theory calculations as well as how they tie to topics of mathematical interest.

This course is part of the 2026 Undergraduate Summer School curriculum. This course will provide a short introduction to loop quantum cosmology.  After a brief overview of the physics and geometry underlying cosmology, we will explore how it is possible to obtain a quantum description of cosmology.  As a part of this, we will discuss conceptual questions underlying quantum cosmology including the problem of time and the lack of an external observer, and some possible resolutions.  Finally, we will see how loop quantum gravity motivates a particular quantization for cosmology that gives loop quantum cosmology.  In the last part of the course, we will study the physics predicted by loop quantum cosmology in the primordial universe.