Mathematical physics, including mathematics, is a research area where novel mathematical techniques are invented to tackle problems in physics, and where novel mathematical ideas find an elegant physical realization. Historically, it would have been impossible to distinguish between theoretical physics and pure mathematics. Often spectacular advances were seen with the concurrent development of new ideas and fields in both mathematics and physics. Here one might note Newton's invention of modern calculus to advance the understanding of mechanics and gravitation. In the twentieth century, quantum theory was developed almost simultaneously with a variety of mathematical fields, including linear algebra, the spectral theory of operators and functional analysis. This fruitful partnership continues today with, for example, the discovery of remarkable connections between gauge theories and string theories from physics and geometry and topology in mathematics.
Format results

15 talksCollection NumberC24031
Talk

Mathematical Physics 2023/24
13 talksCollection NumberC24026Talk

Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics 
Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics 
Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics 
Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics 
Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics 
Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics 
Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics 
Mathematical Physics Lecture
Perimeter Institute for Theoretical Physics


Higher Categorical Tools for Quantum Phases of Matter
15 talksCollection NumberC24016Talk


Analogies between QFT and lattice systems
California Institute of Technology (Caltech)  Division of Physics Mathematics & Astronomy 
Models of anyons with symmetry: a bulkboundary correspondence
University of Minnesota 
Twisted Tools for (Untwisted) Quantum Field Theory
Stony Brook University 
Quantum double models and DijkgraafWitten theory with defects
Catherine Meusburger 
Topological sectors in quantum lattice models
Institut des Hautes Etudes Scientifiques (IHES) 
DouglasReutter 4d TQFT as a generalised orbifold
Vilnius University 
Weak Hopf symmetric tensor networks
University of Vienna


Quantum Field Theory for Cosmology (PHYS785/AMATH872)
24 talksCollection NumberC24003Talk

Quantum Field Theory for Cosmology  Lecture 20240109
University of Waterloo 
Quantum Field Theory for Cosmology  Lecture 20240111
University of Waterloo 
Quantum Field Theory for Cosmology  Lecture 20240116
University of Waterloo 
Quantum Field Theory for Cosmology  Lecture 20240118
University of Waterloo 
Quantum Field Theory for Cosmology  Lecture 20240123
University of Waterloo 
Quantum Field Theory for Cosmology  Lecture 20240125
University of Waterloo 
Quantum Field Theory for Cosmology  Lecture 20240130
University of Waterloo 
Quantum Field Theory for Cosmology  Lecture 20240201
University of Waterloo


Mathematical Physics  Core 2023/24
12 talksCollection NumberC24005Talk

Twisted Holography MiniCourse
6 talksCollection NumberC23050Talk

Twisted Holography MiniCourse  Lecture 20231102
Perimeter Institute for Theoretical Physics 
Twisted Holography MiniCourse  Lecture 20231109
Perimeter Institute for Theoretical Physics 
Twisted Holography MiniCourse  Lecture 20231116
Perimeter Institute for Theoretical Physics 
Twisted Holography MiniCourse  Lecture 20231123
Perimeter Institute for Theoretical Physics 
Twisted Holography MiniCourse  Lecture 20231130
Perimeter Institute for Theoretical Physics 
Twisted Holography MiniCourse  Lecture 20231214
Perimeter Institute for Theoretical Physics


Topological Quantum Field Theories  minicourse
9 talksCollection NumberC23048Talk

Topological Quantum Field Theories Lecture 20231006
Perimeter Institute for Theoretical Physics 
Topological Quantum Field Theories Lecture 20231013
Perimeter Institute for Theoretical Physics 
Topological Quantum Field Theories Lecture 20231020
Perimeter Institute for Theoretical Physics 
Topological Quantum Field Theories Lecture 20231027
Perimeter Institute for Theoretical Physics 
Topological Quantum Field Theories Lecture 20231103
Perimeter Institute for Theoretical Physics 
Topological Quantum Field Theories Lecture 20231110
Perimeter Institute for Theoretical Physics 
Topological Quantum Field Theories Lecture 20231124
Perimeter Institute for Theoretical Physics 
Topological Quantum Field Theories Lecture 20231201
Perimeter Institute for Theoretical Physics


QFT for Mathematicians 2022
28 talksCollection NumberC22011Talk

Welcome and Opening Remarks
Perimeter Institute for Theoretical Physics 
3d Theories and Twists I
Perimeter Institute for Theoretical Physics 
3d Gauge Theory and Elliptic Stable Envelopes I
Columbia University 
Classical BV Formalism and Topological Quantum Field Theory
Seoul National University 

3d B Models and Knot Homology I
University of North Carolina at Chapel Hill 
On Boundary VOA's
Perimeter Institute for Theoretical Physics 
3d Gauge Theory and Elliptic Stable Envelopes II
Stony Brook University


Global Categorical Symmetries
34 talksCollection NumberC22008Talk

Welcome and Opening Remarks
Dalhousie University 
NonInvertible Symmetries in d>2
Stony Brook University 
Monodromy and derived equivalences
Columbia University 
Lessons from SU(N) SeibergWitten Geometry
University of Tokyo 
Vertex algebras and selfdual YangMills theory
Perimeter Institute for Theoretical Physics 
Noninvertible Global Symmetries in the Standard Model
Stony Brook University 
Analytic Langlands correspondence over C and R
Massachusetts Institute of Technology (MIT) 
A (kind of) monoidal localization theorem for the small quantum group
University of Southern California


Women at the Intersection of Mathematics and Theoretical Physics
16 talksCollection NumberC21002Talk

Welcome and Opening Remarks

Perimeter Institute for Theoretical Physics

Dalhousie University

University of Potsdam

University of York

Durham University

Okinawa Institute of Science and Technology Graduate University


Division algebraic symmetry breaking
Humboldt University of Berlin 
State sum models with defects
University of ErlangenNuremberg 
Quantum information and black holes
University of Würzburg 
Researcher Presentations

University of Waterloo

Nordic Institute for Theoretical Physics

Deutsches ElektronenSynchrotron DESY

University of Colima

Emory University


Mathematical Puzzles from Causal Set Quantum Gravity
Raman Research Institute 
On generalized hyperpolygons
University of Illinois at Chicago 
Exploring spacetime beyond classicality
Radboud Universiteit Nijmegen


Octonions and the Standard Model
16 talksCollection NumberC21001Talk

Welcome and Opening Remarks
University of Nottingham 
Finite quantum geometry, octonions and the theory of fundamental particles.
University of ParisSaclay 
Supersymmetry and RCHO revisited
University of Cambridge 
Spin (8,9,10), Octonions and the Standard Model
University of Nottingham 
Gravity as the square of gauge theory
HeriotWatt University 
A Magic Pyramid of Supergravity Theories from YangMills Squared
Imperial College London 
Division algebraic symmetry breaking

Humboldt University of Berlin

Imperial College London


Clifford algebra of the Standard Model
Bulgarian Academy of Sciences


Geometric Representation Theory
24 talksCollection NumberC20030Talk


Singularities of Schubert varieties within a right cell
University of Rome Tor Vergata 
Yangians and cohomological Hall algebras of Higgs sheaves on curves
University of ParisSaclay 
Tate's thesis in the de Rham setting
The University of Texas at Austin 
Fundamental local equivalences in quantum geometric Langlands
Stanford University 
Zalgebras from Coulomb branches
California Institute of Technology 
Cotangent complexes of moduli spaces and Ginzburg dg algebras
University of Luxembourg 


Classical Physics (Core), PHYS 776, September 3  October 4, 2024
15 talksCollection NumberC24031This is a theoretical physics course that aims to review the basics of theoretical mechanics, special relativity, and classical field theory, with the emphasis on geometrical notions and relativistic formalism, thus setting the stage for the forthcoming courses in Quantum Mechanics, and Quantum Field Theory in particular, as well as in General Relativity and Quantum Gravity. Instructor: Aldo Riello Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduatecourses 
Mathematical Physics 2023/24
13 talksCollection NumberC24026We will discuss mathematical aspects of classical and quantum field theory, including topics such as: symplectic manifolds and the phase space, symplectic reduction, geometric quantization, ChernSimons theory, and others. 
Higher Categorical Tools for Quantum Phases of Matter
15 talksCollection NumberC24016Quantum phases have become a staple of modern physics, thanks to their appearance in fields as diverse as condensed matter physics, quantum field theory, quantum information processing, and topology. The description of quantum phases of matter requires novel mathematical tools that lie beyond the old symmetry breaking perspective on phases. Techniques from topological field theory, homotopy theory, and (higher) category theory show great potential for advancing our understanding of the characterization and classification of quantum phases. The goal of this workshop is to bring together experts from across mathematics and physics to discuss recent breakthroughs in these mathematical tools and their application to physical problems.
Scientific Organizers
Lukas Mueller
Alex Turzillo
Davide Gaiotto
Sponsored in part by the Simons Collaboration on Global Categorical Symmetries

Quantum Field Theory for Cosmology (PHYS785/AMATH872)
24 talksCollection NumberC24003This course introduces quantum field theory from scratch and then develops the theory of the quantum fluctuations of fields and particles. We will focus, in particular, on how quantum fields are affected by curvature and by spacetime horizons. This will lead us to the Unruh effect, Hawking radiation and to inflationary cosmology. Inflationary cosmology, which we will study in detail, is part of the current standard model of cosmology which holds that all structure in the universe  such as the distribution of galaxies  originated in tiny quantum fluctuations of a scalar field and of spacetime itself. For intuition, consider that quantum field fluctuations of significant amplitude normally occur only at very small length scales. Close to the big bang, during a brief initial period of nearly exponentially fast expansion (inflation), such smallwavelength but largeamplitude quantum fluctuations were stretched out to cosmological wavelengths. In this way, quantum fluctuations are thought to have seeded the observed inhomogeneities in the cosmic microwave background  which in turn seeded the condensation of hydrogen into galaxies and stars, all closely matching the increasingly accurate astronomical observations over recent years. The prerequisites for this course are a solid understanding of quantum theory and some basic knowledge of general relativity, such as FRW spacetimes.
https://uwaterloo.ca/physicsofinformationlab/teaching/quantumfieldtheorycosmologyamath872phys785w2024
https://pitp.zoom.us/j/96567241418?pwd=U3I1V1g4YXdaZ3psT1FrZUdlYm1zdz09

Mathematical Physics  Core 2023/24
12 talksCollection NumberC24005This 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.

Twisted Holography MiniCourse
6 talksCollection NumberC23050This minicourse will introduce twisted holography, which is holography for BPS subsectors of gauge theory and gravity. We will start by introducing the Bmodel topological string from the spacetime perspective, before discussing branes, backreaction, and the holographic duality.
Zoom: https://pitp.zoom.us/j/98839130613?pwd=SExFK0ZVYzJ3NmJhU1RFa21PWU1qQT09

Topological Quantum Field Theories  minicourse
9 talksCollection NumberC23048A quantum field theory is deemed topological if it exhibits the remarkable property of being independent of any background metric. In contrast to most other types of quantum field theories, topological quantum field theories possess a welldefined mathematical framework, tracing its roots back to the pioneering work of Atiyah in 1988. The mathematical tools employed to define and study topological quantum field theories encompass concepts from category theory, homotopy theory, topology, and algebra.
In this course, we will delve into the mathematical foundations of this field, explore examples and classification results, especially in lower dimensions. Subsequently, we will explore more advanced aspects, such as invertible theories, defects, the cobordism hypothesis, or state sum models in dimensions 3 and 4 (including TuraevViro and DouglasReutter models), depending on the interests of the audience.
Today, the mathematics of topological quantum field theories has found numerous applications in physics. Recent applications include the study of anomalies, noninvertible symmetries, the classification of topological phases of matter, and lattice models. The course aims to provide the necessary background for understanding these applications. 


Women at the Intersection of Mathematics and Theoretical Physics
16 talksCollection NumberC21002 
Octonions and the Standard Model
16 talksCollection NumberC21001Over the years, various researchers have suggested connections between the octonions and the standard model of particle physics. The past few years, in particular, have been marked by an upsurge of activity on this subject, stimulated by the recent observation that the standard model gauge group and fermion representation can be elegantly characterized in terms of the octonions. This workshop, which will be the first ever on this topic, is intended to bring this new community together in an attempt to better understand these ideas, establish a common language, and stimulate further progress.
The workshop will consist of an hourlong talk every Monday at noon (EST), with the first talk on Monday February 8, and the final talk on Monday May 17.

Geometric Representation Theory
24 talksCollection NumberC20030