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

13 talksCollection Number C24026
Talk

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics

Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics


Higher Categorical Tools for Quantum Phases of Matter
15 talksCollection Number C24016Talk


Analogies between QFT and lattice systems
Anton Kapustin California Institute of Technology (Caltech)  Division of Physics Mathematics & Astronomy

Models of anyons with symmetry: a bulkboundary correspondence
Fiona Burnell University of Minnesota

Twisted Tools for (Untwisted) Quantum Field Theory
Justin Kulp Stony Brook University

Quantum double models and DijkgraafWitten theory with defects
Catherine Meusburger 
Topological sectors in quantum lattice models
Clement Delcamp Institut des Hautes Etudes Scientifiques (IHES)

DouglasReutter 4d TQFT as a generalised orbifold
Vincentas Mulevičius Vilnius University

Weak Hopf symmetric tensor networks
Andras Molnar University of Vienna


Quantum Field Theory for Cosmology (PHYS785/AMATH872)
24 talksCollection Number C24003Talk

Quantum Field Theory for Cosmology  Lecture 20240109
Achim Kempf University of Waterloo

Quantum Field Theory for Cosmology  Lecture 20240111
Achim Kempf University of Waterloo

Quantum Field Theory for Cosmology  Lecture 20240116
Achim Kempf University of Waterloo

Quantum Field Theory for Cosmology  Lecture 20240118
Achim Kempf University of Waterloo

Quantum Field Theory for Cosmology  Lecture 20240123
Achim Kempf University of Waterloo

Quantum Field Theory for Cosmology  Lecture 20240125
Achim Kempf University of Waterloo

Quantum Field Theory for Cosmology  Lecture 20240130
Achim Kempf University of Waterloo

Quantum Field Theory for Cosmology  Lecture 20240201
Achim Kempf University of Waterloo


Mathematical Physics  Core 2023/24
12 talksCollection Number C24005Talk

Twisted Holography MiniCourse
6 talksCollection Number C23050Talk

Twisted Holography MiniCourse  Lecture 20231102
Kevin Costello Perimeter Institute for Theoretical Physics

Twisted Holography MiniCourse  Lecture 20231109
Kevin Costello Perimeter Institute for Theoretical Physics

Twisted Holography MiniCourse  Lecture 20231116
Kevin Costello Perimeter Institute for Theoretical Physics

Twisted Holography MiniCourse  Lecture 20231123
Davide Gaiotto Perimeter Institute for Theoretical Physics

Twisted Holography MiniCourse  Lecture 20231130
Davide Gaiotto Perimeter Institute for Theoretical Physics

Twisted Holography MiniCourse  Lecture 20231214
Davide Gaiotto Perimeter Institute for Theoretical Physics


Topological Quantum Field Theories  minicourse
9 talksCollection Number C23048Talk

Topological Quantum Field Theories Lecture 20231006
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231013
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231020
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231027
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231103
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231110
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231124
Lukas Mueller Perimeter Institute for Theoretical Physics

Topological Quantum Field Theories Lecture 20231201
Lukas Mueller Perimeter Institute for Theoretical Physics


QFT for Mathematicians 2022
28 talksCollection Number C22011Talk

Welcome and Opening Remarks
Kevin Costello Perimeter Institute for Theoretical Physics

3d Theories and Twists I
Kevin Costello Perimeter Institute for Theoretical Physics

3d Gauge Theory and Elliptic Stable Envelopes I
Andrei Okounkov Columbia University

Classical BV Formalism and Topological Quantum Field Theory
Philsang Yoo Seoul National University

A and B models in 3d and 4d I
Justin Hilburn Perimeter Institute for Theoretical Physics

3d B Models and Knot Homology I
Lev Rozansky University of North Carolina at Chapel Hill

On Boundary VOA's
Davide Gaiotto Perimeter Institute for Theoretical Physics

3d Gauge Theory and Elliptic Stable Envelopes II
Mykola Dedushenko Stony Brook University


Global Categorical Symmetries
34 talksCollection Number C22008Talk

Welcome and Opening Remarks
Theo JohnsonFreyd Dalhousie University

NonInvertible Symmetries in d>2
Justin Kaidi Stony Brook University

Monodromy and derived equivalences
Andrei Okounkov Columbia University

Lessons from SU(N) SeibergWitten Geometry
Emily Nardoni University of Tokyo

Vertex algebras and selfdual YangMills theory
Kevin Costello Perimeter Institute for Theoretical Physics

Noninvertible Global Symmetries in the Standard Model
ShuHeng Shao Stony Brook University

Analytic Langlands correspondence over C and R
Pavel Etingof Massachusetts Institute of Technology (MIT)

A (kind of) monoidal localization theorem for the small quantum group
Cris Negron University of Southern California


Women at the Intersection of Mathematics and Theoretical Physics
16 talksCollection Number C21002Talk

Welcome and Opening Remarks

Bianca Dittrich Perimeter Institute for Theoretical Physics

Theo JohnsonFreyd Dalhousie University

Sylvie Paycha University of Potsdam

Katarzyna Rejzner University of York

Anne Taormina Durham University

Reiko Toriumi Okinawa Institute of Science and Technology Graduate University


Division algebraic symmetry breaking
Cohl Furey Humboldt University of Berlin

State sum models with defects
Catherine Meusburger University of ErlangenNuremberg

Quantum information and black holes
Johanna Erdmenger University of Würzburg

Researcher Presentations

Karen Yeats University of Waterloo

Sabine Harribey Nordic Institute for Theoretical Physics

Philine van Vliet Deutsches ElektronenSynchrotron DESY

Maria Elena TejedaYeomans University of Colima

Maryam Khaqan Emory University


Mathematical Puzzles from Causal Set Quantum Gravity
Sumati Surya Raman Research Institute

On generalized hyperpolygons
Laura Schaposnik University of Illinois at Chicago

Exploring spacetime beyond classicality
Renate Loll Radboud Universiteit Nijmegen


Octonions and the Standard Model
16 talksCollection Number C21001Talk

Welcome and Opening Remarks
Kirill Krasnov University of Nottingham

Finite quantum geometry, octonions and the theory of fundamental particles.
Michel DuboisViolette University of ParisSaclay

Supersymmetry and RCHO revisited
Paul Townsend University of Cambridge

Spin (8,9,10), Octonions and the Standard Model
Kirill Krasnov University of Nottingham

Gravity as the square of gauge theory
Leron Borsten HeriotWatt University

A Magic Pyramid of Supergravity Theories from YangMills Squared
Mia Hughes Imperial College London

Division algebraic symmetry breaking

Cohl Furey Humboldt University of Berlin

Mia Hughes Imperial College London


Clifford algebra of the Standard Model
Ivan Todorov Bulgarian Academy of Sciences


Geometric Representation Theory
24 talksCollection Number C20030Talk


Singularities of Schubert varieties within a right cell
Martina Lanini University of Rome Tor Vergata

Yangians and cohomological Hall algebras of Higgs sheaves on curves
Olivier Schiffmann University of ParisSaclay

Tate's thesis in the de Rham setting
Sam Raskin The University of Texas at Austin

Fundamental local equivalences in quantum geometric Langlands
Gurbir Dhillon Stanford University

Zalgebras from Coulomb branches
Oscar Kivinen California Institute of Technology

Cotangent complexes of moduli spaces and Ginzburg dg algebras
Sarah Scherotzke University of Luxembourg



Elliptic Cohomology and Physics
11 talksCollection Number C20029Talk

Projective elliptic genera and applications
Fei Han National University of Singapore

Topological Modular Forms and Quantum Field Theory
Davide Gaiotto Perimeter Institute for Theoretical Physics

Equivariant elliptic cohomology with integral coefficients
Lennart Meier Utrecht University

The de Rham model for elliptic cohomology from physics
Arnav Tripathy Harvard University

Quasisymmetric characteristic numbers for Hamiltonian toric manifolds
Jack Morava Johns Hopkins University

Codes, vertex algebras and topological modular forms
Gerd Laures Ruhr University Bochum


Elliptic characteristic classes, bow varieties, 3d mirror duality
Richard Rimanyi University of North Carolina  Chapel Hll


Mathematical Physics 2023/24
13 talksCollection Number C24026We 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 Number C24016Quantum 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 Number C24003This 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 Number C24005This 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 Number C23050This 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 Number C23048A 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 Number C21002 
Octonions and the Standard Model
16 talksCollection Number C21001Over 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 Number C20030 
Elliptic Cohomology and Physics
11 talksCollection Number C20029