Welcome and Opening Remarks

• Aldo Riello (Perimeter Institute)

Room: PI/1-100 - Theatre

Noether’s theorems and gauge symmetries

• Marc Geiler (École Normale Supérieure de Lyon)

Room: PI/1-100 - Theatre This lecture is devoted to Noether’s theorems and the study of the interplay between symmetries and conservation laws, from ordinary mechanics to general relativity. In order to start on a common ground and interest a broad audience, we will begin with a review of Noether’s (first) theorem in ordinary non-relativistic mechanics. This will enable us to settle some subtleties, agree on conventions, and especially explore some curious and lesser-known symmetry features of familiar models (such as particles and celestial mechanics). We will then move on to field theory, and discuss the construction of conserved currents and energy-momentum tensors. This will include a discussion of conserved quantities in general relativity. Finally, we will turn to the core of the topic, which is Noether’s (second) theorem for gauge symmetries. After recalling the basic properties of gauge theories in Lagrangian and Hamiltonian form, we will derive the consequences of gauge symmetry for the construction of conserved charges. For this, we will introduce the so-called covariant phase space formalism, which enables to construct symmetry charges and algebras, and derive (non) conservation laws. This will be illustrated in Maxwell’s theory and in general relativity. In particular, we will focus in depth on the example of three-dimensional gravity as an exactly soluble model in which all aspects of symmetries can be understood. We will end with an outlook towards the notion of asymptotic symmetries and their use in classical and quantum gravity. Ideally, the audience should be familiar with: Hamiltonian mechanics differential forms basic features of general relativity

Lightening Talks Room: PI/1-100 - Theatre

Fitting models to data using Markov Chain Monte Carlo

• Dustin Lang (Perimeter Institute)

Room: PI/1-100 - Theatre

Fitting models to data using Markov Chain Monte Carlo (tutorial)

• Dustin Lang (Perimeter Institute)

Room: PI/4-405 - Bob Room

Noether’s theorems and gauge symmetries

• Marc Geiler (École Normale Supérieure de Lyon)

Room: PI/1-100 - Theatre

Noether’s theorems and gauge symmetries (Q&A)

• Marc Geiler (École Normale Supérieure de Lyon)

Room: PI/1-100 - Theatre

Noether’s theorems and gauge symmetries

• Marc Geiler (École Normale Supérieure de Lyon)

Room: PI/1-100 - Theatre

Knot categorification from mirror symmetry

• Mina Aganagic (University of California, Berkeley)

Room: PI/1-100 - Theatre Two of the most beautiful examples of the interaction between mathematics and physics involve knot theory and mirror symmetry. In this talk, I will describe a new connection between them. The solution to a central problem in knot theory, the knot categorification problem, comes from a new application of mirror symmetry.

Noether’s theorems and gauge symmetries

• Marc Geiler (École Normale Supérieure de Lyon)

Room: PI/1-100 - Theatre

Topological quantum matter and quantum computing

• Peter Lu (Perimeter Institute)

Room: PI/1-100 - Theatre Interacting quantum particles can form non-trivial states of matter characterized by topological order, which features several unconventional properties such as topological degeneracy and fractionalized quasiparticles. In addition, it also provides a promising platform for realizing quantum computing in a robust manner. In this series of lectures, I will introduce the basics of topological order and its connection to quantum computing from various aspects involving lattice models, symmetry, and entanglement structure. Several frontier topics such as fracton topological phases, self-correcting quantum memory, state preparation, and quantum LDPC codes will be briefly discussed.

Noether’s theorems and gauge symmetries (tutorial)

• Marc Geiler (École Normale Supérieure de Lyon)

Room: PI/4-400 - Space Room

Topological quantum matter and quantum computing

• Peter Lu (Perimeter Institute)

Room: PI/1-100 - Theatre

Topological quantum matter and quantum computing

• Peter Lu (Perimeter Institute)

Room: PI/1-100 - Theatre

Topological quantum matter and quantum computing (Q&A)

• Peter Lu (Perimeter Institute)

Room: PI/1-100 - Theatre

Fitting models to data using Markov Chain Monte Carlo

• Dustin Lang (Perimeter Institute)

Room: PI/1-100 - Theatre

Fitting models to data using Markov Chain Monte Carlo (tutorial)

• Dustin Lang (Perimeter Institute)

Room: PI/4-405 - Bob Room

Topological quantum matter and quantum computing

• Peter Lu (Perimeter Institute)

Room: PI/1-100 - Theatre

Effective Field Theory and Symmetries

• John Donoghue (University of Massachusetts Amherst)

Room: PI/1-100 - Theatre These lectures will cover the concepts and techniques of effective field theory. I will try to introduce several of the useful techniques which do not usually get covered in the standard QFT courses and books. We will start with the effective field theory aspects of QED, and end with the treatment of general relativity as a quantum field theory using effective field theory techniques.

Topological quantum matter and quantum computing (tutorial)

• Peter Lu (Perimeter Institute)

Room: PI/4-405 - Bob Room

Introduction to Colloquium Room: PI/1-100 - Theatre

Effective Field Theory and Symmetries

• John Donoghue (University of Massachusetts Amherst)

Room: PI/1-100 - Theatre

The structure of translational tilings

• Rachel Greennfeld (Institute for Advanced Study)

Room: PI/1-100 - Theatre Translational tiling is a covering of a space (e.g., Euclidean space) using translated copies of a building block, called a "tile'', without any positive measure overlaps. What are the possible ways that a space can be tiled? One of the most well known conjectures in this area is the periodic tiling conjecture. It asserts that any tile of Euclidean space can tile the space periodically. This conjecture was posed 35 years ago and has been intensively studied over the years. In a joint work with Terence Tao, we disprove the periodic tiling conjecture in high dimensions. In the talk, I will motivate this result and discuss our proof.

Effective Field Theory and Symmetries

• John Donoghue (University of Massachusetts Amherst)

Room: PI/1-100 - Theatre

Effective Field Theory and Symmetries (Q&A)

• John Donoghue (University of Massachusetts Amherst)

Room: PI/1-100 - Theatre

Effective Field Theory and Symmetries (tutorial)

• John Donoghue (University of Massachusetts Amherst)

Room: PI/1-100 - Theatre

Effective Field Theory and Symmetries

• John Donoghue (University of Massachusetts Amherst)

Room: PI/1-100 - Theatre

Concluding Remarks followed by Group Activity Room: PI/4-405 - Bob Room