Symmetries Graduate School 2023

Jan 23, 2023, 8:30 a.m. → Feb 3, 2023, 5:00 p.m. America/Toronto

PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)

Aldo Riello (Perimeter Institute ), Barbara Soda (Perimeter Institute), Chong Wang (Perimeter Institute ), Cliff Burgess (Perimeter Institute & McMaster University), Emilie Huffman (Perimeter Institute ), Justin Hilburn (Perimeter Institute ), Maxence Corman (Perimeter Institute )

The goal of this Winter School on Symmetries is to introduce graduate students to the effectiveness of symmetry principles across subjects and energy scales. 

From Noether’s celebrated theorem to the development of the standard model of particle physics, from Landau’s to Wilson’s classification of phases of matter and phase transitions, symmetries have been key to 20th century physics. But in the last decades novel and more subtle incarnations of the symmetry principle have shown us the way to unlocking new and unexpected phases of quantum matter, infrared and holographic properties of the quantum gravitational interaction, as well as to advancements in pure mathematics to mention a few.  

The Graduate Winter School on Symmetries will introduce students and young researchers to a variety of applications of the symmetry principle. These will be chosen across contemporary research topics in both theoretical physics and mathematics. Our goal is to create a synergistic environment where ideas and techniques can ultimately spread across disciplines. This will be achieved through a combination of mini-courses, colloquia, and discussion sessions led in collaboration with the students themselves.

https://pirsa.org/C23008

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Monday, January 23

8:30 a.m. Registration

1 Welcome and Opening Remarks

Speaker: Aldo Riello (Perimeter Institute)

2 Noether’s theorems and gauge symmetries

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

Speaker: Marc Geiler (École Normale Supérieure de Lyon)

10:30 a.m. Coffee Break

3 Lightening Talks

12:30 p.m. Lunch Break

4 Fitting models to data using Markov Chain Monte Carlo

Speaker: Dustin Lang (Perimeter Institute)

3:00 p.m. Coffee Break

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

Speaker: Dustin Lang (Perimeter Institute)

Tuesday, January 24

6 Noether’s theorems and gauge symmetries

Speaker: Marc Geiler (École Normale Supérieure de Lyon)

10:30 a.m. Coffee Break

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

Speaker: Marc Geiler (École Normale Supérieure de Lyon)

Wednesday, January 25

8 Noether’s theorems and gauge symmetries

Speaker: Marc Geiler (École Normale Supérieure de Lyon)

12:30 p.m. Lunch Break

9 Knot categorification from mirror symmetry

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.

Speaker: Mina Aganagic (University of California, Berkeley)

3:30 p.m. Coffee Break

4:00 p.m. Meet and Greet with Mina Aganagic

Thursday, January 26

10 Noether’s theorems and gauge symmetries

Speaker: Marc Geiler (École Normale Supérieure de Lyon)

10:30 a.m. Coffee Break

11 Topological quantum matter and quantum computing

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.

Speaker: Peter Lu (Perimeter Institute)

12:30 p.m. Lunch Break

2:00 p.m. Informal Networking over Coffee

12 Noether’s theorems and gauge symmetries (tutorial)

Speaker: Marc Geiler (École Normale Supérieure de Lyon)

Friday, January 27

13 Topological quantum matter and quantum computing

Speaker: Peter Lu (Perimeter Institute)

10:30 a.m. Coffee Break

11:00 a.m. Group Activity

Monday, January 30

14 Topological quantum matter and quantum computing

Speaker: Peter Lu (Perimeter Institute)

10:30 a.m. Coffee Break

15 Topological quantum matter and quantum computing (Q&A)

Speaker: Peter Lu (Perimeter Institute)

12:30 p.m. Lunch Break

16 Fitting models to data using Markov Chain Monte Carlo

Speaker: Dustin Lang (Perimeter Institute)

3:00 p.m. Coffee Break

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

Speaker: Dustin Lang (Perimeter Institute)

Tuesday, January 31

18 Topological quantum matter and quantum computing

Speaker: Peter Lu (Perimeter Institute)

10:30 a.m. Coffee Break

19 Effective Field Theory and Symmetries

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.

Speaker: John Donoghue (University of Massachusetts Amherst)

12:30 p.m. Lunch Break

20 Topological quantum matter and quantum computing (tutorial)

Speaker: Peter Lu (Perimeter Institute)

3:30 p.m. Free Time

5:00 p.m. Networking Dinner

Wednesday, February 1

21 Introduction to Colloquium

10:30 a.m. Coffee Break

22 Effective Field Theory and Symmetries

Speaker: John Donoghue (University of Massachusetts Amherst)

12:30 p.m. Lunch Break

23 The structure of translational tilings

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.

Speaker: Rachel Greennfeld (Institute for Advanced Study)

3:30 p.m. Coffee Break

Thursday, February 2

24 Effective Field Theory and Symmetries

Speaker: John Donoghue (University of Massachusetts Amherst)

10:30 a.m. Coffee Break

25 Effective Field Theory and Symmetries (Q&A)

Speaker: John Donoghue (University of Massachusetts Amherst)

12:30 p.m. Lunch Break

26 Effective Field Theory and Symmetries (tutorial)

Speaker: John Donoghue (University of Massachusetts Amherst)

Friday, February 3

27 Effective Field Theory and Symmetries

Speaker: John Donoghue (University of Massachusetts Amherst)

10:30 a.m. Coffee Break

28 Concluding Remarks followed by Group Activity