Calendar

WeekLecture I InfoLecture II InfoExercisesImportant Info
Week 1
02/03 - 02/07
Lecture 1 (Mon, 02/03)
Course Overview and Intro to Finite Group Theory I

Readings:
  • Dresselhaus Ch. 1.1 - 1.7
  • Dresselhaus Ch. 2.1
  • Weiler - Preface & Appendix B
  • GDL Ch. 3 & 7
Lecture 2 (Wed, 02/05)
Intro to Finite Group Theory II

Readings:
  • Dresselhaus Ch. 1.1 - 1.7
  • Dresselhaus Ch. 2.1
  • Weiler - Preface & Appendix B
  • GDL Ch. 3 & 7
Exercises:
This week only.
* Zoom link for 11-noon and 2-3pm Friday recitations.
* Zoom link for Friday Office Hours 4-6.
* No OH Wednesday.
Week 2
02/10 - 02/14
Lecture 3 (Mon, 02/10)
Linear Algebra: Vector spaces, nullspaces, orthogonality, Kronecker product and change of basis

Readings:
  • Strang 1, 3, 4, 6, 7
  • Laub Ch 13.[1,2,3]
Lecture 4 (Wed, 02/12)
Representations of Finite Groups I: Reps, Irreps, Schur's Lemma, Wonderful Orthogonality Theorem

Readings:
  • Dresselhaus Ch. 2.2-8
Exercises:
Week 3
02/17 - 02/21
Lecture 5 (Tue, 02/18)
Representations of Finite Groups II: Character of Representations

Readings:
  • Dresselhaus Ch. 3.[1-.7]
Lecture 6 (Wed, 02/19)
Representations of Finite Groups III: Tensor Products and Decompose to Irreps

Readings:
  • Dresselhaus Ch. 3.[1-.7]
  • Dresselhaus Ch. 6.[3, 4, 5]
  • Georgi Ch. 1.[15, 16, 17]
  • Serre Ch. 1.5 & 3.2
  • Georgi Ch. 1.15, 1.16
Exercises:
Monday, Feb. 17 is President's Day Holiday. Tuesday, Feb. 18 -- Monday schedule held

Recitation Slides
Week 4
02/24 - 02/28
Lecture 7 (Mon, 02/24)
Vibrational Modes I

Readings:
  • Dresselhaus Ch. 8
  • Wilson Chs 1, 2, 5, 6, 7 (optional)
  • Dresselhaus Ch. 11 (optional)
Lecture 8 (Wed, 02/26)
Vibrational Modes II

Readings:
  • Dresselhaus Ch. 8
  • Muller Ch. 15 (optional)
  • Muller (General Resource)
Exercises:
Week 5
03/03 - 03/07
Lecture 9 (Mon, 03/03)
Intro to Lie Algebra

Readings:
  • Georgi Ch. 2
  • Schwichtenberg Ch 3
Lecture 10 (Wed, 03/05)
SO(2) and SO(3) and their Representations

Readings:
  • Georgi Ch. 3
  • Schwichtenberg Ch. 3
Exercises:
Week 6
03/10 - 03/14
Lecture 11 (Mon, 03/10)
O(3), Cartesian Tensors, and Spherical Harmonics I

Readings:
  • Dresselhaus Ch. 18
  • Hess (general resource)
Lecture 12 (Wed, 03/12)
O(3), Cartesian Tensors, and Spherical Harmonics II

Readings:
  • Dresselhaus Ch. 18
  • Hess (general resource)
Exercises:
Exam Practice Problems:
* 2024 Practice Exam 1:
(blank | solns)
* 2024 Exam 1:
(blank | solns)
Note: Skip all problems on group conv.

Recitation Slides
Week 7
03/17 - 03/21
Lecture 13 (Mon, 03/17)
Exam Logistics and Review of Lec. 1-8
Lecture 14 (Wed, 03/19)
Exam 1 (Lectures 1-8)
Readings:
  • See Exam Details HERE
Recitation Slides

Exam 1 Solutions
MIT Spring Break 3/25 - 3/29
Week 8
03/31 - 04/04
Lecture 15 (Mon, 03/31)
Signals on Spheres and Fourier Transforms on Groups I

Readings:
  • Driscoll and Healy (1994)
  • FFTs on the Rotation Group
  • 3Blue1Brown - Fourier Transform
  • Steve Brunton's Video on Fourier Transform...
  • ... and Convolution Integrals
Lecture 16 (Wed, 04/02)
Signals on Spheres and Fourier Transforms on Groups II

Readings:
  • Applications of Bispectra etc.
  • Symphony -- Appendix F (using multiple SH channels)
Exercises:
Recitation Slides
Week 9
04/07 - 04/11
Lecture 17 (Mon, 04/07)
Group and Steerable Convolution I

Readings:
  • Spherical CNNs (ICLR 2018)
  • Video on Scalable and Equiv. Spherical CNNs (ICLR 2023)
Lecture 18 (Wed, 04/09)
Group and Steerable Convolution II

Readings:
  • Group Equiv. Conv. Nets
  • Tutorial on Group Convolutions by Dr. Rui Wang for 6.S966 Spring 2024
  • Colab for Tutorial
  • UvA DL Notebooks - Group Conv
Exercises:
Recitation Slides
Week 10
04/14 - 04/18
Lecture 19 (Mon, 04/14)
Group and Steerable Convolution III

Readings:
  • Dresselhaus Ch. 4.[1-5]
  • Cohen16 [2.5: Table 1]
  • Harmonic Networks (CVPR 2017)
  • Tensor Field Networks (2018)
  • Clebsch-Gordan Nets (NeurIPS 2018)
  • 3D Steerable CNNs (NeurIPS 2018)
  • Theoretical Aspects of Group Equiv. NNs
  • Cesa22 [2.1: Example 2]
  • Weiler19 [2.5]
Lecture 20 (Wed, 04/16)
Equivariant Activations and Attention

Readings:
  • 6.390 IntroML Ch on Transformers
  • Attention is all you need
  • Equiformer: Equivariant Graph Attention Transformer for 3D Graphs (ICLR 2023)
  • EquiformerV2 (ICLR 2024)
  • Vector Neurons (ICCV 2021)
Exercises:
Recitation Slides
Exam Practice Problems:
* 2024 Practice Exam 2:
(blank | solns)
* 2024 Exam 2:
(blank | solns)
Note: Go back to Practice Exam 1 and Exam 1 and look at group conv. questions.
Week 11
04/21 - 04/25
Lecture 21 (Wed, 04/23)
Exam 2 (Lectures 9-20)
4/21 is a Patriots' Day! No class Monday!
Drop Date is Tuesday 4/22!

Monday Office Hours Remote: Zoom link here
Week 12
04/28 - 05/02
Lecture 22 (Mon, 04/28)
How to product your tensors for great good.
Lecture 23 (Wed, 04/30)
Symmetries were made to be broken.
Week 13
05/05 - 05/09
Lecture 24 (Mon, 05/05)
Symmetry and Physics I: Why condensed matter physicists and friends are obsessed.
Lecture 25 (Wed, 05/07)
Symmetry and Physics II: The Lorentz Group and the Standard Model, i.e. Tess rants about spin 1/2.
Readings:
  • Schwichtenberg Ch 1, 2
Week 14
05/12 - 05/16
Lecture 26 (Mon, 05/12)
Final Exam