Notes
Collections
Physics
On various aspects of theoretical and mathematical physics.
Philosophy
Mostly on the philosophy of science.
Books
Some books I've read recently.
Movies
Some films I've watched recently.
All Notes
Duminil-Copin on AI and Mathematics
First and foremost, it [a mathematical question] is a lighthouse in the night: it illuminates and guides mathematicians in their wanderings.
Generators and Conserved Charges
Symmetries and conserved charges in the Hamiltonian formalism.
Contractions, Lie Derivatives, and Integration
Contracting forms and vector fields, Lie derivatives, integrating forms on submanifolds, and Stokes' theorem.
Symplectic Geometry, Revisited
Rephrasing some earlier results, only this time geometrically.
Miguel Street (1959)
...
Higher-Degree Forms and Exterior Derivatives
Forms of higher degree and the exterior derivative.
Last Year at Marienbad (1961)
Directed by Alain Resnais.
Manifolds, Vectors, and 1-Forms
Manifolds, vectors, 1-forms, and pullbacks/pushforwards.
How Fiction Works (2008)
One way to tell slick genre prose from really interesting writing is to look, in the former case, for the absence of different registers... rich and daring prose avails itself of harmony and dissonance by being able to move in and out of place.
Tensor Spaces and Commuting Actions
The permutation and general linear group have commuting actions on tensor spaces.
Representations of the Permutation Group
Constructing irreducible representations of the permutation group.
Cope - Differences of Opinion
The planet goes on being round.
Ashbery - Late Echo
It is necessary to write about the same old things in the same way, repeating the same things over and over again for love to continue and be gradually different.
Nabokov - Pnin
It surprised him to realise how fond he had been of his teeth.
Meredith - The Illiterate
What would you call his feeling for the words that keep him rich and orphaned and beloved?
A Mind Over Matter (2021)
...
Heaney - Clearances and Postscript
You are neither here nor there, a hurry through which known and strange things pass...
St. Vincent Millay - Love is Not All (Sonnet XXX)
Yet many a man is making friends with death even as I speak, for lack of love alone.
Stoner (1965)
He read and studied, and at last came to find some comfort, some pleasure, and even a ghost of the old joy in that which he did, a learning toward no particular end.
Glück - Reunion
And as he speaks, ah, tenderly he touches her forearm.
Brautigan - At the California Institute of Technology
I don't care how God-damn smart these guys are...
The Invention of Morel (1964)
The habits of our lives makes us presume that things will happen in a certain foreseeable way, that there will be a vague coherence in the world.
Partitions, Young Diagrams, and Tableaux
Keeping track of partitions and permutations.
Oliver - In Praise of Craziness, of a Certain Kind
So, she said, the garden ants could crawl beneath, as under a blanket, and keep warm...
Masefield - An Epilogue
So I trust, too.
Berry - A Meeting
I been eating peaches off some mighty fine trees.
Sarnak and the AlphaZero Test
Mathematics is the understanding, and not the corpus of lemmas and theorems it illuminates.
La Gradiva (2026)
Directed by Marine Atlan.
The Landau Problem
Electrons in two dimensions and the Landau levels.
After Hours (1985)
Directed by Martin Scorsese.
Yi Yi (2000)
Directed by Edward Yang.
Keats - On First Looking into Chapman's Homer
Silent, upon a peak in Darien.
Plutarch - Parallel Lives: Gaius Marius
Tell him, then, that thou hast seen Gaius Marius, a fugitive, seated amid the ruins of Carthage.
The Invite (2026)
Directed by Olivia Wilde.
Borges and Llull - Thinking Machines
On the combinatorics of discovery.
Borges and Rilke - Leopards
You suffer captivity, but you will have given a word to the poem.
Parker and Addonizio - Résumé
You might as well...
Three-Dimensional Oscillators, Revisited
Mixed representations of SU(3) using oscillators.
Is The Oscillator Formalism Complete?
Does the oscillator formalism for higher rank groups furnish all representations?
Symplectic Geometry
The geometry underlying classical mechanics.
The Oscillator Formalism: Higher Dimensions
Extending the oscillator formalism to unitary groups with higher rank.
Canonical Structures
Hamilton's equations, the Poisson brackets, and canonical transformations.
Akhmatova - Forgive Me
Like acrid smoke with lively flame.
Angelou - Come. And Be My Baby
Some people wrap their lives around a cocktail glass.
The Action Principle
The principle of least action.
Hughes - Tired
I'm so tired of waiting, aren't you?
Shakespeare - King Lear, Act 5, Scene 3
Come, let's away to prison. We two alone will sing like birds i' th' cage.
The Oscillator Formalism: Two Dimensions
Using a pair of harmonic oscillators to build up representations of SU(2).
Melville - Moby Dick, Ch. 93
The sea had jeeringly kept his finite body up, but drowned the infinite of his soul. Not drowned entirely, though.
The Noether Current for Electric-Magnetic Duality
Deriving the Noether current for electric-magnetic duality rotations.
Borges - Death and the Compass
Possible, but not interesting.
Calvino - Invisible Cities
Without the stones there is no arch.