RefacteAbout Henry Shin
Hello, I’m Henry.
I’m a mathematician working independently in San Diego. Refacte is where I explore how changing what we track, compare, or allow can make a difficult interaction calculable.
Changing what becomes elementary
A recurrence couples two previous values. A well-chosen weighted difference can turn that interaction into a quantity that updates on its own. For a finitely generated subgroup of a free group, a graph of labelled moves can turn membership into a path test. I’m drawn to the invention behind such changes: finding the viewpoint in which the mechanism becomes available to calculation.
I call this Refactor — changing what becomes elementary. I want to show how the new working objects are found, why their operations are valid, and what they let us conclude. A construction, a test, or a proof that a proposed repair cannot work can each be a useful result.
The mechanism calculi develop this approach at different scales: constructing a basis of tensor chains, exposing a hidden cubic, or reducing graph labels to circuit data. The reading paths connect the smaller examples to these longer arguments. The wider theory is there when it answers a further question.
Mathematical background and research
I studied mathematics at Harvard with Richard Taylor. My work has ranged across group theory, algebra, additive combinatorics, and geometric analysis.
My current paper, Finite generation of permutation twisted cohomology, proves a finite-module theorem for representation-sphere section rings and applies it to the geometry of permutation complexes. The research collection gives the full statements, earlier papers, publication details, and corrections.
Writing and intellectual life
A useful explanation gives another person something they can work with. My essays follow that concern into judgment and intellectual life: what an account preserves, what a conclusion warrants, and what lets people question, correct, and continue an inquiry.
What a New Proof Makes Possible begins with the new operations an argument supplies. When a Description Becomes a Verdict asks whether a description supports the judgment made from it.
Mathematical Life in the Age of AI carries the question into learning, assistance, credit, and shared work. The other essays examine how expertise is sustained and how institutional judgments remain open to challenge. The cross-reading guide connects these questions to particular calculations.
Film interpretation offers another setting in which to examine what an explanation earns. In The Authority of a Vision, I follow the relations between knowledge, belief, and political allegiance in Villeneuve’s Dune.
Other pursuits
I make patterns on large twisty cubes, working out commutators that rearrange small groups of pieces. The pleasure is in composing the moves into a picture without undoing what is already in place.
I also play StarCraft: Brood War and Overwatch. I enjoy reading a changing game, coordinating with teammates, and finding where the next action matters. The Interests page has photographs, game recordings, and more about these pursuits.
Correspondence
If an argument here connects with your work, or you see a step that needs repair, I’d be glad to hear from you.