Bumpless Pipe Dream Builder
Builds bumpless pipe dreams, performs droop moves, computes monomial weights, and exports tikz commands.
Code & interactive tools
Coding stuff, and some tools I built as a vibe engineer. 🥸
Pipe Dream Builder
Builds classical pipe dreams, performs chute moves, computes monomial weights, and exports tikz commands.
InvariantRing^2 Tutorial for Macaulay2
This PreTeXt-powered tutorial walks through the Macaulay2 language using examples from the InvariantRing2 package. It grew out of a course project for MATH 509: Advanced commutative algebra and scheme theory taught by Jarod Alper. I learned about the PreTeXt language from Francesca Gandini.
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Bruhat Graph Builder
Builds Bruhat graphs for $\mathcal S_n$.
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Real lines in a real pencil of real quartic surfaces
A GIF displaying 20 real lines in a real pencil of quartic surfaces, generated using Mathematica. Some lines got plotted on the same surface due to numerical stability issues.
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27 Lines Visualizer
27 Lines, 36 double sixes, and 45 tritangent planes on the Clebsch cubic surface.
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Brackets for Macaulay2
During the Macaulay2 workshop at UMN (2023), I contributed to the Brackets package, which reduces classical $SL_n$ invariants called bracket symbols.
Notes & translations
These are my notes and slides for various talks and seminars. Most have not been proof-read, and correctness is NOT guaranteed.
- WAGS Lightning Talk and Poster
- Monodromy of the Circles of Apollonius
- Cheatsheet for Toric Varieties
- Graduate student talk at WDRP Seminar
- Lightning Talk at Macaulay2 Workshop, Tulane
- Commutative Algebra Notes
- Plücker's Formula and Monodromy of Flexes of Plane Curves
- Lightning Talk at UW Combinatorics and Geometry Seminar
- Degeneracy Loci and Double Schubert Polynomials
- Freudenthal's Magic Square
- Intersection Homology
- Useful Tex Symbols
- Brieskorn (1968) Rational Singularities
- Gromov–Witten Invariants
- Intersection Theory · 3264 and All That
- Equivariant K-Theory — DubTop Seminar (May 2024)
- Intersection Theory · Variations on 27 Lines
- 27 Lines via Bott Residue Formula — 1-2-3 Seminar (Feb 2024)
- Algebraic K-Theory — SAAG (Dec 2023)
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WAGS Lightning Talk and Poster
Slides for my lightning talk at WAGS, University of Oregon.
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Monodromy of the Circles of Apollonius
Notes for the monodromy of the eight Circles of Apollonius, based on the paper Theta Characteristics on Algebraic Curves (Harris 1982).
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Cheatsheet for Toric Varieties
Notes for a reading group on Toric varieties.
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Lightning Talk at Macaulay2 Workshop, Tulane
Slides for my lightning talk at the Macaulay2 Workshop at Tulane, April 2025.
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Commutative Algebra Notes
Here are the notes I took for the first two weeks of MATH 509: Advanced Commutative Algebra and Scheme Theory
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Plücker's Formula and Monodromy of Flexes of Plane Curves
Notes for a learning seminar on “Galois = Monodromy,” based on Galois Groups of Enumerative Problems.
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Lightning Talk at UW Combinatorics and Geometry Seminar
Slides for my lightning talk at the UW Combinatorics and Geometry Seminar.
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Degeneracy Loci and Double Schubert Polynomials
Notes for a seminar talk on degeneracy loci formulas and double Schubert polynomials, based on Section 5.4 of Introduction to the Cohomology of the Flag Variety (Billey-Gao-Pawlowski 2025).
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Freudenthal's Magic Square
Class talk on the exceptional Lie algebras and Freudenthal’s magic square for MATH 507: Algebraic Structures taught by Julia Pevtsova. Delivered with Zachary Wallace-Wells, Zawad Chowdhury, and Bry...
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Intersection Homology
Notes from my November 2024 talk in the eCHT Kan Seminar on intersection homology and perverse sheaves.
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Useful Tex Symbols
A summary of LaTEX math commands I found on the internet.
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Brieskorn (1968) Rational Singularities
English translation of Egbert Brieskorn’s 1968 paper on rational surface singularities.
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Gromov–Witten Invariants
Expository talk given at eCHT Quadratic Curve Counting Seminar
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Intersection Theory · 3264 and All That
MATH 583C notes summarizing the enumration of 3264 conics tangent to 5 given conics in $\mathbb P^2$.
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Equivariant K-Theory — DubTop Seminar (May 2024)
A shallow introduction to several perspectives on equivariant K-theory, with examples and computations. DubTop seminar.
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Intersection Theory · Variations on 27 Lines
MATH 583C lecture notes summarizing different ways of enumerating the 27 lines on a cubic surface.
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27 Lines via Bott Residue Formula — 1-2-3 Seminar (Feb 2024)
Counting the 27 lines on a smooth cubic surface using Atiyah-Bott localization. Includes a 3D model of the Clebsch cubic surface.
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Algebraic K-Theory — SAAG (Dec 2023)
An overview of foundations and computations in algebraic K-theory for the Student AAG Seminar.
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A Theorem a Day
11-20-2025
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Neural Networks with Math
I contributed to Linhang Huang's blog Neural Networks with Math, where we unpack the mathematical ideas behind deep-learning architectures. Here are some notes for the G-CNN architecture: Group Eq...