About Me

I was a PhD student at Harvard between 2018 and 2022. Previously, I did my undergraduate and Part III at Cambridge (2014–2018).

Contact Me

You can email me at dec41@srcf.net.

Adams Spectral Sequence for $tmf$

I have documented the calculation of the Adams spectral sequence of $tmf$ at the prime $2$ here (warning: this downloads a 12MB file behind the scenes).

This calculation was made with computer assistance. There is an online version of the software, and the source can be found on GitHub. See the README on GitHub for technical details.

The software computes the $E_2$ page and products, and propagates differentials via the Leibniz rule. The program is capable of resolving an arbitrary (finite dimensional or finitely generated) Steenrod module and assisting the computation of the associated Adams spectral sequence. It is also designed with the intention to be able to aid other spectral sequence calculations (as long as the modules are over $\mathbb{F}_p$), but no such applications have been coded at the moment. It was initially developed by Hood Chatham and I later joined the development.

The save file for the calculation can be found here, which can be imported into the resolver to reproduce the calculation. (However, doing it on the online version above is unwise)

Steenrod operations

Using an algorithm of Christian Nassau, I calculated some Steenrod operations in Ext of the Steenrod algebra and $A(2)$. The results are documented here, and they go beyond what is in Bruner's tables.

Expository Writings

Some miscellaneous expository writings. The word "expository" refers to the lack of originality, as opposed to any claim of comprehensibility or correctness.

Clicking the title below will lead to a web version of the note, which is an experimental feature — let me know if anything seems broken. Click "pdf" for a downloadable pdf version.

• Construction of synthetic spectra (pdf)
• Adams spectral sequence of $\mathrm{tmf} \wedge \mathbb{RP}^\infty$ (pdf)
• Borwein–Borwein integrals and sums (pdf)
• Homology of the 𝔼_d operad (pdf)
• Complex oriented cohomology theories (pdf)
• Chern–Weil forms and abstract homotopy theory (pdf)
• Introduction to Motivic Homotopy Theory (pdf)
• The Barratt–Priddy–Quillen–Segal theorem (pdf)
• Goodwillie filtration and factorization homology (pdf)
• Bott Periodicity (pdf)
• The Heat Kernel (pdf) ← this is my minor thesis
• Geometric Topology (pdf) ← this is my Part III essay
• Construction of v₁ and v₂ self-maps (pdf)
• Ring Structures on S/p (pdf)
• Global Analysis – Hodge Decomposition Theorem (pdf)
• Clifford Algebra and Bott Periodicity (pdf)
• The Étale Fundamental Group (pdf)
• The Lemniscate Sine (pdf)
• Period 3 orbits (pdf)

Cambridge Course Notes

When I was in Cambridge, I typed up my lecture notes for the courses I attended. They can be found here.

Computer Drawings

As a means of procrastination learning how to use HTML5 canvas, I produced the following drawings/simulations:

• Brownian motion
• Conformal maps

Grid paper

I wrote a web page that produces grid papers. The source code is available on GitHub. Feature requests are welcome.

PDF Cropping

I also wrote a web page that helps you crop PDFs with a specified aspect ratio. Feature requests and bug reports are welcome.

Miscellaneous

• Some Adem relations
• Some LaTeX tricks
• Some formulas about BP

Other Involvements

I co-organized the Bott periodicity seminar during Spring 2019.

I have been on the committee of the Cambridge student societies The Archimedeans, CUPS, the SRCF and the RCSA. I am also a sysadmin of the SRCF.

Privacy Statement

I have a Privacy Statement as required by law (maybe).