talks on topological data analysis, cheeger's inequality

I did two math/theory CS seminars this semester. One was on Simplicial Algebra, and one was on Spectral Graph Theory. I gave some talks for these seminars and wanted to put them here. Really massive thank you to Ivan, Ekene, and Binghui for leading them! I had a great time. :)

The first talk I gave is about topological data analysis and inference; specifically, about geometric sampling, metric measure spaces, and probability theory in barcode space. It follows sections 3.2–3.3 of Rabadan and Blumberg's Topological Data Analysis for Genomics and Evolution. You can find my notes here.

The second is about Cheeger’s inequality (inequalities are always pretty cool tbh), which is a fundamental result in spectral graph theory connecting the second smallest eigenvalue of the graph Laplacian with the conductance of a graph, both of which help us characterize a special type of graph called an expander. I made a presentation, which you can flip through below. You can also find this presentation, as well as the other talks from the Spectral Graph Theory seminar, on Columbia TCS group’s website here.

The third one is about an application of tools from topological data analysis to viral evolution, specifically viral recombination in HIV. It follows pages 303–324 from Rabadan and Blumberg. It’s pretty cool to see how barcode diagrams and zigzag persistence diagrams might actually be useful. You can find my notes here.

some solutions to øksendal’s stochastic differential equations + my ‘talk’ on the black-scholes formula

This spring, I did the Directed Reading Program (DRP) with the Math department; undergrads get paired with a PhD student to read a math book together. Columbia pays for the book. :)

Richard and I read the book on the right. (Thank you Richard for bearing with me!!)
We also worked through a few exercises, and I typed them up this week along with some notes to understand stuff a bit better. Since Øksendal’s own solutions are quite sparse, I wanted to post them here:

Also, I prepared a brief talk about the Black-Scholes formula derived in Chapter 12:

The Debut Venture Fund Landscape

The process to raise a new venture fund has largely been shrouded in mystery and guesswork —what kind of people successfully raise new funds from LPs? What experience do they have? How old do they tend to be? And, most importantly: Are any of these factors correlated with how much money they end up raising? Jaclyn and I analyzed data from Pitchbook to shed some light on the debut venture fund landscape. Check the article out here:

 
 

Remark: Did these analyses by making simple linear regressions before I learned more cool econometrics stuff, or knew anything about causal inference, really… Recently been wanting to mess with this dataset. Will write an update if it happens!

Obsidian as a second brain

This winter break, I travelled to CDMX with Katya and Elliott. And I think this is a funny origin story: We were at the Museo Nacional de Antropología, and saw Aztec obsidian crafts which prompted Elliott to bring up the app that’s also called Obsidian. I’ve been hearing about/playing with the idea of creating and storing a second brain for a while now (notably from Ali Abdaal’s YouTube videos on Roam), and discussing it with them was the final push that made me decide to actually give it a try. People who know me know that I’m big on note-taking and knowledge management systems, so I wanted to take advantage of winter break to start using Obsidian.

update

Check out Robert’s two-part series on Obsidian! He describes his specific approach to second brain-ing called molecular notes, and links to a program he wrote to incorporate spaced repetition into Obsidian—it’s a complete game-changer. It’s very good so please go read it. (I also got a shout-out at the end which made me very happy so you should also go read it for that reason.)

update 2: 1 year in

I’ve been using Obsidian for around a year now, and it’s become my main PKM for storing/playing with the concepts I’m learning about. I’ve finally been able to place a finger on why I like Obsidian so much—it’s irreverent. It’s a really powerful tool to represent any type of idea or relationship (Zettelkasten); you can create a note/node on literally anything. For a sense of what I mean, here’s a snapshot of what my vault looks like now through the “valuation” note!:

litigation finance article for the law review

Litigation funding is when a third-party firm helps a plaintiff to finance their civil lawsuit, in exchange for a share of the potential settlement. It’s an emerging sector with a lot of potential, but its activity in New York is restricted. Over the summer, I wrote an article about this for the Columbia Undergraduate Law Review (CULR) and it just got published! Check it out here:

litigation%2Bfunding.jpg

Litigation Funding: The Case for New York to Revise Section 489
culawreview.org/journal/litigation-funding-the-case-for-new-york-to-revise-section-489

The potential of litigation finance and the current restrictions it faces, specifically with regards to New York Judiciary Law Article 15 Section 489.

Update: It’s been 3 days and for some reason, my article is the first search result when you Google “S489 New York Champerty”! This is really cool, so I’m going to put the screenshot here as a commemoration.

 

short story anthology publication

Note: Publishing this post retrospectively, because I forgot to actually make this post in May 2020.

Over the past year, I’ve been working with the rest of the SAS AT Writing and Publication cohort to publish Up to No Good, an anthology of stories about villains. If you buy it, you’ll find that the first one of those short stories was written by yours truly. My story is about Krampus, a Christmastime villain (which is maybe fitting for me because my birthday is on Christmas).

You can buy the book from Barnes and Noble, and read my short story below:

My Philosophy Essay Got Published

Questions is a peer-reviewed journal of philosophy sponsored by the American Philosophical Association. For their most recent issue, they invited responses to the theme of “What is your favorite philosophical problem?”

I received a similar prompt in a timed AP Lang. argumentative essay, so I built on what I wrote in class and submitted it as a short article to Questions. I’m excited to say that it’s been accepted and published! Check it out:

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Snapshot taken from the Philosophy Documentation Center.

 

Interning at NUS

Recently, I had the privilege of interning with the N.1 institute at the National University of Singapore (NUS). They’re developing a platform called CURATE.AI, which uses artificial intelligence to recommend drug dosages for patients. My internship was led by the wonderful Dr. Agata Blasiak, Dr. Theodore Kee, and Prof. Dean Ho.

This was one of the most insightful experiences I’ve had throughout my high school career. I want to share what I’ve learned, so here is an excerpt of my notes:

Singapore’s Ageing Population & Sector Implications (Dr. Daniel Teh)

  • Problem: Singaporean population growing older & less healthy due to disease. 2 strategies:

    • Invest into researching each disease

    • Invest into ageing, as that's the fundamental factor that underlies all of these diseases

  • Increasing demand in market for ageing-related treatments, and not just in Singapore

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rip socratic.org

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Socratic, a website where people can ask and answer academic questions, will close to new questions and answers on August 15. I've been a regular answerer in the Chemistry section (with a brief foray into math until I realized that using KaTeX for actual math angers me even more than for chemistry—maybe someday I’ll learn). You can see my old answers here. As of today, it looks like I've been able to reach 300,000 people in my short stint:

Socratic has a special place in my heart because, there, I felt like I was helping the world understand the things I am so passionate about; the things I am so eager to share. It was a win-win situation: I got to talk about Chemistry and help other people along the way. 

I started contributing sometime in my sophomore year, and it's sneaked its way into my daily routine since.
A daily, repeating task in my mental to-do list has always been "Answer a Socratic question." I do it every weekday after I come home from school; on weekends, it's usually the first thing in the morning.

And, since I feel like I've been ticking that box off every day since the beginning of time, I think a small part of me will die on August 15. 

But I guess the death of Socratic will be the beginning of something beautiful. I'm hesitant but excited to be working with a group of other excited people on a continuation of Socratic. I’ll write an update if we make something.