This is the personal website of Abhimanyu Pallavi Sudhir. I am a second-year undergraduate at Imperial College, London, studying the G103 (Mathematics, 4YFT MSci) course (Sep 2018 - Jun 2022).
The Winding Number
The Winding Number (2016-present) [website] is the central, organized platform where I post stuff I find academically or intellectually interesting. The articles are focused on key insights, motivating principles or aha moments fundamental to the topic. Topics range from physics to machine learning to philosophy. Some example articles:
- Sigma fields are just Venn diagrams
- What's with e^(-1/x)? On smooth non-analytic functions: part I
- Three domains of knowledge
- Machine learning as function approximation; statistical and neural motivations
- Fractional derivatives (2018-19): I observe that the Grunwald-Letnikov derivative fails to converge even for some elementary functions, contradicting a theorem that seemingly implies that it equals the Riemann-Liouville fractional derivative. I construct a "principal value" for the GL derivative for the theorem to be true in general and lay out directions for future work [arXiv 1] [arXiv 2].
- Generalized determinants (2013-14, 2019): I derive a generalized determinant for non-square matrices and derive some of its properties [paper 1] [paper 2] [review paper].
- On tensors (2012): I unknowingly rediscover tensors and tensor products, which I call "matrices in unit vector notation" [paper].
- Lean (active 2018-19): I formalized some mathematics for Microsoft Research's Lean formal proof verification system, some of which has been accepted into the Lean central math library, such as: [irrational.lean] [filter_product.lean] [hyperreal.lean]. Other significant things I did here include formal sums of divergent sequences [Github] [StackExchange] and getting Lean to mark a first-year Imperial math exam [Github] [Xena blog] [Reddit post].
- PhysicsOverflow (active 2014-17): a community peer review and physics discussion forum I co-founded and moderated for a few years [Website] [APPN White Paper] [Wikipedia].
- MathJax Kannada (2013-14, 2017-18): I translated the MathJax software into Kannada [TranslateWiki].
- Minor but interesting code I've written:
- Continuous Bayesian inference (2019): An RShiny applet to demonstrate Bayesian inference from a continuous stream of data. Demonstrates the principles of commutative probability [Applet].
- Very old stuff
- abhi99ps (~2012): A youtube channel where I recorded some videos on math I didn't understand [Youtube, defunct].
- Psi Epsilon (~2012): A blog where I wrote some articles on math I didn't understand [Wordpress.com, defunct].
- Some book (~2012): A word document where I wrote a book on math I didn't understand.
If you want to contact me, leave a comment on The Winding Number about page.
My profiles on various websites:
- Technical platforms: [Github] [Math Stack Exchange] [Physics Stack Exchange]
- Professional platforms: [LinkedIn]
- Miscellaneous: [Pinterest] [Youtube] [Reddit]
- Imperial College London (2018-22): G103 MSci Mathematics (4-year, full time)
- Dhirubhai Ambani International School, Mumbai (2013-18): IB Diploma 2018, IGCSE 2016
- NUS High School of Mathematics and Science, Singapore (2012-13)
- Bukit View Primary School, Singapore (2006-11)
Stuff I wrote for school projects, conferences, etc.
- WIMP 2020 (Lie theory: the topology of groups)
- UROP 2019 (Highlights of Lie theory)
- IMA TMT 2019 (On fractional derivatives)
- End-of-year project 2019 (Hyperreals and ultraproducts)
Full resume: [CV]