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

### Research projects

**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].

### Projects archive

**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].**Sudoku solver**(2019): A Sudoku solver based on Crook's algorithm (i.e. the way that humans solve it), written in Python and Javascript ports [Github] [Live on Khanacademy].

**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.

### Me elsewhere

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]

### Education

Schools:

**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]