This is the personal website of **Abhimanyu Pallavi Sudhir**. I am a fourth-year undergraduate/Master's student 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
- Engineering as the theory of airlocks
- Machine learning as function approximation; statistical and neural motivations

### Research projects

**Agent-based social simulation**(2020-present): Exploratory work on the reformulation of economic concepts in the language of agent-based simulation and reinforcement learning**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

**Reviewer for Advances in Applied Clifford Algebras (Springer)**(2020-present)**Co-founder and moderator of PhysicsOverflow**(active 2014-17) [Website] [APPN White Paper] [Wikipedia].**Machine learning projects (2020-present):**See list at The Winding Number.**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].**Miscellaneous****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].

### 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] [LessWrong]**Professional platforms:**[LinkedIn]**Miscellaneous:**[Pinterest] [Youtube] [Reddit] [Twitter]

### 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.

- SIAM IMA 2021 (A mathematical definition of property rights)
- 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]