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:

### 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

My profiles on various websites:

### 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.

Full resume: [CV]