Aadrita.space
I am a third year (final year) student pursuing a B.Sc. (Hons) in Mathematics and Computer Science at Chennai Mathematical Institute, India.
My interests have shifted a lot over the last few years, but I do seem to be consistently interested in things which Conway was, and generally in sort of discrete, combinatorial things.
I had an interest in Knot Theory from before joining CMI. This led me to doing a summer reading project on Combinatorial Group Theory, and taking an additional course on Combinatorial Group Theory in my third semester. After that, I did a short reading project on Knot Theory, mostly reading about Virtual Knots. I was also interested in Combinatorial Game (note 'Game' and not 'Group') Theory from before joining CMI. I am still interested in both of these to some extent, but haven't had much time to pursue them.
My favourite courses were probably Discrete Mathematics, Theory of Computation, and Algebra II, which covered Group Theory.
In the summer, I did a research project at TIFR-CAM, which [.......]. I came across Heesch's problem
I am currently trying to do research in automatic sequences and on automatic numbers
This semester, I have started to give talks. Link to slides/references (nothing is LaTeXed):
- The Word Problem, 31 July 2025: An introduction to free groups, group presentations, the proof of the Word Problem (main idea is to simulate the halting problem for Turing Machines with groups) first for semigroups and then for groups, looking at interesting related theorems/proofs (Adian-Rabin Theorem etc.), HNN extensions and looking at some particular examples of groups where the word problem is solved (e.g. residually finite groups, Garside Normal Form for braid groups etc.)
- On the Heesch Number for the Hyperbolic Plane, 12 August 2025: The Heesch Problem is an open problem in tiling concerning the maximum number of 'layers' a shape can surround itself by in the real plane. Its analogue for hyperbolic space has been resolved. The talk was also a rough introduction to Hyperbolic Space.
- Hilbert's Tenth Problem. 29 August 2025: More or less presenting the first five chapters of 'Hilbert's Tenth Problem' by Yuri Matiyasevich (a great book!), which concerns the proof of undecidability of solvability of Diophantine Equations. I tried to present things as they were found chronollogically and to highlight the people and the story behind the development of the proof.
I have also been trying to run a reading group on Combinatorial Game Theory along with another student. We are currently following these notes by Prof. Urban Larsson, and plan to later move on to a combination of 'Winning Ways for your Mathematical Plays' (Berlekamp, Conway, and Guy), 'Lessons in Play: An Introduction to Combinatorial Game Theory' (Albert, Nowakowski, Wolfe) and hopefully even do some research on the open problems presented in 'Combinatorial Game Theory' (Siegal). I would also like to cover learning to use the CG-Suite software developed by Siegal :)
I enjoy programming. Here are some programmes relating to math which I have written:
- Tiling Extensions
- Dynamical Systems, Height Functions (1)
- Dynamical Systems, Height Functions (2)
- Dynamical Systems, Height Functions (2)
...and more tangentially:
- Conway's Game of Life
- Bagh-Chal
- Surreal Numbers