In addition to my studies of the core olympiad curriculum of the IMO, I have been undergoing the apprenticeship in following areas under the guidance of my mentor Yaashaa Golovanov. Additionally, I have earned over 75 international honors, Medals, and Distinctions of which 20 are in the contests of the USA, UK, Canada, and Australia.
Study of Modern Algebraic Structures: groups, rings & modules, fields & galois theory, commutative algebra, representation theory and homological algebra: This is a year long supervised learning under the guidance of my mentor. Our goal is to under these listed topics and attempt to solve good deal of exercises from the textbook: Notes on Abstract Algebra, Richard Elman, UCLA. Here is my current typed report of this ongoing rsearch work.
Knot Theory: This year paper of the BMT (Berkeley), led me to study of Knot theory. I am currently doing a supervised reading of Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory. Here you can access papers and solutions (that we submitted) for the two edition in which I have participated as a member of the Team AMMOC.
Probability, Central limit theorem, and Markov Chains: This years paper of the Caltech Math Meet, where I and Madani led our team to remarkable victory--top 10 place in the power round. This is the solution file that I and Madani prepared, by and large, because this year other team mates were genuinely occupied with their other serious academic affairs.
Axiomatic Set Theory and Continuum Hypothesis: I am expanding upon the paper of the PUMAC, 2025, wherein we were placed in the first quartile. I participated in the past two editions of PUMAC and here are the solution files of our Team. My goal is to read Herbert B Enderton's Elementary Set Theory. I have already finished first five chapters of this book. By the word "finish", we typically mean to convey that we have understood proofs of most of these theorems and have attended large number of exercises whose solutions I discussed with my supervisior.