Papers and slides for Euler Circle Independent Research and Paper Writing, Summer 2022 Session 1

• Aashir Mehrotra: Young diagrams and tableaux Paper Slides
• Adanur Nas: Pell's equation Paper Slides
• Agniv Sarkar: Mordell-Weil and Billing-Mahler theorems Paper Slides
• Arav Bhattacharya: Linear algebra in infinite dimensions Paper Slides
• Arpit Mittal: On the representations and classification of simple complex Lie algebras Paper Slides
• Batyrkhan Sakenov: Model theory, decidability of Euclidean geometry Paper Slides
• Benjamin Hillard: Evolution of fast integer multiplication algorithms Paper Slides
• Brian Hong: An elementary analysis of the Erdős-Kac central limit theorem Paper Slides
• Catherine Li: Random graphs and simplicial complexes Paper Slides
• Eshan Bajwa: The Burnside problem Paper Slides
• Ethan Liu: Cayley graphs Paper Slides
• Eugenie Cha: Riemann surfaces, Teichmüller spaces, and Fenchel-Nielson coordinates Paper Slides
• Ezra Furtado-Tiwari: The Birkhoff ergodic theorem Paper Slides
• Fajr Fatima: Random permutations using analytic combinatorics Paper Slides
• Ganesh Sankar: Diophantine tuples Paper Slides
• Isaac Sun: Euler-Maclaurin formula Paper Slides
• Jinfei Huang: The Rogers-Ramanujan identities Paper Slides
• Josef Elyoussoufi: An introduction to sandpiles Paper Slides
• Kaitlyn Zhang: The generalized Stokes' theorem Paper Slides
• Keun Hyong Kwak: Fractal dimension: a paradox of finite and infinite Paper Slides
• Kevin Shi: Exploring Ehrhart theory Paper Slides
• Krishna Sidde: The Bombieri-Vinogradov theorem Paper Slides
• Leo Ouyang: Diophantine approximations Paper Slides
• Logan Gilbert: The Galois correspondence Paper Slides
• Marco Troper: Analyzing results of Doob's martingale convergence theorem Paper Slides
• Matias Relyea: Proofs and applications of quadratic reciprocity Paper Slides
• Matías Wolosiuk: Model theory and the Ax-Grothendieck theorem Paper Slides
• Matthew Leung: The Black-Scholes model Paper Slides
• Medha Ravi: Origami constructable numbers Paper Slides
• Nandana Madhukara: Hyperbolic 3-manifolds and their constructions Paper Slides
• Nicholas Flach: Group theory of the Rubik's cube Paper Slides
• Nicole Shen: Combinatorial species Paper Slides
• Prishita Dharampal: The axiom of choice and its consequences Paper Slides
• Samvar Shah: Van der Waerden's theorem Paper Slides
• Sarthak Mitra: Posets and the applications of the Möbius function Paper Slides
• Shivaani Venkatachalam: Integral geometry Paper Slides
• Thomas Catalan: An overview of topics in quantum error correction Paper Slides
• Tomiris Kurmanalina: Property and application of Stern-Brocot tree Paper Slides
• Tudor Braicu: An introduction to Ramanujan graphs Paper Slides
• Varun Rao: A historical introduction to transcendental number theory Paper Slides
• Vincent Cheng: Hyperplane arrangements Paper Slides
• Wilson Chen: Class groups of quadratic forms Paper Slides
• Woong Choi: Circumscribing characteristics of Jordan curve Paper Slides
• Youze Zheng: Evolutionary dynamics and its real-world applications Paper Slides
• Yudhister Kumar: Nonstandard methods and applications in Ramsey theory Paper Slides
• Yuxuan Chen: Calculus of variations and further Paper Slides
• Zipeng Lin: Stone-Weierstrass theorem and its forms on different structures Paper Slides