Application of Operator Theory for the Collatz Conjecture

Watch this lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar where Takehiko Mori from Chiba University explores innovative applications of operator theory to the famous Collatz conjecture. Learn how C*-algebras can be used to formulate the Collatz problem in three distinct ways: through single operators, two operators, and Cuntz algebra. Discover the mathematical connections established between the conjecture and the irreducibility of associated C*-algebras, with proofs showing how certain conditions either imply or are equivalent to the Collatz conjecture. The presentation includes discussions on generalizing these connections for similar maps through introduced equivalence relations. Mori, whose expertise lies in operator algebras and their applications to dynamical systems, provides valuable insights into this unsolved mathematical problem during this comprehensive 68-minute talk.