Statistics of Number Fields, Function Fields, and 3-Manifolds

Explore a conference lecture from the Arithmetic Quantum Field Theory Conference where Harvard professor Melanie Matchett Wood delves into the statistical distributions of class groups and fundamental groups across number fields, function fields, and 3-manifolds. Examine the connections between Cohen-Lenstra-Martinet conjectures on number field class group distributions and their analogous manifestations in curves over finite fields and 3-manifold fundamental groups. Learn about collaborative research findings with Liu, Zureick-Brown, and Sawin regarding these distributions, particularly focusing on finite field curves and 3-manifolds. Discover how mathematical concepts and approaches have been exchanged and adapted between number fields, curves over finite fields, and 3-manifold contexts to advance understanding in these interconnected areas of mathematics.