Groups from Elliptic Curves - Isomorphism Testing and the PORC Conjecture

Explore the intricate connections between elliptic curves and finite group theory in this 43-minute mathematical lecture. Delve into a specific family of finite groups characterized by class 2 and exponent p (where p is prime) that precisely encode smooth cubic curves in the plane. Learn about collaborative research on isomorphism testing methods for groups within this family, and discover how these mathematical structures relate to Higman's renowned PORC (Problems of Recognizing Certain Groups) conjecture. Gain insights into advanced algebraic geometry and group theory concepts while understanding the computational challenges involved in distinguishing between different group structures and their geometric interpretations.