Unconditional Class Group Computation and Applications

Explore a comprehensive lecture on unconditional class group computation and its applications in this 56-minute talk by Michael Jacobson from the University of Calgary. Delve into topics such as the class group and unit group, index-calculus in the imaginary quadratic case, and the role of the Generalized Riemann Hypothesis. Examine the importance of class groups in cryptography and testing unproved conjectures. Learn about class group tabulation, including previous tabulations, verification methods, and batch computation techniques. Investigate real quadratic fields and complex cubic fields, and consider potential quantum improvements for unconditional tabulation. This Fields Institute presentation offers valuable insights for mathematicians and cryptography enthusiasts interested in advanced number theory and its practical applications.

Intro
The Class Group and Unit Group
Index-calculus (Imaginary Quadratic Case)
Where do we need GRH?
Summary
Cryptography
Testing Unproved Conjectures
Class Group Tabulation
Previous Tabulations (Highlights)
Verification (Ramachandran, J., Williams 2006)
Computing ha in Batch (Mosunov, J. 2014)
Real Quadratic Fields
Complex Cubic Fields
Quantum Improvements for Unconditional Tabulation?