Computational Algebra Seminar: Voight -- Experiments and expectations in computational algebra

Speaker: John Voight (Sydney)
Title: Experiments and expectations in computational algebra  
Time & Place: 15.00-16.00, Thursday 25 June, SMRI Seminar Room
Abstract: Experimental results have long played a key role in number theory, suggesting 
conjectures, testing heuristics, and guiding the development of algorithms.  At the same 
time, the scale and complexity of modern computations raise new horizons for these 
experiments and new questions for how we use computational algebra software.  In this 
talk, I will discuss several recent examples.  The first is joint work with Blair Butler 
and Edgar Costa on a statistical approach to understanding ranks of elliptic curves.  
The second is joint work with Andreas-Stephan Elsenhans on computing class groups of 
number fields.  I will conclude with some general questions about our expectations for 
computer algebra systems and how these expectations may evolve as formalization and 
AI/machine learning tools become increasingly integrated into mathematical practice.