How Often Does a Polynomial Take Squarefree Values? by Manjul Bhargava

Explore a fascinating lecture on the frequency of polynomials taking squarefree values, delivered by Manjul Bhargava at the ICTS at Ten event. Delve into the concept of squarefree numbers and their significance in mathematics. Examine the scientific method's role in validating theoretical results against experimental data. Uncover the heuristic explanation behind the 6/π² probability of a random integer being squarefree. Investigate the natural progression to studying squarefree values of polynomials and current knowledge in this area. Learn about squarefree values of polynomial discriminants, both with and without the ABC conjecture. Conclude with insights on discriminant polynomials and participate in a Q&A session to deepen your understanding of this intriguing mathematical topic.

ICTS at Ten
How often does a polynomial take squarefree values?
Happy Birthday ICTS!
Squarefree numbers
Scientific Method: Does the theoretical result agree with experiment?
Why 6/pie2? Here is a heuristic explanation:
Actual proof?
Natural next question: Squarefree values of polynomials
What is known?
Squarefree values of polynomial discriminants without ABC
Squarefree values of discriminant polynomials
Q&A