Squarefree values of discriminant polynomials

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• Marti Oller Riera (Cambridge)
• Tuesday 04 February 2025, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Rong Zhou.

Given a multivariable polynomial with integer coefficients, what is the probability that it takes a squarefree value? This was determined by Granville and Poonen assuming the ABC conjecture, but an unconditional proof remains unknown. We will start the talk by discussing a paper by Bhargava, Shankar and Wang that unconditionally determines a result for the discriminants of monic polynomials of any given degree. In the second part of the talk, we will see how the methods of BSW can be interpreted into a more general framework developed by Thorne, and how they can be used to obtain new results for other families of discriminant polynomials.

This talk is part of the Number Theory Seminar series.

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