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Speaker: Dr. Mike Bennett, University of British Columbia

Title: Distance between squares and perfect powers 

Abstract: The modular method originally developed by Wiles to prove Fermat’s Last Theorem has been subsequently used to treat a variety of classical Diophantine problems. In this talk, I will attempt to describe the strengths and limitations of this approach. As an example, I will survey recent work on the classical Lebesgue-Nagell equation x^2+D=y^n, when the prime divisors of D are restricted to a fixed finite set S. This is joint work with Samir Siksek and, in part, with Philippe Michaud-Jacobs. Our results rely upon a combination of various results based upon the modularity of Galois representations, with bounds for linear forms in logarithms.

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