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Hector Pasten, Queen’s University

“Modular forms, ABC and effective unit equation”

In this talk I will give a brief overview of a known approach to the ABC conjecture using modular forms. Then I will explain how this approach actually gives a partial result for the ABC conjecture and Szpiro’s conjecture. As a consequence, we will obtain a new effective proof of the finiteness of solutions to the S-unit equation, which does not involve linear forms in logarithms. This is joint work with Ram Murty.