# Philipp Habegger E Praeger - The Number of Rational Points on a Curve of Genus at least 2 - Pure Mathematics Colloquium

Dates: | 5 March 2021 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers |

Speaker: | Philipp Habegger E Praeger |

Speaker: Philipp Habegger E Praeger, University of Basel

Series: Pure Mathematics Colloquium

Date and Time: Friday 5th March 2021, 3pm - 4pm

Title: The Number of Rational Points on a Curve of Genus at least 2 Abstract: By Faltings's Theorem, formerly known as the Mordell Conjecture, a system of multivariate polynomial equations that defines a smooth projective curve of genus at least 2 has at most finitely many rational solutions. Vojta later gave a second proof. Many authors, including Bombieri, de Diego, Parshin, RĂ©mond, Vojta, proved upper bounds for the number of rational solutions. I will give an overview of Vojta's approach to the Mordell Conjecture. Later I will describe recent joint work with Vesselin Dimitrov and Ziyang Gao on a new uniform upper bound for the number of rational solutions.

### Speaker

Philipp Habegger E Praeger

Role: Speaker

Organisation: University of Basel