AWMA virtual Seminar n°11

The speaker, Dr. Elisa Lorenzo García is maîtresse de conférences at Rennes University (France) and assistant professor at Neuchâtel University (Switzerland). She obtained her PhD at Politecnical University of Catalunya in 2014. She works on effective algebraic geometry and number theory with an eye on the applications to cryptography and coding theory. 

She has been the president of the commission of Women and Mathematics of the RSME (Spanish Mathematical Society) from 2017 to 2019. She is a member of the EGMO (European Girl's Math Olympiad) Advisory Board since 2018. She is also a member of CIMPA since 2020 and has taught courses in several schools in South America, Africa and Asia.



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Date Thursday,  December 02, 2021
Time 14:00-15:00 (UTC)
Speaker Dr. Elisa Lorenzo García
Affiliation Neuchâtel University
Domain Algebraic Geometry
Title Reduction type of hyperelliptic curves in terms of the valuations of their invariants

In this talk we will first review the classical criteria to determine the (stable) reduction type of elliptic curves (Tate) and of genus 2 curves (Liu) in terms of the valuations of some particular combinations of their invariants. We will also revisit the theory of cluster pictures to determine the reduction type of hyperelliptic curves (Dokchitser's et al.). Via Mumford theta constants and Takase and Tomae's formulas we will be able to read the cluster picture information by looking at the valuations of some (à la Tsuyumine) invariants in the genus 3 case. We will also discuss the possible generalization of this strategy for any genus and some related open questions.







Thursday, December 2, 2021