PRR Project

Summary

The Algebra and Geometry Group (AGG) of CIDMA has a strong research presence in several branches of algebra, geometry, and related fields. One of main research lines of AGG is Number Theory, Coding Theory, and Algebraic Geometry. The prospective candidate is expected to be a well-recognized researcher in Number Theory and join AGG to strengthen its research in this area.Number Theory is a fundamental branch of mathematics that delves into the properties and relationships of integers with profound insights into the nature of mathematics itself. Its importance spans various fields, from cryptography and computer science to pure mathematics and beyond. Despite its historical relevance, number theory is an underrepresented research area in Portugal, counting with a few active researchers (the AGG group counts with only one tenure professor). To overcome this issue, members of the AGG group started to organize different dissemination activities (for example the University of Aveiro hosted the "First Portuguese meeting in Number Theory" in 2022, and a summer school took place in Porto in 2023), expecting in the long term to consolidate a research group. The success of this goal depends crucially on hiring a strong, independent and recognized researcher in the field, which justifies the present petition. In particular, we are looking for a candidate with a strong background on several important areas of Number Theory of interest to the AGG, including Q-curves, Diophantine equations, 2-Selmer groups, Fermat equations, Galois representations, Quadratic twists, and Superelliptic curves.Furthermore, the prospective candidate is expected to collaborate in:- training and supervision activities, including supervision of PhD students as well as post-doctoral researchers;- enlarging international contacts and collaborations;- supervision and coordination of scientific projects;- development of outreach activities and cooperation with the society.