AustMS2021 plenary profile – Joaquim Serra

This is the third in a series of interviews with the plenary speakers for the upcoming 65th Annual Meeting of the AustMS.

  1. What is your earliest mathematical memory?

Something I remember well is spending a long time trying to solve a problem which required solving a quadratic equation, by only “rules of three”. The teacher had given it to us so that we failed, in order to motivate the coming lessons on quadratic equations.  I was stubborn enough to find, after hours, a solution using only rules of three. I was very proud about it until I learned what a quadratic equation was,  how easily it was solved

  1. What made you decide to become a mathematician, and when?

I always wanted to do Physics, but then I went to the Physics and Maths olympiads and  I performed rather poorly in the Physics ones, so I decided to try Maths.

  1. Name a favourite paper by a contemporary mathematician, and why (or more than one, if you can’t decide).

The paper “Regularity of flat level sets in phase transitions” of Savin is one of the first papers I read  and among my favorites since then. I remember struggling to understand some proofs at the beginning, but at the same time finding the interplay between PDE and geometry of the level set very beautiful.

  1. What historical mathematician would you like to be able to talk maths with? What would you ask them?

Gauss, who gave deep pure results with the most useful practical applications. After he was updated on today’s state of the art of knowledge, I would ask him what is his opinion on Machine Learning and its implications for Mathematics

  1. What result would you like to see in mathematics in the next 10 years?

Many of them! For instance, the classification of stable solutions  (stable critical point of the energy) of the Allen-Cahn equation in three dimensions.  Or the Cartan-Hadamard conjecture (isoperimetric inequality with Euclidean constant on spaces of nonpositive sectional curvature).