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Associate Professor Mariel Saez

Pontificia Universidad Catolica de Chile

We interviewed Associate Professor Mariel Saez from Pontificia Universidad Catolica de Chile to find out what drives her interest in mathematics and advice she has for future researchers.

Can you tell us about your work? What drives your interest in this field?

I work on geometric analysis. I am interested in the connection between the geometry of objects (i.e. shape, size, etc) and their analytic properties. In physics and nature in general, several phenomena are described in terms of partial differential equations or minimisation of certain energy functionals, which are often considered and studied as analytical objects. On the other hand, the physical nature of the problems allow to interpret these operators geometrically and study them from that perspective. In my opinion, establishing such connection enriches both the analytical and the geometric point view.

What are your favourite applications of your work?

I don’t know much about “real world” applications, but I am really curious about them. Within mathematics, it is really exciting to see questions that seem not analytical or geometric to be solved with techniques of these fields (for instance, the Poincare conjecture)

What are some other areas of your field that are particularly interesting to you?

Mathematics is so broad that to understand areas of mathematics that are far from mine is difficult. I would be very interested in learning more about other techniques that are used, for instance, in algebraic geometry or number theory.

Why did you become a mathematician?

I always liked maths and felt confortable working with numbers. I enjoy the challenge of facing a question and being able to solve it. As a professional mathematician, these questions often take much longer to solve (sometimes years or sometimes never), which can be frustrating at times, but still coming to a solution is very satisfying

Do you have any advice for future researchers?

To be patient and, if they enjoy research, to pursue their own ideas. It may feel like it takes a long time to become a mathematician, but I really like the fact that one is always learning new things.

Why are opportunities such as AMSI Winter School so valuable? What do you hope attendees take from your lectures?

I think it is a great opportunity to have the chance of interacting with mathematicians from all over the world . I hope the attendees learn about problems that they did not know befeore.

Associate Professor Saez will be presenting the topic Curvature Flow of Networks at the 2018 Winter School, hosted by The University of Queensland.

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