AustMS2021 plenary profile – Jennifer Flegg

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This is the sixth 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?

I was listening to my parents talk about something and I interrupted them to ask my dad what a 15% discount meant. I remember his explanation of “one-tenth and then half that again” being really easy to follow. My dad says I then worked out what their discount was going to be (on my brother’s braces); but I don’t remember that I just remember his explanation of how to calculate 15%.  

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

I decided to become a mathematician in my first year of university. I was studying maths and economics in a double degree at the time; business because my parents were worried that I’d have no career options after finishing a maths degree on its own. I didn’t enjoy the economics much but loved studying maths at university and from then there wasn’t another career on my radar. 

  1. Name a favourite paper by a contemporary mathematician, and why (or more than one, if you can’t decide).
  • Jonathan Sherratt and James Murray, “Models of epidermal wound healing”, Proc Biol Sci. 1990 Jul 23;241(1300):29-36. doi: 10.1098/rspb.1990.0061. PMID: 1978332.

This paper started my love of mathematical biology and was the first that I spent many months looking over as part of a research project in my undergraduate degree. I wish I had time to look over papers now like I did this one.  

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

I don’t think I could go past having a chat with Alan Turing about his mathematical work of how biological shapes and patterns develop.  I’d probably have a few questions about cracking the Enigma code too 🙂   

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

Since what I work on is quite applied, this is difficult for me to answer in the way I’m assuming the question was intended. So, I’m going to take this question a bit differently and say that the ‘result’ I’d like to see is more structure/support around interdisciplinary work that involves mathematics and statistics.  

AustMS2021 plenary profile – Gang Tian

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This is the fifth 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?

My mother was a mathematician who made outstanding contributions to Hilbert’s 16th problem. When I was between 5 and 6 years old, she gave me some logical problems. One of them was to find bad ball by balance, say you have 9 balls, one of them is bad, but you do not know this ball ball is heavier or lighter, the problem is to find this bad one by using balance three times. The maximum number of balls one can do is 13. I found it was interesting. 

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

I like mathematics since very young. I decided to become a mathematician when I was in college. One reason is its beauty, the other is its simplicity in some sense, for instance, unlike many other disciplines, I can do mathematics in a rather independent way. 

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

There are a number of papers I enjoyed reading and studying. A particular one is Perelman’s first paper on Ricci flow. It solves some long-standing problems on Ricci flow in an elegant yet simpler way. Moreover, it led to solving the Poincaré conjecture and so on. 

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

Maybe skip this question. Of course, being a geometer, I have the highest respect for Riemann. 

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

I would like to see a fundamental progress on understanding smooth structures of 4-manifolds, such as the smooth Poincaré conjecture for 4-manifolds, through geometric methods.

AustMS2021 plenary profile – Emily Riehl

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This is the fourth 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?

Not the earliest memory but an early memory is being absolutely delighted by Louis Sachar’s Sideways Arithmetic from Wayside School. Problems include EGG + EGG = PAGE, SHE+EEL = ELSE, etc.

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

I’ve loved math my entire life and had decided to become a mathematician by mid high school, when I started learning about proofs.

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

John Bourke’s and Richard Garner’s “Algebraic weak factorisation systems I: accessible AWFS” is absolutely beautiful and on a topic very close to my heart. 

Though I also have to mention the delightful “Homophonic quotients of free groups” by Jean-Francois Mestre, René School, Lawrence Washington, and Don Zagier, which everyone should read immediately.

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

I’d love to hear Emmy Noether describe the insights that lead her to modern algebra.

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

I’d like to see a variant of homotopy type theory which actually computes, includes higher inductive types, and has semantics in any ∞-topos. Mike Shulman has proven that traditional homotopy type theory (without higher inductive types) has semantics in any ∞-topoi, but we’re still working on understanding the semantics of the new experimental “cubical” versions of homotopy type theory which have constructive proofs of univalence.

AustMS2021 plenary profile – Joaquim Serra

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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). 

AustMS2021 plenary profile – Susan Scott

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This is the second 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?

My earliest mathematical memories come from my years at primary school. Things that stand out are the colourful Cuisenaire rods, which all the kids enjoyed. Then there was the rote learning of the times tables up to 12 x12 which was fun as a group chanting activity, like singing songs. I clearly recall our initiation to long division, which was generally hated, although I didn’t mind it in moderation. Lastly, I recall that we had to do written calculations in non-base 10 units, for length, area, volume, speed, currency, etc. That was later removed from the primary school curriculum but, looking back, it is perhaps surprising that most students were able to manage it quite well.

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

At primary school I was very interested by mathematics and science, and I seemed to have an aptitude for it, but at that time, where I grew up, no child would have imagined they were going to become a mathematician. I was absolutely enthralled by watching the first lunar landing, which really sparked my interest in gravity. So I just naturally drifted towards focussing on mathematics and physics and, by the time I was 14, I had decided that I somehow wanted my career to involve those fields.

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

The contemporary mathematical physicist Prof Sir Roger Penrose proved an astonishing singularity theorem in 1965. He showed that, in very general circumstances involving isolated gravitating systems undergoing gravitational collapse, a trapped surface will form, inevitably leading to the formation of a singularity – the heart of a black hole. This result demonstrated that singularities in black holes should be a common feature of our Universe, and yet no candidate for a black hole had been identified at that time. The international astronomy community were in denial about the result, and even Einstein himself would have been shocked to see this consequence of his theory. This incredible breakthrough earned Roger the 2020 Nobel Prize in Physics.

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

I would love to be able to chat with Emmy Noether. She was an extraordinarily gifted mathematician and mathematical physicist with great vision of connections between different branches of mathematics. I would ask her how she became interested in exploring the mathematics behind the then recently presented general theory of relativity due to Einstein. I would also ask how the insight she gained with this work led her eventually to the creation of the deep principle known as Noether’s Theorem, one of the most celebrated results in mathematical physics.

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

The famous singularity theorem due to Roger Penrose actually proves that, in very general circumstances involving isolated gravitating systems undergoing gravitational collapse, a trapped surface will form and thus there will exist an incomplete, causal geodesic. The theorem does not actually prove the existence of curvature singularities as the name suggests. The “completion” of this singularity theorem to prove the existence of curvature singularities has proven to be an intractable problem for more than 50 years. I would love to see that problem cracked in the next 10 years, and I would love to be part of the solution!