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2017 LMS Winners

The London Mathematics Society (LMS) has announced the winners for their various prizes and medals this year. In this blogpost I will give a breakdown of who won.

  • Polya Prize: This was awarded to Professor Alex Wilkie FRS from the University of Oxford due to his contributions to model theory and its connections to real analytic geometry.
  • Senior Whitehead Prize: Professor Peter Cameron, from the University of St Andrews, was awarded this prize for his research on combinatorics and group theory.
  • Senior Anne Bennett Prize: Awarded to Professor Alison Etheridge FRS from the University of Oxford for her “research on measure-valued stochastic processes and applications to population biology” as well as outstanding leadership.
  • Naylor Prize and Lectureship: This was given to Professor John Robert King from the University of Nottingham due to profound contributions to the theory of non-linear PDEs and applied mathematical modelling.
  • Berwick Prize: This was awarded to Kevin Costello of the Perimeter Institute in Canada for his paper entitled The partition function of a topological field theory (published in the Journal of Topology in 2009). In this paper Costello “characterises the function as the unique solution of a master equation in a Fock space.”
  • Whitehead Prize:
    • Dr Julia Gog (University of Cambridge) for her research on the mathematical understanding of disease dynamics, in particular influenza.
    • Dr András Máthé (Univeristy of Warwick) due to his insights into problems in the fields of geometric measure theory, combinatorics and real analysis.
    • Ashley Montanaro (University of Bristol) for her contributions to quantum computation and quantum information theory.
    • Dr Oscar Randal-Williams (University of Cambridge) due to his contributions to algebraic topology, in particular the study of moduli spaces of manifolds.
    • Dr Jack Thorne (University of Cambridge) for research in number theory, in particular the Langlands program.
    • Professor Michael Wemyss (University of Glasgow) for his “applications of algebraic and homological techniques to algebraic geometry.”

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News: Mirzakhani has died at 40

When I read the news that Maryam Mirzakhani had sadly passed away with breast cancer aged 40 I was honestly shocked. I remember finding out that she was the first women to win the Fields Medal in 2014 and feeling a huge sense of pride that we had achieved such a big milestone in mathematics – a mostly male dominated subject.

Professor at Stanford Universtiy, Mirzakhani was awarded the notorious Field’s Medal for her work on complex geometry and dynamic systems. She specialised in areas of theoretical mathematics that “read like a foreign language by those outside of mathematics” such as moduli spaces, Teichmüller thoery, hyperbolic geometry, Ergodic theory and symplectic geometry. By mastering these fields, Mirzakhani could describe the geometric and dynamic complexities of curved surfaces, spheres, donut shapes and even amoebas in a huge amount of detail. Furthermore, her work had implications in a vast amount of fields, ranging from cryptography to the physics of how the universe was created.


Moduli Spaces

Moduli Spaces can be thought of as geometric solutions to geometric classification problems. In broad terms, a moduli problem consists of three main categories:

  1. Objects: which geometric objects do we want to parametrise?
  2. Equivalences: when do we identify two objects as being isomorphic?
  3. Families: how do we allow our objects to vary?

Read more here.

Teichmüller Theory

Teichmüller theory, which brings together an array of fundamental ideas from different mathematical fields (including complex analysis, hyperbolic geometry, differential geometry, etc), is concerned with the Teichmüller space.

To get an short introduction to Teichmüller theory, click here.

Hyperbolic Geometry

Hyperbolic geometry is a non-Euclidean geometry, where the parallel postulate of Euclidean geometry is replaced with:

For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R.” – Wikipedia

Source: debate.org

Ergodic Theory

Ergodic theory was initially developed to solve problems in statistical physics and is a branch of mathematics that studies “dynamical systems with an invariant measure”. An invariant measure is a measure that is preserved by some function.

Symplectic Geometry

Symplectic Geometry is a branch of differential geometry and differential topology that studies symplectic manifolds. These are differentiable manifolds that have a closed, non-degenerate 2-form.


 

“Mirzakhani once described her work as ‘like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out’.”

– Guardian

Mirzakhani will be remembered not only for her extraordinary work, but also as being an inspiration to thousands of women to pursue maths and science.

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NEWS: 13532385396179

Recently, James Davis found a counterexample to John H. Conway’s ‘Climb to a Prime’ conjecture, for which Conway was offering $1,000 for a solution.

The conjecture states the following:

Let n be a positive integer. Write the prime factorisation in the usual way, where the primes are written in ascending order and exponents of 1 are omitted. Then bring the exponents down to the line, omit the multiplication signs, giving a number f(n). Now repeat.”

For example, f(60) = f(2^2 x 3 x 5) = 2235. As 2235 = 3 x 5 x 149, f(2235) = 35149. Since 35149 is prime, we stop there.

Davis had a feeling that the counterexample would be of the form

Screen Shot 2017-06-10 at 2.37.23 PM.png

where p is the largest prime factor of n. This motivated him to look for x of the form

Screen Shot 2017-06-10 at 2.38.05 PM.png

The number Davis found was 13532385396179 = 13 x 53^2 x 3853 x 96179, which maps to itself under f (i.e. its a fixed point). So, f will never map this composite number to a prime, hence disproving the conjecture.

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NEWS: Abel Prize 2017

The Abel Prize 2017 has been awarded to Yves Meyer of the École normale supérieure Paris-Saclay in France due to his “pivotal role in the development of the mathematical theory of wavelets”, which has applications in data compression, medical imagery and the detection of gravitational waves.

Yves Meyer, en 2010, recevant le prix Gauss.

Meyer, aged 77, will receive 6 million Norwegian krone (around £600,000) for the prize, which aims to recognise outstanding contributions to mathematics. It is often called the ‘Nobel Prize’ of mathematics.

The Abel Prize was previously won by Andrew Wiles in 2016, who solved Fermat’s Last Theorem.

Biography

Yves Meyer, born on the 19th July 1939, grew up in Tunis in the North of Africa. After graduating from École normale supérieure de la rue d’Ulm in Paris and completing a PhD in 1966 at the University of Strasbourg, he became a professor of mathematics at the Université Paris-Sud, then the École Polytechnique and then Université Paris-Dauphine. He then moved to École normale supérieure Paris-Saclay in 1995, until formally retiring in 2008, although he still remains an associate member of the research centre.

To read a full biography of Meyer, click here.

Video of the Ceremony

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Sublime Symmetry

The De Morgan Foundation organised a one day synopsium called ‘Sublime Symmetry’ on the 13th January, which explored the mathematics behind William De Morgan’s ceramic designs.

William De Morgan was a ceramic designer in the late Victorian period.

“His conjuring of fantastical beasts to wrap themselves around the contours of ceramic hollowware and his manipulation of fanciful flora and fauna to meander across tile panels fascinated his contemporaries and still captivates today.

The ‘Sublime Symmetry’ exhibition highlights the influence of geometry in William De Morgan’s work, and particularly the use of symmetry to create his designs. This application of geometry naturally produces beautiful and visually striking images. Below are some images of his work:

blog_post_images2blog_post_images1

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symmetries

Source: auckboro.wordpress.com

I find it fascinating how mathematics is so naturally interlaced in art and beauty, and so I really wanted to share this with you. Hopefully you found it interesting as well! The ‘Sublime Symmetry’ exhibition will be at the New Walk Gallery in Leicester until the 4th March, after which it will be displayed at the William Morris Gallery in Walthamstow on the 12th March until the 3rd September. [Source]

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NEWS: Vera Rubin

Vera Rubin died on 25th December 2016, aged 88. Rubin was an American astronomer who pioneered work on galaxy rotation rates.

In the 1960s and 70s, Rubin and her collogue Kent Ford noted a discrepancy between the predicted angular motion of galaxies and their observed motion, whilst studying galactic rotation curves.

Galactic Rotation Curve | Source: en.citizendium.org

This led Rubin to conclude that some unseen mass must be influencing the rotation of galaxies. As a result, in an attempt to explain the galaxy rotation problem, the theory of dark matter was created. The existence of this ‘invisible mass’ was first theorised by Fritz Zwicky in the 1930s but until Rubin and Ford’s work it had not been proven to exist.

Although initially it was met with skepticism from the scientific community, Rubin’s results have been confirmed over the subsequent decades.

Emily Levesque from the University of Washington said in an interview with Astronomy magazine:

This discovery “utterly revolutionised our concept of the universe and our entire field.”

It is considered one of the most significant results of the 20th century.

However, Rubin never received the Nobel Prize for Physics, although she was frequently mentioned as a candidate for it. It has been 53 years since a women has won a Nobel Prize in Physics, and now that Vera Rubin has passed away, she is no longer eligible. But, we can take some consolation in the fact that Rubin was indifferent to not being nominated for the Nobel Prize.

“Fame is fleeting,” Rubin said in 1990 to Discover magazine. “My numbers mean more to me than my name. If astronomers are still using my data years from now, that’s my greatest compliment.”

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NEWS: 2017 Breakthrough Prize in Mathematics

The Breakthrough Prizes is awarded in three categories: Life Sciences, Fundamental Physics and Mathematics, in recognition of great scientific advance.

This year, the Breakthrough Prize in Mathematics was awarded to Belgian mathematician Jean Bourgain, for his “multiple transformative contributions to analysis, combinatorics, partial differential equations, high-dimensional geometry and number theory”.

He has published, on average, 10 papers a year tackling some of the most challenging problems in a range of mathematical fields. For example, his most recent work is on the decoupling theorem: whilst Pythagoras showed that the length of the two shorter sides of a right-hand triangle are related to the hypotenuse, the decoupling theorem, proven by Bourgain and Ciprian Demeter, shows a similar relationship in the superposition of waves.

“It is of course an immense honour for me to be awarded the Breakthrough Prize and also an occasion to thank all those who helped me along my career. Over the years I have been fortunate to interact with several truly exceptional individuals who introduced me to different subjects and from whom I learned a lot. Collaborations on all levels played an important part in my work and are greatly valued. Appointments at research institutions such as the Institut des Hautes Études Scientifiques in Bures/Yvette (France) and the Institute for Advanced Study in Princeton provided ideal conditions for a full dedication to mathematics. I am most grateful for their trust. Last but not least, thanks to my family for their love and continuous support over the years.” – Jean Bourgain

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