Mathematical Mavericks

Apart from funding ground breaking research, the ERC also employs many excellent scientists to manage the grants that we support. We hear from mathematician Maria Teresa Gonzalez Cerveron who tells us how she came to work at the ERC and in turn introduces us to her favourite piece of ERC funded research, from Gil Kalai.
 

Chance encounter

I have been working in the ERC for five and a half years, on the mathematics panel (PE1 in ERC lingo). Certainly you cannot enjoy maths for so long if you are not a mathematician!  Before my last year at high school, I always wanted to be a marine biologist but I changed my mind and decided to become an astronomer. This requires a strong knowledge of maths and so, I ended up studying a maths degree in my hometown of Valencia (Spain) and later a PhD in Ireland at the University of Limerick.

How did I end up working for the ERC? Pure chance. While pregnant with my first child, a friend convinced me to apply for an open call for scientists at an EU research body, the Joint Research Center  (JRC). To my surprise, after doing exams with a 10 day old son in tow, I succeeded. When he was a few months old the ERC called to ask whether I would be interested in coming for an interview. I had no idea what the ERC was or why they would need a mathematician but I came… and I am happy I did!

What does an ERC “Scientific Officer” do?  

As a Scientific Officer at the ERC I have two main tasks: coordinate the evaluations of applications for our grants – the part involving the external experts from the relevant scientific field(s) and the scientific follow-up of granted projects – the assessment of their scientific implementation. My favourite part of the evaluation process is our panel meetings, in which some external experts, the panel members, come together to discuss what grade each application should receive.  The most interesting part is the second step of the evaluation process, when the applicants are interviewed by the panel.

Every now and then, there are some opportunities to work on extra projects, which also I really enjoy: for example, doing a “TED” style talk to explain ERC funded projects to other research oriented sections of the European Commission, or even writing this article!

How to pick a first among equals

The ERC's maths panel covers a wide range of projects in pure and applied maths and statistics. When asked to select my favourite, I found it extremely difficult to choose only one project and researcher. There are many fascinating ones, led by both well-established and respected mathematicians and young rising stars.

Bold and controversial theory

Combinatorics is the area of mathematics concerned with counting.

Gil Kalai is a Professor of mathematics at the Hebrew University of Jerusalem and a Professor of Computer Science at the Interdisciplinary Center Herzliya. In addition, he holds an adjunct professor position at Yale University. He is the recipient of numerous prizes for his contributions to the field of combinatorics and also two ERC Advanced Grants, one in 2012 and one in 2018.

Professor Kalai's current ERC funded research, SensStabComp has four main objectives. What really caught my eye was the fourth part, which for me has a particularly bold and controversial component. Prof. Kalai has a firm belief that is not necessarily supported by the majority of the scientific community, but far from succumbing to peer pressure, he is determined to prove the majority wrong and to do this mathematically.  His Advanced Grant funded project, "Sensitivity, Stability, and Computation", is in the field of combinatorics and is closely related to probability, physics and computer science. It is the link to this last field that adds spice to his proposal.

Let's make some noise for Combinatorics!

Gil Kalai studies noise stability and noise sensitivity. In this context, by noise we understand the errors that occur when computing something. A process is sensitive to noise if the errors that occur while computing strongly affect the output of the process. In the context of computer science, Kalai’s work is linked to that of quantum computing.

The promise of quantum computing

Quantum computers are hypothetical devices that promise to perform computations thousands of times faster than a classical computer. A classical computer stores the information by using 0s and 1s in what we call bits. A bit can only take one value at a time. Quantum computers store information in what we called quantum bits or qbits, qbits can take both values at the same time thanks to a phenomenon called "superposition". This ability allows a quantum computer to calculate in parallel something that a regular computer could only do sequentially, therefore reducing computation times incredibly.

Unfinished Symphony

It is a widely held belief that quantum computers will be able to perform computations that nowadays are inconceivable even with the best supercomputers. Will this really ever happen?  Gil Kalai is sceptical. Qbits are especially sensitive to noise and according to his results, there are reasons to think that the error levels will never be sufficiently reduced.

If you think about a complex sound wave (think of a Beethoven symphony), there is a particular mathematical computation that allows a complex wave to be broken into simpler ones (the wave of every individual instrument).  One of Kalai's results shows that if, this computation is performed in a quantum computer, the errors will affect the high frequency waves, and as a result from the symphony, we will only hear the basses , but not the cellos, violas and violins.

Supporting the community

In addition to being an outstanding mathematician, Gil Kalai is committed to training new generations.  He actively participates in the various online platforms that mathematicians use to collectively solve problems such as the polymath blog or the Mathsoverflow site. He also has his own blog “Combinatorics and more”. This kind of service really struck a chord with me as in addition to having a maths degree and  Phd, I am also a qualified secondary school teacher. I have spent many years teaching both young students and also adults returning to education, first in Spain at school level and later at the University of Limerick.

Will Gil Kalai be able to prove the failure of “Quantum computer supremacy”? I don’t know, but what I am sure about is that, every piece of research produced during his grant will be of great value to the scientific community.