As IMPA reported at 1st august 2018:

### “Researchers from Germany, India, Iran and Italy take home the 2018 Fields Medal”

the whole story:

“Four notable and promising researchers from four different countries – Germany, India, Iran, and Italy – are the winners of the most important international award in mathematics, the Fields Medal. Delivered for the first time in 1936, the medal is recognition for works of excellence and an incentive for new outstanding achievements.

Awarded every four years at the world’s largest mathematics event – the International Congress of Mathematicians (ICM) – the medal will be given this year to Peter Scholze, Akshay Venkatesh, Caucher Birkar, and Alessi Fegalli at ICM’s opening ceremony on August 1^{st}, at Riocentro.

Founded by the Canadian mathematician John Charles Fields to celebrate outstanding achievements, the Fields Medal has already been awarded to 56 scholars of the most diverse nationalities, among them, Brazilian Fields laureate Artur Avila, an extraordinary researcher from IMPA, awarded in 2014 in South Korea. Due to its importance and prestige, the medal is often likened to a Nobel Prize of Mathematics.

The winners of the Fields medal are selected by a group of renowned specialists nominated by the Executive Committee of the International Mathematical Union (IMU), which organize the ICMs. Every four years, between two and four researchers under the age of 40 are chosen. Since 2006, a cash prize of 15 thousand Canadian dollars accompanies the medal.

Meet the winners of the Fields Medal 2018:

Fields awards ceremony 2018, showing medal winners Peter Scholze, Alessio Figalli, Caucher Birkar and Akshay Venkatesh. Photograph: Fabio Motta/Courtesy IMC 2018

**Akshay Venkatesh**

Conquering the greatest honor among the world’s mathematicians before the age of 40 is a notable accomplishment, although the life of Akshay Venkatesh is already marked with precocious feats. Born in New Delhi, India in 1981, and raised in Australia, at age 12 he became a medalist at the International Mathematical Olympiad. From there, he dived into world of mathematics, starting a promising career. When he began his bachelor’s degree in Mathematics and Physics at the University of Western Australia, he was a 13-year-old boy.

At 20, Venkatesh finished his PhD at Princeton University and soon became an instructor at C.L.E. Moore, at the Massachusetts Institute of Technology (MIT), a prestigious position offered to recent graduates in the area of Pure Mathematics, previously occupied by prominent figures such as the American John Nash (1928-1915). Upon leaving in 2004, he became a Clay Research Fellow and was appointed associate professor at the Courant Institute of Mathematical Sciences at New York University.

He became a professor at Stanford University at the age of 27, and as of this year is a faculty member at the Institute for Advanced Study (IAS).

Venkatesh has his feet in Number Theory – an area that deals with abstract issues and had no known application until the arrival of cryptography in the late 1970s – but roves with ease through related topics, such as Theory of Representation, Ergodic Theory, and Automorphic Forms. Armed with a meticulous, investigative and creative approach to research, detecting impressive connections between diverse areas, his contributions have been fundamental to several fields of research in Mathematics. It is no wonder that his work has been recognized by several distinguished awards such as Ostrowisk (2017), Infosys (2016), SASTRA Ramanujan (2008) and Salem (2007).

Previously a guest speaker at the 2010 ICM, Venkatesh has been invited back to speak in Rio this August.

**Alessio Figalli**

Born in Naples, Italy on April 2, 1984, Alessio Figalli belatedly discovered an interest in science. Until high school, his only concern was playing football. The training for the International Mathematical Olympiad (IMO) awakened his interest in the subject and, upon joining the Scuola Normale Superiore di Pisa, chose Mathematics.

Figalli completed his PhD in 2007 at the École Normale Supérieure de Lyon in France, with the guidance of Fields Medal laureate Cédric Villani. He has worked at the French National Center for Scientific Research, École Polytechnique, the University of Texas in the USA and ETH Zürich in Switzerland. A specialist in calculating variations and partial differential equations, he was invited to speak at the 2014 ICM in Seoul. He has won several awards, including: Peccot-Vimont (2011), EMS (2012), Cours Peccot (2012), Stampacchia Medal (2015) and Feltrinelli (2017).

**Caucher Birkar**

Caucher Birkar’s dedication to the winding and multidimensional world of algebraic geometry, with its ellipses, lemniscates, Cassini ovals, among so many other forms defined by equations, granted him the Philip Leverhulme prize in 2010 for exceptional scholars whose greatest achievement is yet to come. Given the substantial contributions of Birkar to the field, that prize was a prophecy: after eight years, the Cambridge University researcher joins the select group of Fields Medal winners at the age of 40.

Birkar, who just this year received recognition for his work as one of the London Mathematical Society Prize winners, was born in 1978 in Marivan, a Kurdish province in Iran bordering Iraq with about 200,000 inhabitants. His curiosity was awakened by algebraic geometry, the same interest that, in that same region, centuries earlier, had attracted the attention of Omar Khayyam (1048-1131) and Sharaf al-Din al-Tusi (1135-1213).

After graduating in Mathematics from Tehran University, Birkar went to live in the United Kingdom, where he became a British citizen. In 2004, he completed his PhD at the University of Nottingham with the thesis “Topics in modern algebraic geometry”. Throughout his trajectory, birational geometry has stood out as his main area of interest. He has devoted himself to the fundamental aspects of key problems in modern mathematics – such as minimal models, Fano varieties, and singularities. His theories have solved long-standing conjectures.

In 2010, the year in which he was awarded by the Foundation Sciences Mathématiques de Paris, Birkar wrote, alongside Paolo Cascini (Imperial College London), Christopher Hacon (University of Utah) and James McKernan (University of California, San Diego), an article called “Existence of minimal models for varieties of general log type” that revolutionized the field. The article earned the quartet the AMS Moore Prize in 2016.

**Peter Scholze**

Peter Scholze was born in Dresden, Germany on December 11, 1987. Only 30 years old, he is already considered by the scientific community as one of the most influential mathematicians in the world.

In 2012, at age 24, he became a full professor at the University of Bonn, Germany. Scholze impresses his colleagues with the intellectual ability he has shown since was a teenager, when he won four medals – three gold and one silver – at the International Mathematical Olympiad (IMO).

The mathematician completed his university graduate and masters in record time – five semesters – and gained notoriety at the age of 22, when he simplified a complex mathematical proof of numbers theory from 288 to 37 pages.

A specialist in arithmetic algebraic geometry, he stands out for his ability to understand the nature of mathematical phenomena and to simplify them during presentations.

At age 16, still a student at the Heinrich-Hertz-Gymnasium – a school with a strong scientific focus – Scholze decided to study Andrew Wiles’ solution to Fermat’s Last Theorem. Faced with the complexity of the result, he realized that he was on the right track in choosing Mathematics as a profession.

He was a guest speaker at ICM 2014 in Seoul, South Korea, and will be a plenary member this year at the Rio de Janeiro Congress.

Scholze has been repeatedly recognized for his contributions to arithmetic algebraic geometry. He collects major mathematics awards, such as EMS (2016), Leibniz (2016), Fermat (2015), Ostrowski (2015), Cole (2015), Clay Research 2014), SASTRA Ramanujan (2013), Prix and Cours Peccot (2012) and, finally, the Fields Medal (2018).”

Reference: IMPA

You can also find some more information from the 1st issue of the Guardian:

Fields medals 2018 winners (from L to R): Caucher Birkar, Alessio Figalli, Akshay Venkatesh, Peter Scholze. Photograph: Handout

### Former refugee among winners of Fields medal – the ‘Nobel prize for maths’

An Kurdish man who came to Britain as a refugee after fleeing conflict two decades ago is one of four men who have been awarded the Fields medal, considered the equivalent of a Nobel prize for mathematics.

The winners of the prize, presented at the International Congress of the International Mathematical Union in Rio de Janeiro, have been announced as Prof Caucher Birkar, 40, from Cambridge University, Prof Akshay Venkatesh, 36, an Australian based at Princeton and Stanford in the US, Prof Alessio Figalli, 34, from ETH in Zurich and Prof Peter Scholze, 30, from Bonn University.

The Fields medal is perhaps the most famous mathematical award. It was first awarded in 1936 and since 1950 has been presented every four years to up to four mathematicians who are under 40. As well as the medal, each recipient receives prize money of 15,000 Canadian dollars (£8,750). With all the prizes this year going to men, the late Maryam Mirzakhani remains the only woman to have received the accolade.

Birkar was born in Marivan in Iran – a Kurdish city heavily affected by the Iran-Iraq war of the 1980s – and studied mathematics at the University of Tehran before coming to the UK in 2000. After a year, he was granted refugee status, became a British citizen and began a PhD.

“When I was in school it was a chaotic period, there was the war between Iran and Iraq and the economic situation was pretty bad,” said Birkar. “My parents are farmers, so I spent a huge amount of time actually doing farming. In many ways it was not the ideal place for a kid to get interested in something like mathematics.”

Birkar says it was his brother who at an early age introduced him to more advanced mathematical techniques.

Prof Ivan Fesenko of the University of Nottingham, one of Birkar’s PhD supervisors, told the Guardian how Birkar, who initially spoke very little English, came to study with him.

“The Home Office sent him to live in Nottingham while they were processing his application for asylum status,” said Fesenko. “He came to me because he was interested in research work related to my general areas.”

Birkar’s talent, says Fesenko, quickly became apparent as he began his PhD. “I thought I should give him some problem – if he solves it, then this will be his PhD. Typically a PhD lasts three or four years. I gave him a problem and he solved it in three months,” said Fesenko.

“He is very, very smart; you start to talk with him and you recognise that he can read your thoughts several steps ahead. But he never uses this to his advantage, he is very, very respectful and he gently helps people to develop further,” said Fesenko.

As with many of the winners of the Fields medal, Birkar’s research is in areas of mathematics that can seem incomprehensible to a lay audience. His citation for the award says he won the medal “for his proof of the boundedness of fano varieties and for contributions to the minimal model program.”

Prof Paolo Cascini of Imperial College London has worked with Birkar. He said that in simple terms Birkar’s work focused on classifying geometrical shapes and describing their building blocks.

Birkar said he hoped the news may “put a little smile on the lips” of the world’s 40 million Kurds.

The youngest for the four winners, Germany’s Peter Scholze, became a professor at the age of just 24, and has been described by previous award committees as “already one of the most influential mathematicians in the world.”

Among his achievements, Scholze invented the theory of perfectoid spaces – which are noted in his citation for the Fields medal, and have been described as a class of fractal structures allowing problems to be moved from one number system to another, making them easier to solve.

“Geometry is the study of space and shape,” said Kevin Buzzard of Imperial College London. “One technique that geometers have introduced is the idea of studying a complicated space by mapping a simpler space onto it. For example, a line is a simpler object than a circle. But if you imagine wrapping a line up into a spring shape and compressing the spring, you have found a way of mapping a line into a circle. Geometers might use this technique to analyse questions about circles, by turning them into perhaps more complex questions about lines.”

Perfectoid spaces, he says, turns this logic on its head. “The counterintuitive idea introduced by Scholze is that to study a geometric object, you might instead want to find a mapping from a space which is so grotesque and twisted that in some sense it cannot be twisted up any more. The result is that instead of ending up having to solve complicated questions about simple objects, you have to solve simple questions about extremely complicated objects.”

The Italian winner, Figalli*, *works in the field of optimal transport, which has its roots in the research of 18th-century mathematician Gaspard Monge, who studied where to send material dug from the ground for use in construction so that the transport costs are as low as possible.

Venkatesh becomes only the second Australian to win the prestigious medal, after Terence Tao in 2006.Venkatesh was recognised for his use of dynamics theory, which studies the equations of moving objects to solve problems in number theory, which is the study of whole numbers, integers and prime numbers.

Venkatesh grew up in Perth and at age 13 became the youngest person to study at the University of Western Australia. He earned first class honours in pure mathematics aged 16 before studying at Princeton.

At UWA, he went straight into second-year maths courses after he proved he could write the exam papers for all the first year subjects he had never taken.

His work also uses representation theory, which represents abstract algebra in terms of more easily-understood linear algebra, and topology theory, which studies the properties of structures that are deformed through stretching or twisting, like a Mobius strip.

Receiving his award on Wednesday, he said: “A lot of the time when you do math, you’re stuck, but at the same time there are all these moments where you feel privileged that you get to work with it.

“You have this sensation of transcendence, you feel like you’ve been part of something really meaningful.”

One of his early mentors, Prof Cheryl Praeger, who has known Venkatesh since he was 12, and supervised his honours thesis when he was 15, said he was always “extraordinary”.

“At our first meeting, I was speaking with Akshay’s mother Svetha, while Akshay was sitting at a table in my office reading my blackboard which contained fragments from a supervision of one of my PhD students.

“At Akshay’s request I explained what the problem was. He coped with quite a lot of detail and I found that he could easily grasp the essence of the research.”

Reference: The Guardian