Optimal Prize - Fields Medal flags new opportunities
Monash University Mathematics Professor Gregoire Loeper was as happy as other mathematicians when he heard that Professor Alessio Figalli was one of the four winners of the prestigious 2018 Fields Medal.
The Fields Medal – awarded once every four years - is commonly regarded as the equivalent to the Nobel Prize in the world of mathematics.
Professor Loeper has worked with Professor Figalli, and has known him since 2006. At that time Figalli was at the start of his PhD, but was already working on leading edge research questions. The results of their collaboration were published later in 2009.
But what really excites Professor Loeper is that Professor Figalli’s success with the Fields Medal is now shining the spotlight on a particular field of Mathematics – Optimal Transport. The 2010 Fields Medallist, Professor Cedric Villani, was also a specialist of Optimal Transport.
The idea of Optimal Transport originated in the 18th century, when Gaspard Monge, a mathematician working for Napoleon Bonaparte tried to find the best way to build a network of earthen fortifications.
Today both Professor Loeper and Professor Figalli are part of a vast community of mathematicians who understand that sometimes the best way of solving mathematical problems is if you view them as a way of transporting matter from one place to another.
“Optimal transport is a fascinating area of mathematics because, while coming from such a natural practical question, it has led to a completely new way of looking at old mathematical problems,” Professor Loeper said.
“Figalli’s contribution to the area is really impressive,” he said.
“While the theory of optimal transport originates from a natural economic question (i.e. cost minimisation), it realises its full power when considered as a mathematical tool, (i.e. as a way to solve other mathematical problems by looking at them from a different perspective).
“The range of areas where optimal transport has led to mathematical breakthroughs is fascinating: cosmology, fluid mechanics and optics are some of the most applied ones, but it has also shed new light on pure areas of Mathematics such as Riemannian geometry, Functional analysis, and many others.”
Nowadays, optimal transport is being applied extensively in the field of probability, in particular to develop new techniques to estimate the price of financial derivatives.
“This field is still in its infancy and is a very exciting field of research,” said Professor Loeper.
“Two Fields medallists in the last eight years were major contributors to the area of optimal transport, and that says a lot,” he said.
“However, this is still a relatively new subject, and the range of its applications is still growing.”
Optimal Transport is a strong research focus in the School of Mathematics at Monash, including its applications to finance and economics. This can lead to PhD programs at the leading edge of mathematics, which can also prepare students for a future in the industry.
Gregoire Loeper has been a Professor of Mathematics at Monash since September 2015. He completed his PhD in Mathematics in 2003, then was appointed Assistant Professor at Claude Bernard Lyon 1 University. He then moved to the finance industry where he worked nine years for Global Equity and Commodity Derivatives within BNP Paribas.
Since his arrival at Monash, he has been the Director of the Master of Financial Mathematics program and the Director of the Centre for Quantitative Finance and Investment Strategies.
His areas of research are Optimal Transport, Non Linear PDE's, Stochastic Control, Mathematical Finance, and Fluid Mechanics.
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