Florian Luca awarded NRF A-rating
- Wits University
One of the world's leading authorities on number theory and analysis, Luca joined Wits in 2014 as Distinguished Professor.
Distinguished Professor Florian Luca has been awarded an A-rating from the National Research Foundation.
Inspiring postgraduate mathematicians and connecting the South African and global mathematics community at the highest level is a key focus for Distinguished Professor Florian Luca.
One of the world’s leading authorities on number theory and analysis, he joined Wits’ School of Mathematics as a Distinguished Professor in June 2014. Prior to moving to Wits he was a professor in the Centre of Mathematical Sciences at the National Autonomous University of Mexico (UNAM), where he was based from 2000 to 2014.
Number theory
Number theory, sometimes called ‘higher arithmetic’ is a vast field of mathematics that includes the study of the properties of whole numbers.
It is one of the oldest mathematical pursuits, dating back 2500 years to a mathematician called Diophantus of Alexandria, sometimes called the father of algebra. He was the first person to study number theory equations, and after whom a subfield of number theory called Diophantine equations is named.
Number theory is situated in the field of theoretical mathematics but aspects of it are providing answers to real world problems in a number of fields, including digital communication, computer technology, secure coding of banking transactions and cryptology.
“As a number theorist I am drawn to questions about integer numbers. Every integer number is a product of prime numbers. Given a typical integer, how many prime numbers does it have? How do these primes sit inside that integer if we order them from smaller to larger? The study of such questions belongs to a part of mathematics called analytic number theory.
“Another area I am drawn to is the study of equations with integer solutions. For example, can we find two squares who sum is a square? Sure we can - 9 16=25 and 9=3^2, 16=4^2, 25=5^2 - and there are many such examples. But can we find two cubes whose sum is a cube? The answer here is no, and this problem is a particular case from a more general assertion made by 18th century French mathematician Pierre de Fermat to the effect that more generally, one cannot find two fourth powers summing to a fourth power, or two fifth powers summing to a fifth power, or two integers which are powers of some same exponent n of other two integers and such that their sum is again such an nth perfect power.
"This problem was finally solved 20 years ago by American number theory mathematician Andrew Wiles,” says Prof Luca, adding that the mathematical community is continuously working on a range of high-level, unsolved theoretical problems.
Working with postgraduates
He is particularly active in his field, publishing between 30 – 50 papers a year over the past 10 years in a field where the average is three papers per year.
He is also a great proponent of co-authoring papers with colleagues and all of his postgraduates in his field, which considerably advances up-and-coming number theorists, with whom he generously shares his global network.
“I don’t let my students graduate unless they have published several papers,” he says. “When they have published and presented papers at conferences and workshops, their research area gets better known and their career prospects are considerably improved.
“I strongly believe in being an advocate of mathematics and I do not miss any opportunity to offer short, intensive courses anywhere in South Africa or the world, and to ensure that my students attend workshops of this kind,” says Prof Luca who has lectured in more than 20 countries.
Wits connection
No stranger to Wits he was on a six-month Visiting Professor appointment here in 2011. “I’m pleased to return to the School of Mathematics on the Distinguished Professor programme and I look forward to growing the postgraduate cohort here.
The School has active research programmes in functional analysis, number theory, combinatorics, graphs theory, topological groups, differential operators and partial differential equations.
Luca brought a PhD student with him from Senegal who is a student at both Wits and the University of Dakar, working on Diophantine equations. Another of his PhD students graduated from Cali University, Colombia, which permits the PhD advisor to be based at another university.
“With all the online communication opportunities this is increasingly happening,” says Prof Luca. “It works particularly well for more mature students who need less face to face contact. I’m open to any kind of supervisory model, with students from Wits and elsewhere coming together in a multi-university context through which we can grow and advance mathematicians.”