Gabriel Bartolini received his Ph.D. in mathematics at Linköping University in 2012. He will hold a postdoctoral position in Professor Antonio F. Costa’s research group at National Distance Education University (UNED) in Madrid, Spain.
Ever since Bernhard Riemann introduced the idea of a Riemann surface in his dissertation in 1851, it has become a central concept in many areas of mathematics. Riemann used it in his study of complex analysis, which is the theory of functions of complex numbers.
A complex number is a sum of a real number and an imaginary one, where the unit of an imaginary number is the square root of minus 1. Real numbers correspond to points of a straight line, and complex numbers to points of a two-dimensional plane in the Cartesian coordinate system.
One way to think about a Riemann surface is by imagining a deformed complex plane. An important property of a certain class of so-called compact Riemann surfaces is the number of holes they enclose. For example, a swim ring and a coffee cup with a handle have precisely one hole each, as opposed to a sphere, which doesn’t have any.
Riemann showed that all compact Riemann surfaces with no holes are equivalent to a sphere. Riemann and other mathematicians were also able to show that all such surfaces with one hole can be described by using one complex parameter. However, it is significantly more difficult to describe compact Riemann surfaces with the number of holes higher than one. Gabriel Bartolini is planning to study geometric properties of Riemann surfaces and their symmetries together with Professor Antonio Costa and his research group in Madrid.