Arend Bayer

Mathematics

Some people love to eat a (x²+y²+z²-13)²-36*(4-z²)=0 for breakfast. That is the polynomial equation that describes a doughnut in the language of mathematics, the shape of which is known as a torus in geometry. Others have their (2x²+y²+z²-1)³-(1/10)*x²z³-y²z³=0 in the right place. This equation describes a three-dimensional heart. Algebraic geometry addresses the geometric properties of the solution sets of polynomial equations that can be used to describe geometric objects. But for the experts it only gets really interesting when they leave the three-dimensional visualisation space and investigate many equations in many unknowns – because it is quite possible to use polynomial equations to describe 20-, 50- or 100-dimensional geometric objects that humans can hardly visualise.

The number of classes and families of possible objects and moduli spaces that can be defined by certain parameters is accordingly infinite. In the last few decades, the mathematical classification of geometric objects has progressed ever further. Arend Bayer was initially inspired by the role such geometric objects played in string theory in theoretical physics. String theory works on the assumption that there are extra dimensions beyond the 3+1 dimensions of space-time; these extra dimensions are curled up in shapes described by polynomial equations. This enables algebraic geometry to underpin observations in and assumptions of string theory. Conversely, Bayer has incorporated novel concepts from string theory, in particulary Bridgeland’s theory of stablity and wall-crossing, as standard tools in algebraic geometry for answering fundamental questions in the classification of polynomial geometric shapes and their moduli spaces.

In recruiting Arend Bayer, Freie Universität Berlin wants to gain a leading representative of algebraic geometry who is set to reinforce the worldwide reputation of the Department of Mathematics. Moreover, young mathematicians will benefit from his presence as a mentor and patron. Through his mentoring experience and his work in the Equality, Diversity and Inclusion Committee at University of Edinburgh, Arend Bayer is also deeply familiar with the difficulties encountered by under-represented groups in the mathematical community.

Brief bio

The mathematician Arend Bayer completed his doctorate at the Max Planck Institute for Mathematics in Bonn in 2006. After post-doc positions at the University of Utah and MSRI, Berkeley, both United States, he moved to the University of Connecticut, USA, as an assistant professor in 2009 and, in 2012, to the University of Edinburgh, where he is now Professor of Algebraic Geometry. Bayer is a Fellow of the Royal Society of Edinburgh and has received numerous awards such as the University of Cambridge’s Adams Prize in Mathematics in 2015, the Edinburgh Mathematical Society’s Whittaker Prize and the London Mathematical Society’s Whitehead Prize in 2016. He has been invited speaker at the International Congress of Mathematicians in 2022. Having been awarded an ERC Starting Grant in 2013, he also received an ERC Consolidator Grant in 2019.

Arend Bayer has been selected for a Humboldt Professorship and is currently conducting appointment negotiations with the German university that nominated him for the award. If the negotiations end successfully, the award will be granted in 2025.