Peter Feller: inaugural lecture
On 26 October, Professor Peter Feller gave his inaugural lecture entitled: "Knots and geometry". He has been assistant professor at the Department since September 2019.
Laudatio by Robert Weismantel, Head of Department
Peter Feller received his PhD from the University of Bern in 2014. During a period of five years he was a postdoc at various places including Boston College, the Max Planck Institute in Bonn and finally ETH. He was awarded an SNSF Excellenza Professorial Fellowship starting in 2019. Hence, we may expect to have him at ETH for a couple of years and we are very glad about this. His research area is low dimensional topology, which is the study of manifolds of dimension 4 or less and geometric structures on them. A particular focus of his work is knot theory and applications to the study of 3- and 4-manifolds. Since he is interested in visualisation in general you will see that he will show very nice pictures. He has had various achievements in the past, among them in the 3-d case is his joint work with Alessandro Sisto and Gabriele Viaggi. He was able to give an effective proof of the theorem that random closed oriented 3-manifolds carry a hyperbolic structure.
In the 4-d situation, he was able to use 3-d tools to extend the result of Freedman relating the Alexander Polynomial and the topological sliced genus of a knot. He is also very interested in algebraic geometry and has contributed to this field. In particular in collaboration with Immanuel van Santen he was able to show, under some dimension conditions, that embeddings of smooth affine algebraic varieties into matrix groups exist.
This is in a nutshell what Peter Feller has done so far. The topic of low dimensional topology is what he is going to follow up within the next couple of years at ETH.