email: peter.feller(you know the symbol)mpim-bonn.mpg.de
I am interested in low-dimensional topology—the study of geometric objects of dimension four or less. One-dimensional objects that lie (in a potentially knotted way) in three-dimensional space—known as knots—fascinate me because their study relates to many other fields of mathematics. Often knot theory provides an approach toward visualizing more complicated objects.
In my research, I am in particular concerned with positive braids, mapping classes, algebraic knots and links, and the slice genus. I think notions of sliceness for knots provide a great point of view to understand the differences between smooth and topological 4-manifolds.I also care about complex plane curve singularities and their deformations and hope to understand them using positive braids and tools from Heegaard-Floer theory.
And I wonder in how many ways complex algebraic varieties embed in affine space.
Maybe there are as many algebraic embeddings of the complex numbers in three-dimensional affine space as there are knots in the three-sphere,
probably (k)not; however, we should find out!
In Fall 2016, I actively participated in the Junior Trimester Program in Topology at HIM. Themes that we considered there are knot concordance, trisections (a version of Heegaard splittings for 4-manifolds), Freedman's disk theorem, and the surgery exact sequence.
My PhD thesis On the signature of positive braids and adjacency for torus knots was advised by Sebastian Baader at the University of Bern.My work is openly available on the ArXiv.