News:
I am coorganizing the lowdimensional topology conference Swiss Knots 2019. In Zurich from the 16th to the 19th of July 2019. Check it out!
About me:
I am a postdoc in the Geometry, groups and dynamics group at ETH Zurich.
Previously, I was a postdoctoral fellow at the Max Plack Institute for Mathematics in Bonn,
and before that I was at Boston College.
My PhD thesis
was advised by Sebastian Baader at the University of Bern.
For more, consult my CV or contact me directly.
How to find or contact me:
Office: HG G 27.1
Address: ETH Zurich,
Department of Mathematics, Raemistrasse 101, 8092 Zurich, Switzerland.
email: peter.feller(you know the symbol)math.ethz.ch
ETHZ Geometry Seminar:
Do you like Geometry and Topology? Check out ETHZ's Geometry Seminar.
Research Interests:
I am interested in lowdimensional topology—the study of geometric objects of dimension four or less.
Onedimensional objects that lie (in a potentially knotted way) in threedimensional 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 lowdimensional topology research, I am in particular concerned with mapping classes, algebraic knots and links, notions of positivity for 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 4manifolds.
I also care about complex plane curve singularities and their deformations and hope to understand them using positive braids and tools from HeegaardFloer 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 threedimensional affine space as there are knots in the threesphere,
probably (k)not; however, we should find out!
List of Publications:
For more details you can consult my detailed list of publications, where you find abstracts and pretty pictures.

Balanced algebraic unknotting, linking forms, and surfaces in three and fourspace.
[ArXiv:1905.08305]
With Lukas Lewark. 
Almost positive links are strongly quasipositive.
[ArXiv:1809.06692]
With Lukas Lewark and Andrew Lobb. 
Up to topological concordance links are strongly quasipositive.
[ArXiv:1802.02493], in press at J. Math. Pures Appl.
With Maciej Borodzik. 
Calculating the homology and intersection form of a 4manifold from a trisection diagram.
[ArXiv:1711.04762][Proc. Natl. Acad. Sci. USA, Trisections of Smooth Manifolds Special Feature]
With Michael Klug, Trent Schirmer, and Drew Zemke. 
Braids with as many full twists as strands realize the braid index.
[ArXiv:1708.04998], in press at J. Topol.
With Diana Hubbard. 
On classical upper bounds for slice genera.
[ArXiv:1611.02679]
[Selecta Math.]
With Lukas Lewark. 
Khovanov width and dealternation number of positive braid links.
[ArXiv:1610.04534], in press at Math. Res. Lett.
With Sebastian Baader, Lukas Lewark, and Raphael Zentner. 
Uniqueness of Embeddings of the Affine Line into Algebraic Groups.
[ArXiv:1609.02113], in press at J. Algebraic Geom.
With Immanuel van Santen. 
On the Upsilon invariant and satellite knots.
[ArXiv:1604.04901][Math. Z.]
With JungHwan Park and Arunima Ray. 
On cobordisms between knots, braid index, and the Upsiloninvariant.
[ArXiv:1602.02637]
[Math. Ann.]
With David Krcatovich. 
On the topological 4genus of torus knots.
[ArXiv:1509.07634]
[Trans. Amer. Math. Soc.]
With Sebastian Baader, Lukas Lewark, and Livio Liechti. 
Alternating numbers of torus knots with small braid index.
[ArXiv:1508.05825]
[Indiana Univ. Math. J.]
With Simon Pohlmann and Raphael Zentner. 
On 2bridge knots with differing smooth and topological slice genera.
[ArXiv:1508.01431]
[Proc. Amer. Math. Soc.]
With Duncan McCoy.  A sharp signature bound for positive fourbraids. [ArXiv:1508.00418] [Q. J. Math.]
 The degree of the Alexander polynomial is an upper bound for the topological slice genus. [ArXiv:1504.01064] [Geom. Topol.]
 Optimal Cobordisms between Torus Knots. [ArXiv:1501.00483] [Comm. Anal. Geom.]

Holomorphically Equivalent Algebraic Embeddings.
[ArXiv:1409.7319]
With Immanuel van Santen. 
Signature and the Alexander polynomial. (An appendix to Livio Liechti's
`Signature, positive Hopf plumbing and the Coxeter transformation.'
[ArXiv:1309.3791]
[Osaka J. Math.])
With Livio Liechti.  The signature of positive braids is linearly bounded by their first Betti number. [ArXiv:1401.5336] [Internat. J. Math.]
 Gordian adjacency for torus knots. [ArXiv:1301.5248] [Algebr. Geom. Topol.]