I am an assistant professor 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 J 59
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.
Within Geometry and Topology I am drawn to 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 knot theory research I am in particular concerned with knot concordance. Terms such as algebraic knots and links, notions of positivity for links, and the slice genus often appear in my work. I think the notion of concordance for knots provide a great point of view to understand the differences between smooth and topological 4-manifolds. I also think that knots and links provided a great point of view to study 3-manifolds. However, currently I am focused on studying 3-manifolds via the mapping class group (buzzword: Heegaard splittings) and the curve complexe of surfaces.
I am also interested in 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 and affine algebraic groups.
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!
Uniform models and short curves for random 3-manifolds.
With Alessandro Sisto and Gabriele Viaggi.
Embedding spheres in knot traces.
With Allison N. Miller, Matthias Nagel, Patrick Orson, Mark Powell, and Arunima Ray.
Non-orientable slice surfaces and inscribed rectangles.
With Marco Golla.
Genus one cobordisms between torus knots.
With JungHwan Park.
A note on the topological slice genus of satellite knots.
With Allison N. Miller and Juanita Pinzon-Caicedo.
Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space.
With Lukas Lewark.
Almost positive links are strongly quasipositive.
With Lukas Lewark and Andrew Lobb.
Up to topological concordance links are strongly quasipositive.
[ArXiv:1802.02493][J. Math. Pures Appl.]
With Maciej Borodzik.
Calculating the homology and intersection form of a 4-manifold from a trisection diagram.
[ArXiv:1711.04762][Proc. Natl. Acad. Sci. USA]
With Michael Klug, Trent Schirmer, and Drew Zemke.
Braids with as many full twists as strands realize the braid index.
With Diana Hubbard.
On classical upper bounds for slice genera.
With Lukas Lewark.
Khovanov width and dealternation number of positive braid links.
[ArXiv:1610.04534][Math. Res. Lett.]
With Sebastian Baader, Lukas Lewark, and Raphael Zentner.
Uniqueness of Embeddings of the Affine Line into Algebraic Groups.
[ArXiv:1609.02113][J. Algebraic Geom.]
With Immanuel van Santen.
On the Upsilon invariant and satellite knots.
With JungHwan Park and Arunima Ray.
On cobordisms between knots, braid index, and the Upsilon-invariant.
With David Krcatovich.
On the topological 4-genus of torus knots.
[Trans. Amer. Math. Soc.]
With Sebastian Baader, Lukas Lewark, and Livio Liechti.
Alternating numbers of torus knots with small braid index.
[Indiana Univ. Math. J.]
With Simon Pohlmann and Raphael Zentner.
On 2-bridge knots with differing smooth and topological slice genera.
[Proc. Amer. Math. Soc.]
With Duncan McCoy.
- A sharp signature bound for positive four-braids. [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.
With Immanuel van Santen.
Signature and the Alexander polynomial. (An appendix to Livio Liechti's
`Signature, positive Hopf plumbing and the Coxeter transformation.'
[Osaka J. Math.])
With Livio Liechti.
- The signature of positive braids is linearly bounded by their first Betti number. [ArXiv:1311.1242] [Internat. J. Math.]
- Gordian adjacency for torus knots. [ArXiv:1301.5248] [Algebr. Geom. Topol.]