Homepage of Benjamin Matthias Ruppik

Hello and welcome! You have landed on the website of a mathematician who is working on Topological Deep Learning and Representation Learning in Data Science. My name is Ben Ruppik (he/him) and I hold a PhD in Low-dimensional Topology from the Max Planck Institute for Mathematics and University of Bonn. Currently, I am part of the Dialog Systems and Machine Learning lab led by Prof. Milica Gašić at Heinrich-Heine-University Düsseldorf, exploring the use of Topological Data Analysis (TDA) in Natural Language Processing and Task-oriented Dialogue Systems. On this website, you will find some of my projects, publications, and other resources related to my research interests. You are welcome to reach out to me via e-mail or LinkedIn in German or English!

Selected Papers and Preprints

For a complete list, follow the links to arXiv; ORCID iD icon ORCID; Google Scholar; ResearchGate.

Thesis

Iterated Whitehead double of the dual knot in the Poincare homology sphere

Casson-Whitney unknotting, Deep slice knots and Group trisections of knotted surface type

Advisors: Arunima Ray and Peter Teichner.

PhD thesis published at University of Bonn.

Main new results:
  • An explicit construction of regular homotopies between rim surgeries (which subsumes some of the previous applications to twist-spun knots).
  • A generalization of the fusion number upper bound for the Casson-Whitney number to higher genus ribbon surfaces in the 4-sphere.
  • The stabilization number of Suciu's ribbon 2-knots \(R_{k}\) is equal to 1.
  • The Casson-Whitney distance of the standard unknotted \(\mathbb{RP}^{2}\) and Suciu's associated \(\mathbb{RP}^{2}\)-knots \(R_{k} \# \mathbb{RP}^{2}\) is equal to 1.
  • Partial results of the algebraic Casson-Whitney number of Suciu's knots.
  • The (+1)-trace on the right handed trefoil knot contains infinitely many non-local knots in its boundary which exhibit the difference between shallow topological sliceness and smooth deep sliceness. This is an interplay between Freedman's construction of a topological slice for 3-fold iterated positively clasped Whitehead doubles on the one hand, and the Heegaard-Floer \(\tau\)-invariant giving a smooth obstruction for sliceness in \(\partial X \times [0,1]\).
  • Group trisections of knotted surface type of the trefoil group, which comes from a bridge trisection of Suciu's ribbon 2-knots.

Resources

Activities

Summer Term 2023

Teaching
Talks
Conferences

Winter Term 2022/2023

Teaching
Talks
Conferences

Summer Term 2022

Teaching
Conferences

Winter Term 2021/2022

Talks

Summer Term 2021

Talks
Conferences

Winter Term 2020/2021

Talks
Conferences

Summer Term 2020

Talks
Conferences/Workshops

Winter Term 2019/2020

Talks
Conferences
  • Winter Braids X, Pisa, February 17 - 21, 2020
  • Low-dimensional topology workshop, Regensburg, October 21 - 23, 2019.

Summer Term 2019

Talks
Conferences

Winter Term 2018/2019

Summer Term 2018

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2018.

Winter Term 2017/2018

Summer Term 2017

  • Material for the rep 'Introduction to Geometry and Topology' in the summer term 2017.
  • Handout (.pdf) for a talk on the First Lie Theorem.

Summer Term 2016

Other

Links: Github, MathStackExchange