Daniel Lütgehetmann

I am researching artificial intelligence based on neuroscientific insights at INAIT. This page reflects my previous academic work and is kept online just for reference. In my last academic position I was a postdoc at the Institute of Mathematics at the University of Aberdeen. I did my PhD at Berlin Mathematical School under the supervision of Holger Reich.

My main research interests were configuration spaces of graphs and Teichmüller theory.

Here are the slides of my talk at the Young Topologist Meeting 2017.

Topological complexity of configuration spaces of fully articulated graphs and banana graphsjoint with David Recio-Mitter

In this paper we determine the topological complexity of configuration spaces of graphs which are not necessarily trees, which is a crucial assumption in previous results. We do this for two very different classes of graphs: fully articulated graphs and banana graphs. We also complete the computation in the case of trees to include configuration spaces with any number of points, extending a proof of Farber. At the end we show that an unordered configuration space on a graph does not always have the same topological complexity as the corresponding ordered configuration space (not even when they are both connected). Surprisingly, in our counterexamples the topological complexity of the unordered configuration space is in fact smaller than for the ordered one. ( link )

Thesis: Representation Stability for Configuration Spaces of Graphs

We consider for two based graphs G and H the sequence of graphs G_k given by the wedge sum of G and k copies of H. We show that the sequence of representations of the symmetric group given by the rational homology of the configuration space of these spaces is representation stable in the sense of Church and Farb. Furthermore, we extend this result to more general stabilization of the graph. We also prove that for 3-vertex connected graphs the sequence of first cohomology groups of configuration spaces of these graphs induced by forgetting particles satisfies representation stability. ( link )

Representation Stability for Configuration Spaces of Graphs

We consider for two based graphs G and H the sequence of graphs G_k given by the wedge sum of G and k copies of H. We show that the sequence of representations of the symmetric group given by the rational homology of the configuration space of these spaces is representation stable in the sense of Church and Farb. ( link )

The Homology of Configuration Spaces of Graphsjoint with Safia Chettih

We show that the homology of configuration spaces of finite graphs is torsion free. Furthermore, we give a concrete generating set for the homology of configuration spaces of finite trees. ( link )

Master's Thesis: Configuration Spaces of Graphs

We investigate the cohomology of configuration spaces of graphs and its behaviour when stabilizing the number of particles. ( pdf )

Bachelor's Thesis: The Lipschitz Distance on Outer Space

We give an overview on the Lipschitz distance on Outer Space. ( pdf )

Cycles of the Homology of Configuration Spaces of Graphs

This is an animation of a basis of the integral homology of the configuration spaces of certain graphs. We calculated the homology with the help of CHomP and Sage.

• Neural Implementations of Learning Models November 16-17, 2017 in Lausanne, Switzerland (Symposium)
• BMS-BGSMath Junior Meeting 2017 Talk: Configuration spaces in algebraic topology slides October 09-10, 2017 in Barcelona, Spain (Meeting)
• Topology Ecuador 2017 August 14-18, 2017 in Galápagos, Ecuador (Conference)
• EMALCA, Ecuador 2017 August 07-11, 2017 in Quito, Ecuador (Summer School)
• Young Topologists Meeting 2017 Talk: Configuration Spaces of Graphs slides July 03-07, 2017 in Stockholm, Sweden (Conference)
• Groups, Manifolds & K-Theory June 05-09, 2017 in Münster, Germany (Conference)
• Moduli and Traces: A celebration of the mathematical life of Ib Madsen April 20-21, 2017 in Copenhagen, Denmark (Conference)
• Junior Geometry Seminar Talk: Configuration Spaces of Graphs February 10, 2017 in Cambridge, United Kingdom (Seminar)
• The Farrell-Jones conjecture October 24-28, 2016 in Bonn, Germany (Workshop)
• 2016 West Coast Algebraic Topology Summer School August 8-13, 2016 in Eugene, USA (Summer School)
• Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics August 1-5, 2016 in Providence, USA (Workshop)
• 7th European Congress of Mathematics July 18-22, 2016 in Berlin, Germany (Congress)
• Young Topologists Meeting 2016 July 4-8, 2016 in Copenhagen, Denmark (Conference)
• Topology of Manifolds June 27 - July 1, 2016 in Lisbon, Portugal (Conference)
• Workshop on Automorphisms of free groups November 9-13, 2015 in Copenhagen, Denmark (Workshop)
• Conference on Topology and Geometry August 17-21, 2015 in Bonn, Germany (Conference)
• First Chicago Summer School in Geometry and Topology June 21-27, 2015 in Chicago, USA (Summer School)
• Topological Combinatorics of Configuration Spaces May 24-30, 2015 in Oberwolfach, Germany (Oberwolfach Seminar)
• Homotopy theory, manifolds and field theories May 4-8, 2015 in Bonn, Germany (HIM Introductory School)
• DMV-PTM Meeting 2014 September 17-20, 2014 in Poznan, Poland (Conference)
• Satellite Conference for DMV-PTM Meeting 2014 September 15-16, 2014 in Bedlewo, Poland (Conference)
• Young Topologists Meeting 2014 June 30 - July 4, 2014 in Copenhagen, Denmark (Conference)
• Topology of high-dimensional manifolds August 26-30, 2013 in Bonn, Germany (HIM Summer School)
• Topology and Groups June 18-22, 2012 in Berlin, Germany (Summer School)