Christian Hirsch

Christian Hirsch

Associate Professor for Data Science and Statistics

Aarhus University

Christian Hirsch

I am Associate Professor for Data Science and Statistics at Aarhus University, where I am studying random networks motivated from biology and health sciences via techniques from topological data analysis and stochastic geometry. I am a member of the Stochastics group at the Department of Mathematics. I am also affiliated with the AU DIGIT Centre.

Before that, I was Assistant Professor at the University of Groningen and at the University of Mannheim. I was Postdoc at Aalborg University, at the LMU Munich and the WIAS Berlin. I received my PhD from Ulm University.

You can also access my full CV.

June 26 - June 30, 2023. Danish-Swedish summer school on TDA and spatial statistics

Interests

  • Statistical foundations of topological data analysis
  • Large deviations theory in stochastic geometry
  • Percolation theory of spatial random networks

Education

  • PhD in Mathematics, 2014

    Ulm University

  • Diploma in Mathematics, 2010

    LMU Munich

Projects

Topological data analysis

Topological data analysis is based on an equally simple as intriguing principle. Leverage invariants from algebraic topology to gain novel insights into data. TDA is now applied in a wide variety of disciplines.

Large deviations

What is the probability that a random geometric graph in a sampling window has atypically few or atypically many edges or triangles? What are the sources leading to such rare events? These examples illustrate the core questions of large devations in geometric probability.

Spatial random networks

In the context of the Internet of Things and in 5G cellular networks, Device-to-Device (D2D) communication plays a key role. This technology aims to reduce the load on the base station by allowing users to communicate with one another, either directly or through several intermediate steps.

Research

Quickly discover relevant content by filtering publications.

Asymptotic properties of one-layer artificial neural networks with sparse connectivity

A law of large numbers for the empirical distribution of parameters of a one-layer artificial neural networks with sparse connectivity …
C. Hirsch, M. Neumann, V. Schmidt
PDF Project
Asymptotic properties of one-layer artificial neural networks with sparse connectivity

Face and cycle percolation

We consider face and cycle percolation as models for continuum percolation based on random simplicial complexes in Euclidean space. …
C. Hirsch, D. Valesin
PDF Project
Face and cycle percolation

Limit theory of sparse random geometric graphs in high dimensions

We study topological and geometric functionals of l∞-random geometric graphs on the high-dimensional torus in a sparse regime, where …
G. Bonnet, C. Hirsch, D. Rosen, D. Willhalm
PDF Project
Limit theory of sparse random geometric graphs in high dimensions

Large deviations for the volume of k-nearest neighbor balls

We prove a large deviation principle for the point process associated to k-element connected components in ℝd with respect to the …
C. Hirsch, T. Kang, T. Owada
PDF Project
Large deviations for the volume of k-nearest neighbor balls

Topology-based goodness-of-fit tests for sliced spatial data

In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In …
A. Cipriani, C. Hirsch, M. Vittorietti
PDF Project
Topology-based goodness-of-fit tests for sliced spatial data
See all publications

Teaching

Supervision

  • Postdocs
  • PhD theses
    • N.N. Lundbye (since 02/23). Statistical foundations of TDA
    • P. Juhasz (since 11/22). TDA-based models of evolving higher-order networks
    • D. Willhalm (since 05/20). Large deviations in stochastic geometry
  • MSc theses
    • L. de Jonge (07/21). Absence of WARM percolation on geometric networks
    • Y. Couzinié (09/18). Sublinearly reinforced Pólya urns on graphs of bounded degree
    • F. Rudiger (09/18). Recurrence and transience of graphs generated by point processes
    • A. Hinojosa Calleja (08/16). Interference in ad-hoc telecommunication systems in the high-density limit
    • E. Rolly (06/16). Gibbs-Masse für Trajektorien von Nachrichten in einem Kommunikationsnetzwerk
    • A. Tóbiás (04/16). Highly dense mobile communication networks with random fadings
  • BSc theses
    • B. Hautorp (??/23). TBA
    • B. Buttenschøn (??/23). TBA
    • L. Kriouar (07/21). Analysis of financial data with time series and persistent homology
    • H. Hong (07/21). Geometric and topological approaches to mode clustering
    • J. Langenbahn (12/19). Konvergenz des Pseudo-Marginalen MCMC Verfahren
    • H. Blocher (02/18). Poisson Matching
    • F. Brück (06/17). Percolation properties of Poisson graphs

Contact