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. More details soon.

Interests

  • statistical foundations of topological data analysis
  • spatial statistics
  • continuum percolation theory
  • central limit theorems and large deviations theory in stochastic geometry

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 in stochastic geometry

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.

Inference in channel models

Channel modeling lies at the very foundation of wireless communication and is the basis for simulations of more complex communication systems.

Random network models for synaptic plasticity

Despite many parallels, there remain fundamental differences how artificial and real neural networks operate. This leads to the question:What properties should a dynamic network have to support the learning of complex patterns?

Wireless communication 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.

Preprints and Publications

Quickly discover relevant content by filtering publications.

Large deviation principle for geometric and topological functionals and associated point processes

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. Owada
PDF Project
Large deviation principle for geometric and topological functionals and associated point processes

Sharp phase transition for Cox percolation

We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation …
C. Hirsch, B. Jahnel, S. Muirhead
PDF Project
Sharp phase transition for Cox percolation

Upper large deviations for power-weighted edge lengths in spatial random networks

We study the large-volume asymptotics of the sum of power-weighted edge lengths in Poisson-based spatial random networks. In the regime …
C. Hirsch, D. Willhalm
PDF Project
Upper large deviations for power-weighted edge lengths in spatial random networks

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

Absence of WARM percolation in the very strong reinforcement regime

We study a class of reinforcement models involving a Poisson process on the vertices of certain infinite graphs G. When a …
C. Hirsch, M. Holmes, V. Kleptsyn
PDF Project
Absence of WARM percolation in the very strong reinforcement regime
See all publications

Teaching

Supervision

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

Contact