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 and Head of the Degree program Data Science. I am also affiliated with the AU DIGIT Centre and the AU Quantum Campus.

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.

Joining Göttingen + open positions. I will move to the University of Göttingen in October 2026, where I am building a new group. I am currently looking for a PhD student and a postdoctoral researcher working broadly around stochastic geometry, random networks, and related topics.

PhD position · Postdoctoral position

Starting dates are flexible, and informal inquiries are very welcome.

Save the date, 02-06 Aug ‘27. Aarhus summer school on Hidden Information in Data: Topology, Inference, and Learning. Details TBA.

Interests

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

Projects

Topological data analysis

Many modern data sets have an underlying shape. Clusters, loops, branches, voids, or higher-order structures that are not visible from standard summaries alone. Topological data analysis provides mathematical tools for detecting such structure and studying how robust it is under noise. My work develops probabilistic limit theorems and statistical methods that help turn these topological summaries into reliable quantitative tools.

Large deviations

Random systems usually behave in a typical way, but the rare exceptions are often the most informative. Large deviation theory asks how unlikely events occur and what their most likely mechanisms are. In spatial probability, this leads to questions such as whether an unusually dense network is caused by a global change in the system or by a small localized anomaly. My work studies such rare-event mechanisms in geometric and network-based models.

Spatial random networks

Many networks are shaped by geometry. Neurons, particles, wireless devices, social contacts, or biological structures are not connected in an abstract space, but through spatial constraints and local interactions. Spatial random networks combine ideas from probability, geometry and statistical physics to model such systems. My research studies how connectivity, spreading, clustering and large-scale behavior emerge from local spatial rules.

Research

Quickly discover relevant content by filtering publications.

Normal approximation for subgraph counts in age-dependent random connection models

We study normal approximation of subgraph counts in a model of spatial scale-free random networks known as the age-dependent random …
C. Hirsch, R. Lachièze-Rey, T. Owada
PDF Project
Normal approximation for subgraph counts in age-dependent random connection models

Random Connection Hypergraphs

In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the …
M. Brun, C. Hirsch, P. Juhász, M. Otto
PDF Project
Random Connection Hypergraphs

Modelling active particle motion from fluorescence correlation spectroscopy data

Active colloids (also known as motors, swimmers) have attracted enormous attention in the past two decades. The field has evolved …
M. A. Ramos Docampo, C. Duan, N. Wang, M. Pandey, P. de Dios Andes, C. Hirsch, B. Städler
PDF Project
Modelling active particle motion from fluorescence correlation spectroscopy data

A mathematical analysis of hierarchical Hopfield models

The central question that we address is: How can structured information be stored in a hierarchical Hopfield model involving hidden …
M. Heydenreich, C. Hirsch, M. Löwe
PDF
A mathematical analysis of hierarchical Hopfield models

Functional central limit theorem for topological functionals of Gaussian critical points

We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics …
C. Hirsch, R. Lachièze-Rey
PDF Project
Functional central limit theorem for topological functionals of Gaussian critical points
See all publications

Teaching

Supervision

  • Postdocs
  • PhD theses
    • C. Duan (08/25-). Large-deviation analysis of interacting particles
    • N.N. Lundbye (02/23-). Statistical foundations of TDA
    • P. Juhasz (11/22 - 12/25). TDA-based models of evolving higher-order networks
    • D. Willhalm (05/20 - 04/24). Limit theory for spatial random networks. Now, Machine Learning Scientist at Layer 6.
  • MSc theses
    • C. Perch (06/25). Monte Carlo Methods and Importance Sampling Techniques for Forecasting Macroeconomic Risks
    • R.H. Nielsen (06/25). Analyzing the Simulation of Semistationary Processes
    • M.H. Petersen-Westergaard (06/25). Efficient Monte Carlo Methods for Estimating Nonlinear Financial Models
    • L. de Jonge (07/21). Absence of WARM percolation on geometric networks. Completed PhD degree at the University of Osnabrück.
    • Y. Couzinié (09/18). Sublinearly reinforced Pólya urns on graphs of bounded degree. Now, Postdoc at the Tokyo Institute of Technology.
    • 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. Completed PhD degree at the Universitat de Barcelona.
    • 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. Now, Assistant Professor at Budapest University of Technology.
  • BSc theses
    • D.H. Groth and V.S. Bergenser (06/26). Premium Control in a Mutual Insurance Company
    • T. Sørensen (06/26). High-resolution mesh generation from sparse point clouds
    • O.E. Bech and E.J. Elberg (06/25). Improving Coronary artery segmentation for tachycardia patient
    • J.S. Knudsen and F. Nordberg (06/25). Prediction of coronary artery calcification in breast cancer radiotherapy CT-scan
    • C.D. Fuglkjær and M. Fridorf (06/25). Federated learning with applications in dentistry
    • K.B. Bräuner and A. Kristensen (05/24). Forudgående tidsbestilling for patienter
    • J. Borg (05/24). Markov beslutningsteori: Optimal opladning af elbiler
    • A.P. Diakovasilis and L.V. Jacobsen (05/24). Optimal ambulanceudsendelse
    • M.-C. Mociran (05/24). Optimering af blodplader oplagring
    • F. Tækker (05/24). Screening og behandling af kroniske sygdomme
    • C. Teoridis (05/24). Optimal tildeling af forespørgsler blandt tradløse sensornetværk og databaser
    • C.S. Pallesen (05/24). Forudgående patientkonsultationsplanlægning
    • H.C. Hansen (01/24). Convex hull algorithms for the triangulation/construction of alpha complexes
    • B.H. Kristensen (06/23). Asymptotic normality of tessellation - based persistent Betti numbers
    • B. Buttenschøn (06/23). A law of large numbers for wide one-layer neural networks
    • F. Brück (06/17). Percolation properties of Poisson graphs. Completed PhD at the TU Munich.
    • 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. Now, PhD student at LMU Munich.

Contact