Christian Hirsch

Assistant Professor for Topological Data Analysis

University of Groningen

Christian Hirsch

I am Assistant Professor for Topological Data Analysis at the University of Groningen. I am affiliated with both the CogniGron and the Probability and Statistics Group, where I am studying random networks motivated from materials science and biology via techniques from topological data analysis and stochastic geometry.

Before that, I was Assistant Professor 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.

Interests

limit theorems in topological data analysis
stochastic channel models
statistical modeling and analysis of networks in materials science
random networks in statistical physics
interplay between dynamical systems and probability

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.

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.

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.

Preprints and Publications

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Maximum likelihood calibration of stochastic multipath radio channel models

We propose Monte Carlo maximum likelihood estimation as a novel approach in the context of calibration and selection of stochastic …

C. Hirsch, A. Bharti, T. Pedersen, R.P. Waagepetersen

PDF Project

Maximum likelihood calibration of stochastic multipath radio channel models

Extremal life times of persistent loops and holes

Persistent homology captures the appearances and disappearances of topological features such as loops and holes when growing disks …

N. Chenavier, C. Hirsch

PDF Project

Extremal life times of persistent loops and holes

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

Functional central limit theorems for persistent Betti numbers on cylindrical networks

We study functional central limit theorems (FCLTs) for persistent Betti numbers obtained from networks defined on a Poisson point …

J. Krebs, C. Hirsch

PDF Project

Functional central limit theorems for persistent Betti numbers on cylindrical networks

WARM percolation on a regular tree in the strong reinforcement regime

We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter $\alpha$ which …

C. Hirsch, M. Holmes, V. Kleptsyn

PDF Project

WARM percolation on a regular tree in the strong reinforcement regime

See all publications

Teaching

Fall 2020 Caput Statistics: Topological Data Analysis
Spring 2020 Probability Theory
Spring 2020 Stochastic Processes
Fall 2019 Markov Decision Processes in Artificial Intelligence
Fall 2019 Seminar on Mathematical Methods in Artificial Intelligence
Spring 2019 Probability Theory
Fall 2018 Topics in Statistics 2: Neural Networks and Deep Learning
Fall 2017 Stochastic Processes
Spring 2017 Seminar on Neural Networks
Fall 2016 Seminar on the Poisson Point process (in German)
Spring 2014 Spatial Statistics II (TA)
Fall 2013 Spatial Statistics I (TA)
Spring 2012 Stochastic Networks II (TA)
Fall 2011 Stochastic Networks I (TA)
Spring 2011 Markov Chains and Monte Carlo Simulation (TA)

Supervision

PhD theses
- D. Willhalm (since 05/20, University of Groningen). Large deviations in stochastic geometry
MSc theses
- L. de Jonge (since 10/20, University of Groningen). Percolation in reinforcement-based models for synaptic plasticity
- 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
- 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