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 an Associate Fellow of the Aarhus Institute for Advanced Studies. 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.

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

PhD in Mathematics, 2014

Ulm University

Diploma in Mathematics, 2010

LMU Munich

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.

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.

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.

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**Fall 2024**Monte Carlo Simulation**Spring 2024**Markov Decision Processes**Fall 2023**Monte Carlo Simulation**Spring 2023**Topological Data Analaysis**Fall 2022**Monte Carlo Simulation**Spring 2022**Numerisk lineær algebra (consultation hours)**Fall 2021**Topological Data Analysis**Spring 2021**Probability Theory**Spring 2021**Stochastic Processes**Fall 2020**Topological Data Analysis**Spring 2020**Probability Theory**Spring 2020**Stochastic Processes**Fall 2019**Markov Decision Processes**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**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)

**Postdocs**- M. Otto (since 02/22).

**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 (05/20 - 04/24).
*Limit theory for spatial random networks*

- N.N. Lundbye (since 02/23).
**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*

- L. de Jonge (07/21).
**BSc theses**- 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* - 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*

- K.B. Bräuner and A. Kristensen (05/24).