Presently I’m a postdoc in the group of Kaie Kubjas at Aalto University, Finland. Before that, I spent a year in the non-linear algebra group of Bernd Sturmfels at the Max-Planck-Institute for Mathematics in the Sciences, Leipzig.
I received my PhD within the MathCoRe research training group at Otto-von-Guericke-Universität Magdeburg under the supervision of Thomas Kahle and Volker Kaibel working on a topic in algebraic statistics.
I have a broad interest in the fundamental laws and limits in probability, information theory and geometry. My research is focussed on conditional independence: suppose you observe some factors in a (random) experiment; how does that knowledge change the interdependence of the remaining factors? This is a question in the area of probabilistic reasoning and I am looking for the universal laws governing such reasoning tasks — and ways to prove them algebraically using computers.
The analogue to have in mind is Pappus’s theorem in plane geometry. But instead of points and collinearity, I want to discover the hidden relations of random variables in terms of stochastic independence.
These topics touch algebra, statistics, geometry and computer science. I maintain the website gaussoids.de which contains various computer-readable data about Gaussian conditional independence structures and related objects.
T. Boege: Algebra in probabilistic reasoning, Computeralgebra-Rundbrief 71:15–20, 2022,
T. Boege, S. Petrović, and B. Sturmfels: Marginal Independence Models, Proceedings of the 47th International Symposium on Symbolic and Algebraic Computation 2022:263–271, 2022, DOI:10.1145/3476446.3536193,
MarginalIndependence, auxiliary code and data:
T. Boege, T. Kahle, A. Kretschmer, F. Röttger: The geometry of Gaussian double Markovian distributions, Scandinavian Journal of Statistics, 2022, DOI:10.1111/sjos.12604,
math.ST/2107.00134. Data: Double Markovian relations.
T. Boege, J. I. Coons, C. Eur, A. Maraj, and F. Röttger: Reciprocal Maximum Likelihood Degrees of Brownian Motion Tree Models, Le Matematiche 76(2):383–398, 2021, DOI:10.4418/2021.76.2.6,
T. Boege: Selfadhesivity in Gaussian conditional independence structures, Proceedings of the 12th Workshop on Uncertainty Processing (WUPES ’22), May 2022,
SelfadhesiveGaussianCI. This set of research data won the “FAIRest MathRepo page” award 2022 at the “MaRDI, Oscar and MathRepo” conference in Berlin.
T. Boege: Incidence geometry in the projective plane via almost-principal minors of symmetric matrices, Mar 2021,
T. Boege: Gaussoids are two-antecedental approximations of Gaussian conditional independence structures, Annals of Mathematics and Artificial Intelligence 90:645–673, 2022, DOI:10.1007/s10472-021-09780-0,
math.ST/2010.11914. Code related to computations:
gaussant-code. The published version contained misprints for a couple of months. They have been corrected under the above DOI and a statement was published here.
T. Boege, A. D’Alì, T. Kahle, and B. Sturmfels: The Geometry of Gaussoids, Foundations of Computational Mathematics, 19(4):775–812, 2019, DOI:10.1007/s10208-018-9396-x,
math.CO/1710.07175. Data: Gaussoids.de.
T. Boege: The Gaussian conditional independence inference problem, doctoral dissertation, Otto-von-Guericke-Universität Magdeburg, June 2022, DOI:10.25673/86275. dissert.pdf (published version), Defense slides. I won the dissertation prize of the University of Magdeburg in the academic year 2021/2022. They produced a short portrait film:
T. Boege: Construction Methods for Gaussoids, M.Sc. thesis, Otto-von-Guericke-Universität Magdeburg, Sep 2018, mthesis.pdf.
T. Boege: On Permutations with Decidable Cycles, B.Sc. thesis, Otto-von-Guericke-Universität Magdeburg, Dec 2016,