Presently I’m a postdoc 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 unobserved 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: Selfadhesivity in Gaussian conditional independence structures, Proceedings of the 12th Workshop on Uncertainty Processing (WUPES ’22), May 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: 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, 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, 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.
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,