Presently I’m a postdoc at UiT The Arctic University of Norway in Tromsø under the supervision of Cordian Riener. Before that I spent a year in the group of Liam Solus at KTH Stockholm, Kaie Kubjas’s group at Aalto University and in the non-linear algebra group of Bernd Sturmfels at MPI-MiS 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 and CInet, a more high-tech and more general repository for software and research data conditional independence.
0000-0001-7284-182.T. Boege: The entropy profiles of a definable set over finite fields, cs.IT/2502.20355, 2025.
T. Boege: No eleventh conditional Ingleton inequality, Experimental Mathematics 33(4):808–816, 2024, DOI:10.1080/10586458.2023.2294827, cs.IT/2204.03971. MathRepo: ConditionalIngleton.
math.CO/2407.17826, 2024. MathRepo: SymmetricPrincipalMinorSigns.T. Boege, L. Solus: Real birational implicitization for statistical models, math.ST/2410.23102, 2024.
T. Boege, M. Drton, B. Hollering, S. Lumpp, P. Misra, D. Schkoda: Conditional Independence in Stationary Diffusions, Stochastic Processes and their Applications, 2025, DOI:10.1016/j.spa.2025.104604. math.ST/2408.00583.
T. Boege, K. Kubjas, P. Misra, and L. Solus: Colored Gaussian DAG models, math.ST/2404.04024, 2024. Code: coloredDAGs.
T. Boege: Algebra in probabilistic reasoning, Computeralgebra-Rundbrief 71:15–20, 2022, math.ST/2211.04164.
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, math.ST/2112.10287. MathRepo: MarginalIndependence, auxiliary code and data: CI-models-from-graphs.
T. Boege, T. Kahle, A. Kretschmer, and F. Röttger: The geometry of Gaussian double Markovian distributions, Scandinavian Journal of Statistics 50(2):665–696, 2023, 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, math.ST/2009.11849.
T. Boege, J. H. Bolt, and M. Studený: Self-adhesivity in lattices of abstract conditional independence models, Discrete Applied Mathematics 361:196–225, 2025, DOI:10.1016/j.dam.2024.10.006, math.CO/2402.14053, 2024. Data: CInet/selfadhe-lattices.
T. Boege: Selfadhesivity in Gaussian conditional independence structures, Proceedings of the 12th Workshop on Uncertainty Processing (WUPES ’22) and International Journal of Approximate Reasoning 163, 2023, DOI:10.1016/j.ijar.2023.109027, cs.IT/2205.07667, MathRepo: 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, math.ST/2103.02589, 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, and T. Kahle: Construction Methods for Gaussoids, Kybernetika 56(6):1045–1062, 2020, DOI:10.14736/kyb-2020-6-1045, math.CO/1902.11260. Data: Special gaussoids.
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.
math.HO/2211.12071.T. Boege: The Gaussian conditional independence inference problem, doctoral dissertation, Otto-von-Guericke-Universität Magdeburg, 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, mthesis.pdf, 2018.
T. Boege: On Permutations with Decidable Cycles, B.Sc. thesis, Otto-von-Guericke-Universität Magdeburg, math.LO/1612.05136, 2016.