Mathematics

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.

Here is my full CV (last updated 21 June 2022).

Publications and preprints

T. Boege: Selfadhesivity in Gaussian conditional independence structures, Proceedings of the 12th Workshop on Uncertainty Processing (WUPES ’22), May 2022, cs.IT/2205.07667, MathRepo: SelfadhesiveGaussianCI.
T. Boege: No eleventh conditional Ingleton inequality, Apr 2022, cs.IT/2204.03971, MathRepo: ConditionalIngleton.
T. Boege, S. Petrović, and B. Sturmfels: Marginal Independence Models, Dec 2021, math.ST/2112.10287. MathRepo: MarginalIndependence, auxiliary code and data: CI-models-from-graphs.
T. Boege, T. Kahle, A. Kretschmer, F. Röttger: The geometry of Gaussian double Markovian distributions, Jul 2021, 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, math.ST/2103.02589.
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, math.ST/2009.11849.
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.

Theses

T. Boege: The Gaussian conditional independence inference problem, doctoral dissertation, Otto-von-Guericke-Universität Magdeburg, June 2022, 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, math.LO/1612.05136.

Talks

27 June 2022: Gaussian conditional independence beyond graphical models, Annual Meeting of the Institute of Mathematical Statistics (IMS), London.
3 June 2022: Selfadhesivity in Gaussian conditional independence structures, WUPES ’22, Kutná Hora.
24 May 2022: Introduction to matroids and chromatic polynomials, Geometry of Lorentzian polynomials day, Online.
5 May 2022: Marginal independence models, Applied Algebra and Analysis Online seminar, TU Braunschweig.
5 May 2022: Laws of conditional independence, Vista seminar on “Reusability of research data across mathematics”, University of Leipzig.
20 April 2022: Entropies and Ingleton’s inequality, Non-linear algebra seminar, MPI-MiS Leipzig.
10 March 2022: The laws of Gaussian conditional independence, Tagung der Fachgruppe Computeralgebra, München.
28 January 2022: Marginal independence models, TATERS, Boise State University. Recording is available until mid-2022.
14 October 2021: The Gaussian CI inference problem (real algebra version), Non-linear algebra seminar, MPI-MiS Leipzig.
5 October 2021: Reasoning in Statistics through Algebra, Annual colloquium of MathCoRe, Potsdam.
13 September 2021: The Gaussian CI inference problem (information theory version), Mini symposium at the Department of Decision-Making Theory, Institute of Information Theory and Automation, Prague.
7 September 2021: The Gaussian CI inference problem (algorithmic reasoning version), Algorithms seminar, Universiteit Utrecht.
28 July 2021: The Gaussian CI inference problem (geometry version), Discrete Mathematics / Geometry seminar, TU Berlin.
22 August 2019: On discrete representability of Gaussian CI models — From the perspective of the identity matrix, Workshop in memory of František Matúš, Institute of Information Theory and Automation, Prague.

MathCoRe seminar in Magdeburg:

28 April 2021: Two universality results for Gaussian CI models.
04 November 2020: Computational methods in Gaussian conditional independence inference.
16 October 2019: Gaussian conditional independence structures around the identity matrix.
10 October 2018: Constructions methods for gaussoids.

WISST mini-seminar in Magdeburg:

27 April 2021: What is… a Galois connection?
09 February 2021: What is… the Lefschetz principle?
27 October 2020: What is… the Real Nullstellensatz?
04 February 2020: What is… a hyperfield?
10 December 2019: What is… a polymatroid?

Organization

August 2022: Leipzig-Magdeburg seminar day at MPI-MiS Leipzig, together with Thomas Kahle.
June 2022: Mathematical Software: How to get started tutorial at MPI-MiS Leipzig, together with Ronald Kriemann and Javier Sendra.
March – June 2022: Non-linear algebra seminar at MPI-MiS Leipzig, together with Alessandro Neri.
April 2021: Graduate student meeting on Applied Algebra and Combinatorics, together with Angélica Torres Bustos, Beatriz Pascual Escudero and Benjamin Smith, virtually in Copenhagen.
December 2020 – October 2021: MathCoRe fellow seminar at OvGU Magdeburg.

Activities

December 2022: Workshop on Algebraic structures in statistical methodology, MFO Oberwolfach.
August 2022: European Women in Mathematics General Meeting, Aalto University.
July 2022: Workshop on Algorithmic aspects of information theory, Schloss Dagstuhl.
July 2022: 47th International Symposium on Symbolic and Algebraic Computation (ISSAC), Lille.
June 2022: Annual Meeting of the IMS, London.
June 2022: Conference on the Mathematics of Complex Data, KTH Stockholm.
June 2022: Arctic MSCA Symposium with Cordian Riener, UiT Tromsø.
June 2022: 14th Nordic Combinatorial Conference (NORCOM), UiT Tromsø.
June 2022: 12th Workshop on Uncertainty processing (WUPES), Kutná Hora.
May 2022: Saxonian seminar day on Algebra and geometry, TU Dresden.
March 2022: Combinatorial cowork space on Algebraic and geometric combinatorics, Kleinwalsertal.
March 2022: Tagung der Fachgruppe Computeralgebra, Online, München.
November 2021: MaRDI kickoff workshop, MPI-MiS Leipzig.
1 October 2021: Mathematics in the Sciences Day, MPI-MiS Leipzig.
12–18 September 2021: Research stay at UTIA Prague with Milan Studený.
August 2021: Conference SIAM AG, Texas A&M.
July 2021: Mini-course on Convex Geometry, MPI-MiS Leipzig.
April ~~2020~~ 2021: Graduate student meeting in Applied algebra and combinatorics, Online, Copenhagen.
April 2021: Compact course Algebra of tensors, MathCoRe Magdeburg.
August 2020: Compact course Polynomial optimization, MathCoRe Magdeburg.
June – July 2020: Working group on Linear spaces of symmetric matrices, MPI-MiS Leipzig.
June – August 2020: Mentoring of Garett Cunningham in summer project Formal conditional independence structures. Organized by DAAD-RISE, executed online.
March 2020: Spring school on Mathematical statistics, MPI-MiS Leipzig, canceled.
March 2020: Workshop Algebraic structures in statistical methodology, MFO Oberwolfach, canceled.
October 2019: Workshop on Graphical models: Conditional independence and algebraic structures, TU München.
September 2019: Compact course Statistical data acquisition and analysis, MathCoRe Magdeburg.
August 2019: Workshop in memory of František Matúš, UTIA Prague.
July 2019: Conference SIAM AG, University of Bern.
June 2019: Workshop on Applied algebra, TU Braunschweig.
June 2019: Compact course Invitation to non-linear algebra, MPI-MiS Leipzig.
February 2019: Graduate student meeting in Applied algebra and combinatorics, MPI-MiS Leipzig.
January 2019: Workshop on Theoretical computer science and algebraic geometry, MPI-INF Saarbrücken.
June 2018: Macaulay2 Workshop, MPI-MiS Leipzig.
July 2016: Foundations of Mathematics: Univalent foundations and set theory, ZiF Bielefeld.