Mathematics

Presently I’m a postdoc in the non-linear algebra group of Bernd Sturmfels at MPI Leipzig.

I did my PhD studies within the MathCoRe research training group at Otto-von-Guericke-Universität Magdeburg under the supervision of Thomas Kahle and Volker Kaibel.

My research interests lie in independence structures, which include matroids, gaussoids and the like, their axioms, synthesis problems, geometry and complexity. In my dissertation, I worked on the Gaussian conditional independence inference problem. Recently I have been interested in conditional independence of discrete random variables and the mixed volumes of convex bodies as well.

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.

Publications

T. Boege, T. Kahle, A. Kretschmer, F. Röttger: The geometry of Gaussian double Markovian distributions, Jul 2021, math.ST/2107.00134.
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, Oct 2020, math.ST/2010.11914. Code related to computations: gaussant-code.
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.
T. Boege, A. D’Alì, T. Kahle, and B. Sturmfels: The Geometry of Gaussoids, Foundations of Computational Mathematics, 19(4):775-812, Aug 2019, DOI:10.1007/s10208-018-9396-x, math.CO/1710.07175.

Theses

T. Boege: Construction Methods for Gaussoids, M.Sc. thesis, Otto-von-Guericke-Universität Magdeburg, Sep 2018, mthesis-ovgu.pdf.
T. Boege: On Permutations with Decidable Cycles, B.Sc. thesis, Otto-von-Guericke-Universität Magdeburg, Dec 2016, math.LO/1612.05136.

Talks

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?

Activities

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. Jointly organized with Angélica Torres Bustos, Beatriz Pascual Escudero and Benjamin Smith.
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, Oberwolfach, canceled.
October 2019: Workshop on Graphical models: Conditional independence and algebraic structures, München.
September 2019: Compact course Statistical data acquisition and analysis, MathCoRe Magdeburg.
August 2019: Workshop in memory of František Matúš, UTIA CAS, Prague.
July 2019: Conference SIAM AG, Bern.
June 2019: Workshop on Applied algebra, 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.