About Me

Since June 2021, I am an assistant professor at University of Twente in the Discrete Mathematics & Mathematical Programming group. Since September 2023, I am a guest professor at FU Berlin as acting head of the Discrete Geometry and Topological Combinatorics group substituting for Günter Ziegler.
CONTACT: g.((surname))(at)utwente.nl OR ((prename)).((surname))(at)math.fu-berlin.de
  • Broadly interested in the interplay between geometric and combinatorial objects with applications in optimization and data science
  • Improvement of teaching via modern methods
  • Sustainability in research and society

Short CV

Georg Loho
Georg Loho




  • Oriented Matroids from Triangulations of Products of Simplices
    with Marcel Celaya, Chi Ho Yuen (arxiv)(publication)
    Selecta Mathematica (2024)
  • The Worst-Case Complexity of Symmetric Strategy Improvement
    with Tom van Dijk, Matthew Maat (arxiv)(conference)
    CSL (2024)
  • Face posets of tropical polyhedra and monomial ideals
    with Ben Smith (journal)(arxiv)
    The Electronic Journal of Combinatorics (2023)
  • Tropical Positivity and Determinantal Varieties
    with Marie-Charlotte Brandenburg, Rainer Sinn (journal)(arxiv)
    Algebraic Combinatorics (2023)
  • Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes
    with Christian Haase, Christoph Hertrich (arxiv)(conference)
    ICLR 2023
  • On the Correlation Gap of Matroids
    with Edin Husić, Zhuan Khye Koh, László A. Végh (arxiv)(conference)
    IPCO 2023
  • Tropical Carathéodory with Matroids
    with Raman Sanyal (journal)(arxiv)
    Discrete & Computational Geometry (2023)
  • Interior point methods are not worse than Simplex
    with Xavier Allamigeon, Daniel Dadush, Bento Natura, László A. Végh (arxiv)(conference)
    FOCS 2022
  • Generalized permutahedra and positive flag Dressians
    with Michael Joswig, Dante Luber, Jorge Alberto Olarte (journal)(arxiv)(conference)
    FPSAC 2022
  • Beyond Value Iteration for Parity Games: Strategy Iteration with Universal Trees
    with Zhuan Khye Koh (conference)(arxiv)(video)
    MFCS 2022
  • Patchworking Oriented Matroids
    with Marcel Celaya, Chi Ho Yuen (journal)(arxiv)(video)
    Journal of the London Mathematical Society (2022)
  • On complete classes of valuated matroids
    with Edin Husić, Ben Smith, László A. Végh (arxiv)(conference)
    ACM-SIAM Symposium on Discrete Algorithms 2022
  • Tropical Ehrhart Theory and Tropical Volume
    with Matthias Schymura (publication)(arxiv)(slides)
    Research in the Mathematical Sciences, 7(30) (2020)
  • Matching fields and lattice points of simplices
    with Ben Smith (publication)(arxiv)(slides)
    Advances in Mathematics, 370 (2020), 107232
  • Abstract tropical linear programming
    The Electronic Journal of Combinatorics (2020)
  • Signed tropical convexity
    with László A. Végh (publication)(arxiv)(slides)
    11th Innovations in Theoretical Computer Science Conference (ITCS 2020), LIPIcs, Volume 151 (2020), pp. 24:1-24:35
  • Monomial tropical cones for multicriteria optimization
    with Michael Joswig (publication)(arxiv)(slides)
    SIAM J. Discrete Math., 34(2) (2020), 1172-1191.
  • Linear Programs and Convex Hulls Over Fields of Puiseux Fractions
    with Michael Joswig, Benjamin Lorenz, Benjamin Schröter (publication)(arxiv)
    Mathematical Aspects of Computer and Information Sciences: 6th International Conference (MACIS 2015), Revised Selected Papers, LNCS Volume 9582 (2016), pp 429-445
  • Weighted digraphs and tropical cones
    with Michael Joswig (publication)
    Linear Algebra Appl. 501 (2016), 304-343.
  • MatchTheNet - An Educational Game on 3-Dimensional Polytopes
    with Michael Joswig, Benjamin Lorenz, Rico Raber (publication)(game homepage)
    33rd International Symposium on Computational Geometry (SoCG 2017), LIPIcs, Volume 77 (2017), pp 66:1--66:5


  • The Real Tropical Geometry of Neural Networks
    with Marie-Charlotte Brandenburg, Guido Montúfar (arxiv)
  • Quotients of M-convex sets and M-convex functions
    with Marie-Charlotte Brandenburg, Ben Smith (arxiv)
  • Signed tropical halfspaces and convexity
    with Mateusz Skomra (arxiv)(video)


Doctoral Thesis “Combinatorics of Tropical Linear Programming”

Further Talks

  • Survey Talk: Oriented Matroids and Signed Tropical Convexity (video) (slides)


  • Poster for 7ECM (July 18 – 22, 2016)
  • Poster for Einstein Workshop Discrete Geometry and Topology (March 13-16, 2018)

Further Material

Current Teaching

  • Vorlesung / Projekt Mathematik & Nachhaltigkeit
  • Vorlesung Geometrie
  • Research Seminar of the Group Discrete Geometry and Topological Combinatorics
More details on WHITEBOARD

Former Teaching

Winter 2023/2024

  • Discrete Geometry III
  • (Pro)Seminar Mathematik & Nachhaltigkeit
  • (Pro)Seminar Mathematik, KI & Lehre
  • Research Seminar of the Group Discrete Geometry and Topological Combinatorics

2021 - 2023

see list @UT

Winter 2020/2021

Before 2021

  • Galois Theory (WiSe 2018)
  • Anneaux et corps (Rings and fields, SoSe2018)
  • Computerorientierte Mathematik I & II (WiSe2013, WiSe2014, SoSe2015, WiSe2015, SoSe2016, SoSe2017, WiSe2017)
  • Topologie (WiSe2016)
  • Diskrete Geometrie I (SoSe2014)
  • Funktionentheorie I (SoSe2013, Universität Würzburg)

Some supervised theses



  • Girls' Day 2024
  • Festvortrag bei der Landesrunde der 63. MO in Bayern (slides)
  • Pi-Day 2024 am Käthe-Kollwitz-Gymnasium (slides)


Some past events

Further Interests

Software development

Educational Game

Math Olympiad
I am involved in the organisation of the mathematical olympiad in Bavaria. For more information see:

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