About Me

Since June 2021, I am an assistant professor at University of Twente in the Discrete Mathematics & Mathematical Programming group.
Contact: g.((surname))(at)utwente.nl

Short CV

Georg Loho
Georg Loho

News

  • Together with Mateusz Skomra, we are looking for an internship candidate on the topic Understanding games and linear programming through tropical geometry -- check out the description!
  • We are welcoming a new PhD student, Matthew Maat, co-supervised together with Tom van Dijk!

Research

Broadly interested in the interplay between geometric and combinatorial objects with applications in optimization and data science

Publications

  • Tropical Carathéodory with Matroids
    with Raman Sanyal (journal)(arxiv)
    Discrete & Computational Geometry (2022)
  • Interior point methods are not worse than Simplex
    with Xavier Allamigeon, Daniel Dadush, Bento Natura, László A. Végh (arxiv)
    FOCS 2022
  • Generalized permutahedra and positive flag Dressians
    with Michael Joswig, Dante Luber, Jorge Alberto Olarte (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
    (publication)(arxiv)
    The Electronic Journal of Combinatorics, P2.51 (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

Preprints

  • On the Correlation Gap of Matroids
    with Edin Husić, Zhuan Khye Koh, László A. Végh (arxiv)
  • Signed tropical halfspaces and convexity
    with Mateusz Skomra (arxiv)
  • Tropical Positivity and Determinantal Varieties
    with Marie-Charlotte Brandenburg, Rainer Sinn (arxiv)
  • Oriented Matroids from Triangulations of Products of Simplices
    with Marcel Celaya, Chi Ho Yuen (arxiv)
  • Face posets of tropical polyhedra and monomial ideals
    with Ben Smith (arxiv)

Thesis

Doctoral Thesis “Combinatorics of Tropical Linear Programming”
(publication)(slides)

Further Talks

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

Posters

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

Current Teaching

see list @UT

Former Teaching

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)

Events

Upcoming

Some past events

Further Interests

Software development
polymake

Educational Game
MatchTheNet

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

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