Alheydis Geiger
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Inselstr. 22
04103 Leipzig

Office: G3 08


+49 341 9959 824

+49 341 9959 658

Alheydis Geiger

Research interests

My main focus is the area of tropical geometry. In particular in its connections to algebraic geometry, enumerative geometry, combinatorics and polyhedral geometry, matroid theory, and its computational aspects. 



Positive del Pezzo Geometry (joint with Nick Early, Marta Panizzut, Bernd Sturmfels and Claudia Yun), arXiv:2306.13604

Self-dual matroids from canonical curves (joint with Sachi Hashimoto, Bernd Sturmfels and Raluca Vlad), Experimental Mathematics (2023)

Tropical Geometric Counting Problems (PhD Thesis)

Towards tropically counting binodal surfaces (joint with Madeline Brandt), La Matematica. Official Journal of the Association for Women in Mathematics (2023)

A tropical count of real bitangents to plane quartic curves (joint with Marta Panizzut), arXiv:2112.04433, accepted for publication at The Electronic Journal of Combinatorics, 06.2023

Computing tropical bitangents to smooth quartic curves in polymake (joint with Marta Panizzut), Journal of Symbolic Computation, vol. 120, 2024

A tropical count of binodal cubic surfaces (joint with Madeline Brandt), Le Matematiche, Vol 75 No 2 (2020)

On Realizability of lines on tropical cubic surfaces and the Brundu-Logar normal form, Le Matematiche, Vol 75 No 2 (2020)

Curriculum vitae

Since August 2023 I am post-doc in the math software group lead by Michael Joswig  at MPI MiS in Leipzig.

From July 2022-August 2023 I was a post-doctoral researcher in the Non-Linear Algebra Group by Bernd Sturmfels at MPI MiS in Leipzig.


  • July 2022 PhD (Universität Tübingen), "Tropical Geometric Counting Problems", supervisor Prof. Hannah Markwig
  • March 2020 Master of Science (Universität Tübingen), Masterthesis: Tropical Cubic Surfaces - Enumeration and Lines, supervisor: Prof. Hannah Markwig.
  • Sep. 2018 Master of Science (University of Warwick), Masterthesis: Realisability of infinite families of tropical lines on general smooth cubic surfaces, supervisor: Prof. Diane Maclagan
  • Oct. 2016 Bachelor of Science (Universität Tübingen)

Conferences, Seminars and Talks

  • Up-coming: 25.-28.9.2023, DMV Meeting, Ilmenau, Talk: "Positive del Pezzo Geometry" 
  • 7.-11.8.2023, Algebraic, Tropical, and Logarithmic workshop, Banff, Talk: "Self-dual matroids from canonical curves"
  • 10.-14.7.2023, SIAM AG, Eindhoven, Talk: "Positive del Pezzo Geometry" in the Minisymposium "Real Algebraic Geometry"
  • 28.-29.6.2023, 24 Hours of Combinatorial Synergies, Magdeburg, Talk: "Positive del Pezzo Geometry"
  • 15.6.2023, Joint Algebra Seminar, Aachen (online), Talk: "Positive del Pezzo Geometry"
  • 15.6.2023, Oberseminar Algebra, Chemnitz, Talk: "Positive del Pezzo Geometry"
  • 31.5.-2.6.2023, Computeralgebra Fachschaftstagung, Hannover, Talk: "Self-dual matroids from canonical curves - computational challenges"
  • 29.-31.3.2023, Regional Workshop in Algebraic Geometry, Jena, Talk: "Self dual matroids from canonical curves"
  • 17.2.2023, LMS workshop on Tropical Mathematics, Talk: "Self-Duality in Tropical Geometry"
  • 24.-25.11.2022MOM workshop on MaRDI, OSCAR and MATHREPO, Talk: "Self-dual matroids from canonical curves - computational challenges"
  • 22.11.2022,  Algebra Seminar Osnabrück, Talk: "A tropical count of real bitangents to plane quartic curves"
  • 14.-18.11.2022, Newton-Okunkov Bodies & Tropical Geometry, Frankfurt, Talk: "Self dual matroids from canonical curves"
  • 7.11.2022, Moduli Day, MPI MiS Leipzig, Talk: "Self dual matroids from canonical curves"
  • 01.08.-05.08.2022 "Young Researchers Conference in Non-Archimedean and Tropical Geometry", Regensburg, Introductory Lecture: "Applications of tropical geometry"
  • 20.06.-24-06.2022 "MEGA", Kraków, Poland
  • 15.03.-17.03.2022, "Lectures on Theta - Replacement", MPI MiS Leipzig
  • 29.11.-1.12.2021 „Women in Algebra and Symbolic Computation II“, SFB-TRR 195, Bad Dürkheim, Talk: „Towards counting tropical binodal surfaces“
  • 24.-30.10.2021, Oberwolfach Seminar: Tropical Curves, Logarithmic Structures, and Enumerative Geometry
  • 13.-16.09.2021, Fifth annual conference of the SFB-TRR 195, RWTH Aachen, Talk: "Counting tropical binodal surfaces" and Joint Talk: "A tropical proof of Plücker's Theorem" with Marta Panizzut
  • 16.08.-20.08.2021 SIAM Conference on Algebraic Geometry, Talk: "Deformations of Bitangent Classes of Tropical Quartic Curves"
  • 07.06.-11.06.2021 MEGA Conference, University Tromsø - The Artic University of Norway, Online.
  • 11.05.2021 Seminar Talk"Deformations of Bitangent Classes of Tropical Quartic Curves", Tübingen.
  • 22.01.2021 "TGIZ-Tropical geometry in Zoom", Goethe Universität Frankfurt am Main, Talk"Deformations of bitangent classes of tropical quartic curves"
  • 13.07.-16.07.2020 "International Congress on Mathematical Software", TU Braunschweig, Online Conference, Talk"Tropical Algebraic Geometry - A tropical count of binodal cubic surfaces"
  • 09.12.-11.12.2019 „Women in Algebra and Symbolic Computation“, SFB-TRR 195, Bad Dürkheim, Talk: „Tropical Cubic Surfaces“
  • 29.07.-02.08.2019 „Young Researchers Conference in Non-Archimedean and Tropical Geometry“, Universität Regensburg, Talk: „Relative Realisability of infinite families of tropical lines on general smooth tropical cubic surfaces“
  • 08.05.2019 Researchseminar, TU Berlin, Talk: "Realisability of infinite families of tropical lines on general smooth cubic surfaces"


Workshops and more


Summer Schools

  • 05.09.-09.09.2022 "Combinatorial Methods in Algebraic Geometry", Cambridge, England
  • 23.05.-27.05.2022 "International Summer School on Tropical Geometry", Valladolid, Spain
  • 06.09.-10.09.2021 "Computeralgebra", RWTH Aachen
  • 23.08.-27.08.2021 "Tropical homology and Hodge theory", online format
  • 26.07.-06.08.2021 "Combinatorial Algebraic Geometry",LMs-Bath Symposium, University of Bath, virtual format
  • 28.06.-02.07.2021 "Tropical Moduli Spaces", EWM/EMS Mittag Leffler summer school, virtual format
  • 06.2020-07.2020 "Algebraic and Tropical Online Meetings"
  • 03.06.2019-07.06.2019 „New Perspectives in Gromov-Witten Theory“, Summer School at Sorbonne Université, Paris


  • Summersemester 2023: Introduction to tropical geometry
  • winter term 2021/2022: teaching assistant for "Commutative Algebra", Lecturer: Thomas Markwig
  • Since winter term 2020/21: Conductor of the training for mentors in the mentoring programm for first year students(in the winter term 2020/21 together with Sophia Jahns, since summer term 2021 single-handedly)
  • winter term 2020/2021: teaching assistant for "Introduction to algebraic geometry and commutative algebra", Lecturer: Hannah Markwig
  • summer term 2020: teaching assistant for "Algebra", Lecturer: Hannah Markwig
  • 2014-2020: support class teacher for different lectures
08.09.2023, 10:16