Alheydis Geiger

Alheydis Geiger is a Researcher at the Max Planck Institute for Mathematics in the Sciences (MPI MiS) in Leipzig, Germany. Since June 2025, she has led an independent DFG-funded project within the priority program "Combinatorial Synergies." Previously, she held post-doctoral positions in the Non-Linear Algebra Group (2022-2023) and math software group (2023-2025) at MPI MiS under Bernd Sturmfels and Michael Joswig, respectively.

Her academic background includes:

• PhD in Mathematics from Universität Tübingen (2022), supervised by Prof. Hannah Markwig
• Master of Science from Universität Tübingen (2020), supervised by Prof. Hannah Markwig
• Master of Science from University of Warwick (2018), supervised by Prof. Diane Maclagan
• Bachelor of Science from Universität Tübingen (2016)

Geiger specializes in tropical geometry, investigating its intersections with algebraic geometry, enumerative geometry, combinatorics, polyhedral geometry, and matroid theory. Her work emphasizes computational approaches to geometric counting problems, particularly in real algebraic contexts. Key contributions include tropical enumerations of bitangents to quartic curves and lines on cubic surfaces.

Analysis of her 2020-2025 publications reveals consistent focus on tropical enumerative geometry, with increasing emphasis on real tropical methods and computational implementations using tools like polymake. Collaborations frequently involve MPI MiS researchers including Marta Panizzut and Bernd Sturmfels, spanning theoretical advances in del Pezzo surfaces, matroid theory, and binodal surface geometry.

She currently directs a DFG-funded independent research project on combinatorial synergies in tropical geometry. No student advising roles or additional grants are documented in available sources.

Geiger actively contributes to MPI MiS research groups, notably the Non-Linear Algebra Group and math software development initiatives, participating in conferences, workshops, and summer schools related to nonlinear algebra and tropical methods.