Research Group

The Nonlinear Algebra group at MiS works on fundamental problems in algebra, geometry and combinatorics that are relevant for nonlinear models. This involves algebraic geometry (complex and real), commutative algebra, combinatorics, polyhedral geometry, and more. On the applications side, we are especially interested in statistics, optimization and the life sciences.

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The theory, algorithms, and software of linear algebra are familiar tools across mathematics, the applied sciences, and engineering. This ubiquity of linear algebra masks the fairly recent growth of nonlinear algebra in mathematics and its application. The proliferation of nonlinear methods, notably for systems of multivariate polynomial equations, has been fueled by recent theoretical advances, efficient software, and an increased awareness of these tools. This connects to numerous branches in the mathematical sciences.

Tropical geometry is a mathematical theory that connects algebraic and discrete geometry through the study of tropical varieties. The process of tropicalization allows for the degeneration of an algebraic variety to a skeleton that can be studied using techniques from discrete geometry and combinatorics.

Algebraic geometry studies algebraic varieties, which are solution sets of polynomial equations. It has applications in diverse areas of science and mathematics. The Nonlinear Algebra Group works at the intersection of algebraic geometry and its applications in a variety of disciplines.

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Miscellaneous

06.05.24
Congratulations to Kemal Samuel Rose on the successful defense of his thesis on “Sparse polynomial system(s) in optimization” as well as on his new position at KTH Royal Institute of Technology in Stockholm. Well done!

Announcements

26.04.24
In the April Feature Column of the American Mathematical Society İrem Portakal and Bernd Sturmfels speak about game theory and the fascinating geometric structure of equilibria.
Explore the shape of decision-making in the context of a simple cooperative game: what to do for date night.

Announcements

22.04.24
Irina Bobrova, Anna-Laura Sattelberger and Simon Telen represent young researchers in the Young Academy of the European Mathematical Society (EMYA). Discover how they would like to contribute to strengthen the role of and prospects of young mathematicians in Europe.

Announcements

14.03.24
Leonie Kayser, Barbara Betti and Anton Ullrich are the new PhD representatives of our institute. Leonie also represents us in the Max Planck Society’s PhD network. Congratulations & much success!

Announcements

05.03.24
A collaboration between the mathematicians Claudia Fevola, Simon Telen and the physicist Sebastian Mizera paves the way to more accurate predictions in the Standard Model of particle physics. Their results have just been published in Physical Review Letters.

In Conversation

19.02.24
In a video interview, the project leaders of UNIVERSE+ share insights into the project’s objectives and their personal motivation to create a new mathematical language to describe physical phenomena on all scales. Discover the very positive about positive geometry!

Accolades

10.01.24
In recognition of his outstanding scientific contributions in the field of algebraic geometry, our director Bernd Sturmfels has been awarded an honorary doctorate from the University of Chicago. Warmest congratulations!

Research Group Leader

Interdisciplinary frontiers of algebraic geometry

Research Group Leader

Numerical Algebraic Geometry

Scientist

Real Algebraic Geometry, Convex Algebraic Geometry, Polynomial Optimization

Scientist

Tropical Geometry, Algebraic Geometry, Commutative algebra, Combinatorics

Scientist

Algebraic Statistics, Phylogenetics, Tropical Geometry

Scientist

Scientist

Scientist

Scientist

Algebraic Geometry, Enumerative Geometry, Commutative Algebra, Combinatorics

Scientist

Scientist

Applied Algebraic Geometry

Scientist

Applied Algebraic Geometry, (Non-Noetherian) Commutative Algebra, Model Theoretic Algebra

PhD Student

Computer Algebra, Tropical Geometry

PhD Student

Computer Algebra, Tropical Geometry

PhD Student

Numerical Nonlinear Algebra

PhD Student

PhD Student

PhD Student

Algebraic Geometry, Combinatorics

PhD Student

Algebraic Geometry, Algebraic Statistics, and Combinatorics

PhD Student

Differential Algebra

PhD Student

Affiliated Member

Affiliated Member

Affiliated Member

Applied Algebraic Geometry and Numerical Nonlinear Algebra

Affiliated Member

Algebraic Geometry, Algebraic Analysis, Commutative Algebra, Combinatorics

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2024Preprint

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2024seminar

28.05.24
04.07.24
conference

15.07.24
19.07.24
conference

29.07.24
02.08.24
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- Francesca Tombari (MPI MiS, Leipzig)

- Dan Bath (KU Leuven)

- Svala Sverrisdottir (University of California, Berkeley)

- Andreas Kretschmer (MPI MiS, Leipzig)

- Maximilian Wiesmann (MPI MiS, Leipzig)

- Swiatoslaw Gal (University of Wrocław)

- Laura Casabella (MPI MiS, Leipzig)

- Gianni Petrella (University of Luxembourg)

- Shmuel Onn (Technion, Haifa)

- Thomas Kahle (Otto von Guericke University, Magdeburg)

- Pepijn Hulsbergen (University of Leipzig)