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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In Conversation

Feb 19, 2024
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

Jan 10, 2024
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!

Press Releases

Dec 18, 2023
Michael Joswig and his team, in collaboration with ETH Zurich and Carnegie Science, introduce a new approach for modeling genetic interactions in PNAS. They identify master regulators in entire genetic networks, offering a novel theoretical framework.

Accolades

Dec 7, 2023
Our director, Bernd Sturmfels, was recently awarded an honorary doctorate by the University of Bern during its Dies Academicus festivities. The recognition comes in light of his remarkable contributions to mathematical research and the promotion of gender diversity.

Accolades

Nov 21, 2023
Hanna Tseran successfully defended her PhD thesis on activation functions in neural networks. She continues to work on deep learning theory in the Matsuo Laboratory at the University of Tokyo. Well done Hanna, and our best wishes!

Press Releases

Oct 26, 2023
The European Research Council (ERC) has granted a €10 million Synergy Grant to the UNIVERSE+ project. The project aims to develop a new mathematical language to describe physical phenomena at all scales, from particles to the universe's structure.

Math Planck People

Aug 9, 2023
The most recent addition to our Math Planck People is postdoc Lisa Seccia. Lisa is researching Combinatorial, Computational, and Pure Commutative Algebra in the Nonlinear Algebra Group.

Math Planck People

Jul 26, 2023
Alessio Borzì is a recent postdoc in the Nonlinear Algebra group and the latest individual to reveal their academic journey and interests in our Math Planck People series.

Research Group Leader

Interdisciplinary frontiers of algebraic geometry

Research Group Leader

Numerical Algebraic Geometry

Scientist

Tropical Geometry, Algebraic Geometry, Commutative algebra, Combinatorics

Scientist

Scientist

Scattering Amplitudes, Combinatorial and Tropical Geometry

Scientist

PhD Student

Computer Algebra, Tropical Geometry

PhD Student

Computer Algebra, Tropical Geometry

PhD Student

Numerical Nonlinear Algebra

PhD Student

PhD Student

algebraic geometry, algebraic statistics, and combinatorics

PhD Student

Differential Algebra

PhD Student

Applied Algebraic Geometry and Numerical Nonlinear Algebra

PhD Student

Algebraic Statistics and Combinatorial and Commutative algebra

PhD Student

Affiliated Member

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- Leonard Schmitz (Greifswald University)

- Bernd Sturmfels (MPI MiS, Leipzig)

- Samantha Fairchild (MPI MiS, Leipzig)

- Raluca Vlad (Brown University)

- Aryaman Jal (KTH Stockholm)

- Rosa Preiß (MPI MiS, Leipzig)

- Érika Roldán (MPI MiS, Leipzig)

- Dan Kaplan (Hasselt University)