Research Group
Nonlinear Algebra
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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Research
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.
Research Topics
Tropical Geometry
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
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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News
Announcements
Mar 14, 2024
Representing the interests of Doctoral Researchers
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
Mar 5, 2024
New mathematical tools for studying particle collisions
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
Feb 19, 2024
Promising Start to the Positive Geometry Project
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
Bernd Sturmfels Granted Honorary Doctorate from Uni Chicago
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
A New Mathematical Language for Biological Networks
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
Bernd Sturmfels Granted Honorary Doctorate for Outstanding Contributions to Mathematics
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
Exploring Complexity - Hanna Tseran's PhD Thesis on Deep Maxout Neural Networks
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
Positive Geometry – Millions in Funding for UNIVERSE+ Project
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
Lisa Seccia
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.
Members
Publications
Events
Upcoming Conferences, Workshops, etc.
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