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.

/

/

/

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.

We are one of four groups that constitute the ERC Synergy project
Positive Geometry in Particle Physics and Cosmology.
We study structures in combinatorics and algebraic geometry that arise from
fundamental physics, such as positive Grassmannians, amplituhedra, spinor helicity varieties,
scattering equations, Feynman integrals, canonical differential forms, and much more.

Our group is part of the DFG priority program Combinatorial
Synergies. This is a Germany-wide network, aimed at building a community
of researchers in combinatorics that takes a broad perspective
on this field. The collaboration is centered around
combinatorial structures arising in the following nine domains:
Enumeration, Statistics, Commutative Algebra, Mathematical Physics,
Dynkin Classification, Convexity, Lattice Points, Matroids, and
Nonlinear Optimization.

/

Job Openings

02.10.24
The Max Planck Institute for Mathematics in the Sciences in Leipzig offers two PhD positions, to be based in the Algebraic Analysis group of Anna-Laura Sattelberger and the Nonlinear Algebra group of Bernd Sturmfels. The prospective PhD students will be part of the UNIVERSE+ Project.

Miscellaneous

27.09.24
We congratulate Dmitrii Pavlov on the successful defense of his thesis: „Real Algebraic Geometry for Physics and Optimization“! His next career step takes him to TU Dresden. Heartfelt congratulations!

Miscellaneous

02.08.24
We look back on a special conference week on Effective Methods in Algebraic Geometry featuring 200 participants, inspiring talks and discussions, and a lively scientific exchange.

Accolades

15.07.24
Barbara Betti and Laura Casabella have been awarded the Gustavo Mezzetti Prize in Italy for the best master's theses in the field of algebra. The two doctoral candidates and friends share an outstanding first place. Congratulations!

Accolades

12.06.24
Claudia Fevola has been honored by the Max Planck Society as one of its top junior scientists. In recognition of her outstanding scientific achievements during her doctoral studies she has been awarded the 2024 Otto Hahn Medal. Congratulations!

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.

Research Group Leader

Interdisciplinary frontiers of algebraic geometry

Research Group Leader

Numerical Algebraic Geometry

Group Leader

Scientist

Scientist

Tropical Geometry, Algebraic Geometry, Commutative algebra, Combinatorics

Scientist

Algebraic Statistics, Phylogenetics, Tropical Geometry

Scientist

Scientist

Scientist

Multigraded Commutative Algebra, Combinatorial Algebraic Geometry

Scientist

Scientist

Applied Algebraic Geometry

Scientist

Ph.D. Student

Computer Algebra, Tropical Geometry

Ph.D. Student

Ph.D. Student

Computer Algebra, Tropical Geometry

Ph.D. Student

Numerical Nonlinear Algebra

Ph.D. Student

Ph.D. Student

Ph.D. Student

Algebraic Geometry, Combinatorics

Ph.D. Student

Algebraic Geometry, Algebraic Statistics, and Combinatorics

Ph.D. Student

Algebraic Geometry, Algebraic Statistics, and Combinatorics

Ph.D. Student

Affiliated Member

Real Algebraic Geometry, Convex Algebraic Geometry, Polynomial Optimization

Email
w/o

Affiliated Member

Affiliated Member

Affiliated Member

Affiliated Member

Preprint

2024Preprint

2024Preprint

2024inJournal

2024Preprint

2024inJournal

2024inJournal

2024inJournal

2024Preprint

2024Preprint

2024seminar

16.10.24
11.12.24
seminar

22.10.24
10.12.24
seminar

23.10.24
06.11.24
Max Planck Institute for Physics (n.n.)
Live Stream

conference

25.11.24
28.11.24
/

- Emanuele Delucchi (SUPSI)

- Leonie Kayser (MPI MiS, Leipzig)

- Emma Cardwell (Harvard University)

- Sibren Lagauw (Katholieke Universiteit Leuven)

16:00

- Bernd Sturmfels (MPI MiS, Leipzig)

- Nikolai Bobenko (University of Geneva)

- Eric Pichon-Pharabod (MPI MiS, Leipzig)

- Francesca Zaffalon (MPI MiS, Leipzig)

- Danai Deligeorgaki (KTH Stockholm)

- Barbara Betti (MPI MiS, Leipzig)

- Alessio Caminata (University of Geneva)