Combinatorics and Algebraic Geometry of Tensors

• Applicant: Professor Dr. Mateusz Michalek
• Subject Area: Mathematics ; Theoretical Computer Science
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 467575307

How fast can one multiply matrices? This very basic question is the main motivation for our project. As we will argue it is related to tensors, algebra and geometry. Classical linear algebra provides some of the most useful and often applied tools both in pure and applied mathematics. The new challenging problems, coming with the advances in computational sciences, arise in non-linear algebra. Just as matrices form the basic objects of linear algebra, tensors constitute the focal point of multilinear algebra. It turns out that their properties are much more complicated then those of matrices. This leads to central, fundamental open problems that often can be phrased in both geometric and algebraic language. As tensors are ubiquitous in many different branches of mathematics, also the tools to study them often require an interplay of different methods. In our project we will focus on important tensor problems, solving them through the application of combinatorial, algebraic and geometric methods.

• DFG Programme: Research Grants