Algebra and Algebraic Geometry

Cutting-edge challenges in science require up-to-date methods, especially if high-dimensional data is involved in areas like data analysis or machine learning. The overriding topic of this CIMPA school is recent developments in algebra and geometry with a strong focus on applications. Chemical reaction networks, dynamical systems, and optimization are examples of fields where sophisticated tools from algebraic statistics, combinatorics, toric geometry, or tropical geometry have been applied successfully in the past years.

The main objective of this school is to introduce modern algebraic and geometric as well as directly related methods with emphasis on those ones used in applications. Introductory courses will lay the foundations on recent developments in combinatorial algebra, tropical combinatorics, or on models in statistics like graphical models. More advanced lectures treat applied areas mentioned before (like dynamical systems), in particular their connection to algebra and geometry as well as the use of symmetries and other approaches to reduce complexity for high-dimensional phenomena. In training sessions, the participants of the school can deepen their learned skills and can discuss topics with others.