Bernd Sturmfels Livres

The book presents a comprehensive exploration of invariant theory, blending accessible textbook material with advanced research insights. It introduces the Groebner bases method as a key tool for tackling central problems algorithmically. Students will appreciate the clear introduction to this evolving mathematical field, while researchers will benefit from a rich array of research ideas, application hints, detailed algorithms, examples, and problems to explore. This dual approach makes it suitable for both learners and seasoned mathematicians.

Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties.

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.