Talk: Amir Hashemi

link:

https://meet.iut.ac.ir/b/ram-08w-sde-muf

Title:‎‎ Involutive bases and their applications‎

Amir ‎Hashemi‎

‎Isfahan University of Technology and IPM

‎

‎Abstract: Grobner bases and the first algorithm to compute them were introduced by Bruno Buchberger is his PhD thesis in 1965. Since then, the theoretical and computational issues related to Grobner bases have been extensively developed and Grobner bases have become a powerful and a widely used tool in polynomial ideal theory.  However, they do not inherit, in general, all algebraic and combinatorial properties of the ideal such as satiety, Castelnuovo-Mumford regularity, depth and Cohen-Macaulayness. Therefore, involutive bases were introduced, as a special kind of Grobner bases, with additional properties.  In this talk, we review the theories of Grobner bases and involutive bases and discuss some applications of these concepts in commutative algebra and algebraic geometry.