Date & Time: Tuesday, July 19, 2016, 15:30-17:00.
Venue: Room No. 216

Title: Koszul Algebras

Speaker: Dr. Neeraj Kumar, Indian Statistical Institute, Bangalore

Abstract: In this talk, we shall first see some examples of a minimal graded free resolution of a finitely generated graded module $M$ over a commutative ring $R$. Given a field $K$, a positively graded $K$-algebras $R$ with $R_0=K$ is called "Koszul" if the field $K$ has an $R$-linear free resolution when viewed as an $R$-module via the identification $K=R/R_{+}$. We shall review the classical invariant Castelnouvo-Mumford regularity of a module and define Koszul algebras in terms of regularity. We shall also discuss several other characterizations of Koszul algebras. Then I will present some results on Koszul property of diagonal subalgebras of bigraded algebras; in particular, Koszul property of diagonal subalgebras of Rees algebras for a complete intersection ideal generated by homogeneous forms of equal degrees. At the end, I will present several problems concerning Koszul algebras.