# Colloquium abstracts

**Rajib Sarkar**

TIFR, Mumbai

November 25, 2021

**Castelnuovo-Mumford Regularity of Quadratic Sequences with applications to Binomial Ideals**: Cutkosky-Herzog-Trung and independently Kodiyalam proved that the Castelnuovo-Mumford regularity of powers of homogeneous ideals in a polynomial ring is bounded above by a linear function. Given a homogeneous ideal, finding this linear function is a very difficult task. In this talk, we will compute the linear function for the ideals generated by homogeneous quadratic sequences. For this, we will start with the definition of d-sequence and its generalization to the quadratic sequence. We then talk about the regularity upper bound of powers of an ideal generated by a quadratic sequence in terms of its related ideals and degrees of generators. We then apply these results to the binomial edge ideals for several computations.