#### Chandrasekhar Hall

#### d-sequences, quadratic sequences, their Rees algebras and Castelnuovo-Mumford regularities.

#### Jayanthan A V

##### IIT Madras

*d-sequences were introduced by Huneke and he used the theory of d-sequences to study depth(R/I^n). Raghavan generalized the concept of d-sequences to quadratic sequences. We study certain binomial ideals, generated by a subset of 2-minors of a 2xn matrix of variables, their Rees algebras, certain first Betti numbers and first syzygies. We also study of the Castelnuovo-Mumford regularity of powers of homogeneous quadratic sequences in polynomial rings and use them to obtain the regularity of powers of some of the d-sequence binomial ideals.*

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