Tue, September 8, 2020
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6:00pm [6:30pm] Irena Swanson, Purdue University
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Date and Time: 8 September 2020, 6:30 pm IST/ 1:00 pm GMT/ 09:00 am EDT (joining time : 6:15 pm IST - 6:30 pm IST) Google Meet link: https://meet.google.com/tmh-yngo-ksk Speaker: Irena Swanson, Purdue University Title: Primary decomposition and powers of ideals Abstract: This talk is about associated primes of powers of an ideal in Noetherian commutative rings. Brodmann proved that the set of associated primes stabilizes for large powers. In general, the number of associated primes can go up or down as the exponent increases. This talk is about sequences $\{ a_n \}$ for which there exists an ideal $I$ in a Noetherian commutative ring $R$ such that the number of associated primes of $R/I^n$ is $a_n.$ This is a report on my work with Sarah Weinstein, with Jesse Kim and ongoing work with Roswitha Rissner.