Fri, February 19, 2021
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6:00pm [6:30pm] Bernd Ulrich, Purdue University, West Lafayette, IN, USA
Description:
Speaker:* Bernd Ulrich, Purdue University, West Lafayette, IN, USA* Date/Time: *19 February 2021, 6:30pm IST/ 1:00pm GMT/ 8:00am EST* (joining time: 6:15 pm IST - 6:30 pm IST) Google meet link: https://meet.google.com/kav-pjey-rir Title:* Generalized multiplicities and integral dependence* Abstract: The talks will give a survey about multiplicity based criteria for the integral dependence of ideals. This subject has close connections with equisingularity theory and intersection theory, which will be discussed as well. The first numerical criterion for integral dependence was proved in the 1960s by Rees who treated the case of zero-dimensional ideals using the Hilbert-Samuel multiplicity. Criteria for arbitrary ideals require generalized notions of multiplicities. We will discuss various such notions and talk about how they are used to detect integral dependence. The most recent results are from joint work with Claudia Polini, Ngo Viet Trung, and Javid Validashti. For more information and links to previous seminars, visit the website of VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar.