Seminar Announcement
Date: Tuesday, 18 February 2025
Time: 2:00 PM
Venue: Seminar Hall
Root Clusters
Shubham Jaiswal
IISER Pune.
18-02-25

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Abstract

The talk is on our work Cluster Magnification, Root Capacity, Unique Chains, Base Change & Ascending Index which is inspired from the work of M Krithika and P Vanchinathan on Cluster Magnification and the work of Alexander Perlis on Cluster Size. We establish the existence of polynomials for a given degree and cluster size over number fields which generalizes a result of Perlis. We state the Strong cluster magnification problem and establish an equivalent criterion for that. We also discuss the notion of weak cluster magnification. We provide an important example answering a question about Cluster Towers. We introduce the concept of Root capacity. We also introduce the concept of unique descending and ascending chains for extensions and explicitly compute some interesting examples. We establish results about all these phenomena under a particular type of base change and discuss some other related results about strong cluster magnification and unique chains. The talk concludes with results about ascending index for a field extension which are analogous to results about cluster size.