Speaker: Shubham Jaiswal
Affiliation: IISER Pune
Title: Root Clusters
Date and Time: October 16, 2024, 14:30:00 Hours
Venue: A-369
Asbtract: The talk is on our work Root Clusters, Magnification, Capacity, Unique chains and Base change 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 given degree and cluster size over number fields which generalises 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. Finally we establish results about all these phenomena under a particular type of base change. The talk concludes with results about strong cluster magnification and unique chains and some properties of the ascending index for a field extension. Link to the paper on arxiv: https://arxiv.org/abs/2405.06825.
Affiliation: IISER Pune
Title: Root Clusters
Date and Time: October 16, 2024, 14:30:00 Hours
Venue: A-369
Asbtract: The talk is on our work Root Clusters, Magnification, Capacity, Unique chains and Base change 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 given degree and cluster size over number fields which generalises 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. Finally we establish results about all these phenomena under a particular type of base change. The talk concludes with results about strong cluster magnification and unique chains and some properties of the ascending index for a field extension. Link to the paper on arxiv: https://arxiv.org/abs/2405.06825.