Mathematical Research Seminar - Archive
2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
The Erdős-Ko-Rado theorem describes the largest family of pairwise-intersecting k-element subsets of a fixed base set: for small k, this is the family of all sets containing some common element. The Hilton-Milner theorem describes what happens if we disallow a common element.
I will present recent progress from joint work with Denys Bulavka and Francesca Gandini on the Hilton-Milner theorem and extensions.
In this talk, we present an interesting correspondence between partially symmetric tensors over (for ), linear systems of conics in , and subspaces of . We review the history of classifying these linear systems in up to projective equivalence, an open problem dating back to 1908. We outline recent advances, showing how properties of the quadric Veronesean in can be utilized to identify a set of complete invariants for projectively inequivalent pencils and webs of conics in . These results contribute to the classification of partially symmetric 3x3xr tensors over Fq under the action of the group stabilising rank-1 tensors.