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Oscar Finegan

Research student, School of Mathematics

Overview

I am currently working on obtaining my PhD in Algebraic Geometry, specifically working with the derived categories of schemes.


I am co-organiser for both the Geometry in Cardiff (GiC) and CALF seminars.

Research

Research interests

My current research is focussed on providing explicit formulas for the derived tensor product in various situations, namely when a collection of local complete intersections (lcis) inside of a smooth ambient variety intersect in a non-lci. Essential to this study is the fact that the resulting object can be non-equidimensional, that is, different components of the geometric object may have different dimensions. I hope to obtain some results dependent on what kind of non-equidimensionality our resulting scheme has.

Thesis

Skein-Triangulated Representations Of Generalised Braids

The ordinary braid group Br_n is a well-known algebraic structure which encodes configurations of n non-touching strands (“braids”) up to continious transformations (“isotopies”). There are many examples where Br_n acts categorically on the derived category of an algebraic variety: the minimal resolutions of Kleinian singularities, the cotangent bundles of flag varieties, etc.


To understand the derived category for the cotangent bundles of partial flag varieties, one needs a generalisation of the braid group to the generalised braid category. One may hope to understand categorical actions (so called skein-triangulated representations) of this new object on the derived category of (cotangent bundles of) partial flag varieties.

Funding source

EPSRC

Supervisors