Research

I currently have two preprints out, which you can find below. 

In the first, I lift algorithms to compute parabolic Kazhdan-Lusztig polynomials for the Weyl groups of type D with a maximal parabolic subgroup of type A, thereby providing an Ext-quiver and relations presentation of the basic algebra for the anti-spherical Hecke category of the corresponding type.

In the second, I use this presentation to provide an isomorphism to the generalised Khovanov arc algebras of type D. 

Preprints:

• Isotropic meta Kazhdan--Lusztig combinatorics I: Ext-quiver presentation for the Hecke category

• Isotropic Meta Kazhdan-Lusztig Combinatorics II: Isomorphism to the generalised Khovanov arc algebra

I am currently working on categorifications of the Temperley-Lieb algebra. Both better understanding Elias's presentation in Type A and trying to generalise this construction to other types.

I am also trying (with Alice Dell'Arciprete) to use the work in the preprints above to better understand certain important idempotent truncations of the arc algebra in type D.