Notes

Miscellaneous notes and slides from over the years. Some of them contain a few mistakes which I haven't fixed, and likely many that I haven't noticed - proceed with caution.

• Plethystic substitutions in categorification. Talk for the Informal Categorification Seminar
• Categorification of the Virtual Artin Groups. Based on Thiel's original paper for type A and the recent definition of the Virtual Artin groups by Bellingeri, Paris and Thiel.
• The deal with foams I. Talk on Robert and Wagner's original paper.
• The deal with foams II. Talk on Robert and Wagner's 'symmetric' paper.
• Triply graded homology. Talk for the Knot homology and DAHA seminar.
• Introduction to Hecke algebras and affine Hecke algebras. Talk for the Cherednik algebras and applications seminar.
• Symmetric groups and the Heisenberg category. Talk for the Finite groups in Valencia conference.
• The char \(p\) story. An overview of the representation theory of (linear) algebraic groups in defining characteristic \(p\).
• The dihedral cathedral. Talk for the Modern techniques in representation theory seminar.
• Jantzen filtration theorem (Humphreys' cat \(\mathcal{O}\) book, Chapter 5)
• The BGG resolution (account of the classical BGG paper)
• The Lie group \(\widetilde{SL}_2(\mathbb{R})\) is not a matrix group.
• The octonionic plane and a map \(S^{15} \to S^8\) with Hopf invariant 1.
• Periodicity of Clifford algebras
• Category \(\mathcal{O}\) and Soergel bimodules. My Part III Essay, supervised by Amit Hazi.
• Hindman's theorem via ultrafilters. An application of topological dynamics in combinatorics.