Research

Research Interests:

Perverse sheaves on topologically stratified spaces;

Triangulated categories, t-structures and hearts;

Finite dimensional algebras, quiver representations;

Silting and tilting theory;

Spaces of Bridgeland stability conditions on the constructible derived category.

Publications

When are there enough projective perverse sheaves? (with J. Woolf) (Glasgow Mathematical Journal, 1-12. doi:10.1017/S0017089521000021, March 2021), journal link, arXiv version.

Wall And Chamber Structure For A Special Biserial Algebra Coming From Perverse Sheaves On $\mathbb{n}^n$ (with M. Lanini), arXiv version.

In Preparation

Perverse shevaes and highest weight categories (with J. Woolf).

Quiver Description of Perverse Sheaves (with J. Woolf).

Indecomposable Perverse Sheaves (with J. Woolf).

Organisation

Working group on ”Gluing simple-minded collections and silting objects”, Algebra Oberseminar IAZ, University of Stuttgart, November & December 2022.

Mini-course ”Stability spaces from an algebraic viewpoint”, Università di Roma Tor Vergata, 6th- 10th June 2022. 

Co-organiser with Martina Lanini, speaker Jon Woolf, University of Liverpool.

Research Visits

University of Liverpool (01/07/2023 - 08/07/2023), Dr. Jon Woolf.

Università degli Studi di Roma "Tor Vergata" (02/05/2023 - 04/05/2023), Prof. Martina Lanini.

Universität Stuttgart (14/01/2023 - 21/01/2023), IAZ (Institute of Algebra and Number Theory).

Ruhr-Universität Bochum (04/05/2022 - 29/07/2022), Prof. Dr. Markus Reineke's research group.

Talks

A Series of Two Talks on Perverse Sheaves, Seminar Representation Theory, Università di Verona. 

Perverse sheaves: introduction and examples, 16th May 2023.

On the global dimension of perverse sheaves, 24th May 2023.

Highest weight perverse sheaves, 27th April 2023, FD seminar (online).

Introduction to gluing simple-minded collections and silting objects, Working group, Algebra Oberseminar IAZ, University of Stuttgart, 8th November 2022.

Two Lectures on Perverse Sheaves, Algebra Oberseminar IAZ, University of Stuttgart.

Part 1: Introduction to perverse sheaves and examples, 25th October 2022

Part 2: Projective and quasi-hereditary perverse sheaves, 8th November 2022.

Quasi-hereditary Perverse Sheaves, STAR (Silting Theory, Algebras and Representations), meeting of the Network on Silting Theory, Charles University Prague, 12th-16th September 2022.

Perverse Sheaves, Finite Dimensional Algebras and Quivers, ABCD-Seminar (Aachen-Bochum-Cologne Darstellungstheorie Seminar), Aachen, 12th July 2022.

Coxeter groups and Kazhdan–Lusztig polynomials, Arbeitsgemeinschaft: Geometric Representation Theory (organised by D. Juteau, S. Riche, W. Soergel, G. Williamson), Oberwolfach, 3rd-9th April 2022.

Perverse Sheaves, Finite Dimensional Algebras and Quivers, ARTS (Algebra and Representation Theory Seminar), 28th May 2021

Perverse Sheaves and Finite Dimensional Algebras, Seminario Padova-Verona MALGA (online), 4th December 2020.

Perverse Sheaves, Finite Dimensional Algebras and Quivers, Early Career Topology Researchers, University of Sheffield, 6th-7th June 2019.

Perverse Sheaves and Finite Dimensional Algebras, Connections and Directions in Representation Theory and Related Topics, University of Leeds, 14th-16th April 2019.

Derived Categories, t-structures and Hearts, Working Seminar on Bridgeland Stability Conditions, University of Liverpool, 2nd April 2019.

Derived Functors, Working Seminar on Fourier-Mukai Transforms, University of Liverpool, 25th October 2017.

Perverse Sheaves as Modules, TTT103 (Transpenine Topology Triangle), University of Liverpool, 30th June 2017.

Triangulated Categories, University of Liverpool, October 2015.