I am an Associate Professor in the maths department at UCL. I'm part of the geometry group.
I'm interested in the interactions between geometry, algebra and theoretical physics. More specifically, I work on derived categories of coherent sheaves and their various generalizations. A longer summary of my research, written for the general public, is here.
Publications and preprints (arXiv)
(xviii) Equivariant Fukaya categories at singular values (with Yankı Lekili)
(xvii) Serre functors of residual categories via hybrid models (with Federico Barbacovi) To appear in Bull. LMS.
(xvi) Line fields on punctured surfaces and twisted derived categories
(xv) Discriminants and semi-orthogonal decompositions (with Alex Kite) Comm. Math. Phys. 390 (2022), 907-931
(xiv) A non-commutative Bertini theorem (with Jørgen Rennemo and Michel Van den Bergh) J. Noncommutative Geometry 13 (2019), no. 2, 609-616.
(xiii) Hori-mological projective duality (with Jørgen Rennemo)
Duke Math. J. 168 (2019), no. 11, 2127-2205.
(xii) All autoequivalences are spherical twists
(xi) A new 5-fold flop and derived equivalence
(x) Quintic threefolds and Fano elevenfolds (with Richard Thomas)
(ix) K-theoretic and categorical properties of toric Deligne-Mumford stacks (with Tom Coates, Hiroshi Iritani and Yunfeng Jiang)
(viii) The Pfaffian-Grassmannian equivalence revisited (with Nick Addington and Will Donovan)
(vii) Mixed braid group actions from deformations of surface singularities (with Will Donovan) Comm. Math. Phys. 335 (2015), no. 1, 497-543.
(vi) D-brane probes, branched double covers, and non-commutative resolutions (with Nick Addington and Eric Sharpe) Adv. Theor. Math. Phys. 18 (2014), no. 6, 1369-1436.
(v) Window shifts, flop equivalences and Grassmannian twists (with Will Donovan) Compositio Math. 150 (2014), no. 6, 942-978.
(iv) The closed state space of affine Landau-Ginzburg B-models
(iii) Equivalences between GIT quotients of Landau-Ginzburg B-models
(ii) Gauge theory in higher dimensions, II (with Simon Donaldson)
The A-infinity deformation theory of a point and the derived categories of local Calabi-Yaus
Group Representation Theory
Federico Barbacovi (graduated 2023)
Bradley Doyle (graduated 2021)
Alex Kite (graduated 2019)
If you're interested in doing a PhD with me you should apply to the LSGNT. Applications are normally open in November/December each year.
The universal closed state space of an open TFT
The 7 Colour Theorem
The Incredible Predictive Power of String Theory
The Geometry of Gauged Linear Sigma Models