Ed Segal

I am a Teaching Fellow in the geometry group in the Mathematics department at Imperial College London.

Contact

OfficeHuxley 677
AddressImperial College London
180 Queen's Gate
London SW7 2AZ
UK
Email edward.segal04@imperial.ac.uk

Research interests

I'm interested in the interactions between geometry, algebra and theoretical physics. More specifically, I work on topological field theories, derived categories, and related things. A longer summary of my research, written for the general public, is here.

Publications and preprints (arXiv)

(xiii) Hori-mological projective duality   (with Jørgen Rennemo)

(xii) All autoequivalences are spherical twists
To appear in Int. Math. Res. Not.

(xi) A new 5-fold flop and derived equivalence
To appear in Bull. London Math. Soc.

(x) Quintic threefolds and Fano elevenfolds   (with Richard Thomas)
To appear in J. Reine Angew. Math. (Crelle).

(ix) K-theoretic and categorical properties of toric Deligne-Mumford stacks   (with Tom Coates, Hiroshi Iritani and Yunfeng Jiang)
Pure Appl. Math. Q. 11 (2015) no. 2, 239-266.

(viii) The Pfaffian-Grassmannian equivalence revisited   (with Nick Addington and Will Donovan)
Alg. Geom. 2 (2015), no. 3, 332-364.
Here's a video of a lecture I gave at the Newton Institute on this topic.

(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
J. Noncommutative Geometry. 7 (2013), no. 3, 857-883.

(iii) Equivalences between GIT quotients of Landau-Ginzburg B-models
Comm. Math. Phys. 304 (2011), no. 2, 411-432.

(ii) Gauge theory in higher dimensions, II   (with Simon Donaldson)
Surveys in Differential Geometry 16 (2011), 1-14.

(i) The A-infinity deformation theory of a point and the derived categories of local Calabi-Yaus
J. Algebra 320 (2008), no. 8, 3232-3268.
This is essentially my PhD thesis, my advisor was Richard Thomas. The thesis version has an extra appendix on A-infinity algebras with some pretty pictures.

Notes

The universal closed state space of an open TFT
These are some short notes on a particular result in 2-dimensional topological field theory.

The 7 Colour Theorem
I gave a talk at the KCL Maths School, and one of the students made these beautiful notes.

Teaching

M4/5P52 - Manifolds, Autumn 2016

M4/5P46 - Lie Algebras, Spring 2015

M3/4/5P12 - Group Representation Theory, Spring 2014