Ed Segal

I've recently moved to UCL, where I am a Lecturer in Algebraic Geometry. I'm part of the geometry group.

Contact

Office605
AddressDepartment of Mathematics
University College London
Gower Street
London WC1E 6BT
UK
Email e dot segal at ucl dot ac dot uk

Research interests

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.

Post-docs

I'm hiring a postdoc to work with me on my ERC funded project Birational Geometry, B-branes and Artin Stacks. The post is for two years, starting in the spring or summer of 2018. The closing date for applications is 26th November.
Find out more and/or apply.

Publications and preprints (arXiv)

(xiv) A non-commutative Bertini theorem   (with Jørgen Rennemo and Michel Van den Bergh)

(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

Manifolds
These are the complete lecture notes for a 4th-year undergraduate/MSc level course on differential geometry, which I taught at Imperial College for three years. They cover the foundations of manifolds, tangent vectors, and differential forms, up to Stokes' Theorem.

Group Representation Theory
Complete notes for a 3rd-year undergraduate course on representation theory, which I also taught for three years at Imperial. They cover the basics of representations of finite groups over the complex numbers (Maschke's Theorem, Schur's Lemma, character tables) and finish with the classification of semi-simple algebras. Here are the exercises.

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.