Topics in Geometry

Welcome to the LSGNT Topics in Geometry course for 2021/22.

Course structure

This is not a normal lecture course. Every week you'll have a different lecturer, covering some essential aspect of geometry. Lectures don't build on each other directly but later ones might end up using stuff from earlier ones.

The lecturers will set you problems and exercises, of wildly varying difficulty. These are for you to do because doing exercises is how you learn maths. Do as many of the exercises as you can. At least one of them needs to be written up and submitted to Kay within 10 days of the lecture (even if you couldn't solve it completely).

A week after each lecture you'll have a `wrap-up session' where you discuss the exercises and the lecture as a group. There won't be a lecturer at the wrap-up session, instead one of you will act as the `owner' for that week's topic and lead the session. I'll also send along the 2nd year who owned the topic last year for extra guidance.

The website for last year's course has lots of useful things including lecture notes, videos of talks, and further links and advice. I also recommend looking at the 2019 site because it has lots of words of wisdom from Richard Thomas.


Lectures are in Room 144, Huxley building, Imperial College. Lectures will also be streamed live online on BigBlueButton (check your email for the link and access code). Some lectures will just be online.

Lectures will be recorded and the links to the videos will appear here.

Wrap-up sessions are in the Imperial CDT Space, Teaching Room 2 (402B).


Lectures are on Fridays 3pm-5pm (except the first one which starts at 2.40pm). Wrap-up sessions are on the following Friday, 11am-1pm.

Date Topic Lecturer Owner 2nd year
01/10/21Spec and Proj
Exercises | Video | Slides | Other notes
Ed Segal David Angdinata Edwin Hollands
08/10/21Complex and Kähler manifolds
Notes and Exercises | Video
Lorenzo FoscoloEnric Solé-Farré Wojtek Wawrów
15/10/21Poincaré duality (online only)
Exercises | Video
Michael SingerMichela BarbieriSara Veneziale
22/10/21Morse theory and Instantons
Notes with exercises | Video
Steven SivekAnanya Satoskar Ilaria Di Dedda
29/10/21Chern classes (online only)
Notes with exercises | Video
Dario BeraldoMartin Ortiz Bence Hevesi
05/11/21Blowing up
Notes with exercises | Video
Richard ThomasAmelia Livingston Pascale Voegtli
12/11/21Positivity in Algebraic Geometry
Notes | Exercises | Video
Paolo CasciniSiqi Yang Dmitry Ulyumdzhiev
19/11/21Toric varieties
Notes with exercises | Video
Johannes Nicaise Thamarai Valli VenkatachalamRobert Crumplin
26/11/21Moment maps and Hamiltonian reduction
Notes with exercises | Video
Yankı LekiliDaniil Mamaev Wei Zhou
03/12/21Special HolonomySimon SalamonInés García Francesco Vigano
10/12/21Plateau's problem Giuseppe TinagliaNick Manrique Lucy Phillips
17/12/21Final wrap-up. No lecture.