Welcome to the LSGNT Topics in Geometry course for 2021/22.
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 139, 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).
The lectures for term 2 are divided into two streams, differential/analytic geometry and algebraic/symplectic geometry, which alternate weeks. Since you now have projects to work on you are not expected to attend all lectures and wrap-ups, instead you should pick one of the two streams and attend all of those. Of course you are welcome to attend extra lectures if you wish (especially if a particular topic appeals to you).
Lectures are on Fridays 3pm-5pm. Wrap-up sessions are on the following Friday, 11am-1pm.
Date | Topic | Stream | Lecturer | Owner | 2nd year |
14/1/22 | Minimal surfaces and the Allen-Cahn equation Exercises | Video |
Diff/An | Marco Guaraco | Nick Manriquewin | Kobe Marshall-Stevens |
21/1/22 | Hodge Theory Video (requires Imperial login) |
Alg/Symp | Nick Shepherd-Barron | Sebastian Monnet | Dingli Liang |
28/1/22 | Gauge theory Notes with exercises |
Diff/An | Lorenzo Foscolo | Enric Solé-Farré | |
4/2/22 | Moduli of curves | Alg/Symp | Alessio Corti | Mads Christensen | Pascale Voegtli |
11/2/22 | The Atiyah-Singer index theorem
Video |
Diff/An | Michael Singer | Nicolo Cavalleri | Jamie Bell |
18/2/22 | The Weil conjectures
Video |
Alg/Symp | Dario Beraldo | Diego Chicharro | Lilybelle Cowland Kellock |
25/2/22 | Geometric measure theory Video |
Diff/An | Costante Bellettini | Mel Levin | Myles Workman |
4/3/22 | Floer cohomology and Fukaya categories | Alg/Symp | Yankı Lekili | Yuan Yang | Robert Crumplin |
11/3/22 | Riemannian convergence theory I | Diff/An | Simon Donaldson | Ananya Satoskar | |
18/3/22 | Geometric representation theory Video (requires Imperial login) |
Alg/Symp | Travis Schedler | Martin Ortiz | |
25/3/22 | Riemannian convergence theory II | Diff/An | Simon Donaldson |
Date | Topic | Lecturer | Owner | 2nd year |
01/10/21 | Spec and Proj Exercises | Video | Slides | Other notes | Ed Segal | David Angdinata | Edwin Hollands |
08/10/21 | Complex and Kähler manifolds Notes and Exercises | Video | Lorenzo Foscolo | Enric Solé-Farré | Wojtek Wawrów |
15/10/21 | Poincaré duality (online only) Exercises | Video | Michael Singer | Michela Barbieri | Sara Veneziale |
22/10/21 | Morse theory and Instantons Notes with exercises | Video | Steven Sivek | Ananya Satoskar | Ilaria Di Dedda |
29/10/21 | Chern classes (online only) Notes with exercises | Video | Dario Beraldo | Martin Ortiz | Bence Hevesi |
05/11/21 | Blowing up
Notes with exercises | Video | Richard Thomas | Amelia Livingston | Pascale Voegtli |
12/11/21 | Positivity in Algebraic Geometry
Notes | Exercises | Video |
Paolo Cascini | Siqi Yang | Dmitry Ulyumdzhiev |
19/11/21 | Toric varieties
Notes with exercises | Video | Johannes Nicaise | Thamarai Valli Venkatachalam | Robert Crumplin |
26/11/21 | Moment maps and Hamiltonian reduction
Notes with exercises | Video | Yankı Lekili | Daniil Mamaev | Wei Zhou |
03/12/21 | Special Holonomy (online only)
Slides, exercises and other links | Video | Simon Salamon | Inés García | Francesco Vigano |
10/12/21 | Plateau's problem (online only) at 1.30pm Slides with exercises | Video | Giuseppe Tinaglia | Nick Manrique | Lucy Phillips |