Welcome to the LSGNT Topics in Geometry course for 2025/26.
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.
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.
There are some notes of talks on the websites for last year's course and the 2023-24 course (which was run by Yankı Lekili). Also see the 2019 course for words of wisdom from Richard Thomas.
Lectures are in Room 658, Huxley building, Imperial College. Wrap-ups this term are in 408 (except 13th Mar. which is in 341).
Lectures are on Fridays 3pm-5pm, wrap-up sessions are on the following Friday, 11am-1pm.
| Date | Topic | Lecturer | Owner | 2nd year |
| 23/1/26 | Special Holonomy Notes | Simon Donaldson | Edward Young | Yichen Zhang |
| 30/1/26 | Geometric Invariant Theory | Alessio Corti | Anna Bresciani | Patrick Luo |
| 6/2/26 | Ordinary Double Points | Richard Thomas | Edison Xie | Ashesh Bati |
| 13/2/26 | Geometric Representation Theory | Travis Schedler | Haoming Yang | Chingun Erdenebileg |
| 20/2/26 | Ricci Flow | Stephen Lynch | Oliver Seaman | Natasha Diederen |
| 27/2/26 | Homogenous Dynamics | Selim Ghazouani | Adam Baranski | Silvia Gangeri |
| 6/3/26 | Deformation Theory | Ed Segal | Kyaw Shin Thant | Simon Alonso |
| 13/3/26 | Jacobians | Nick Shepherd-Barron | Ivan Noden | Naina Praveen |
| 20/3/26 | Quantum Cohomology | Yankı Lekili | Oliver Sokvari | Andy Yang |
| Date | Topic | Lecturer | Owner | 2nd year |
| 26/9/25 | Spec and Proj Old slides | Exercises | Ed Segal | Haoming Yang | Simon Alonso |
| 3/10/25 | Poincaré duality Notes | Exercises | Steven Sivek | Kyaw Shin Thant | Xander Povey |
| 10/10/25 | Vector bundles and Chern classes Notes with exercises | Richard Thomas | Julian Huber | Naina Praveen |
| 17/10/25 | Complex and Kähler geometry Old notes with exercises | Aleksander Doan | Anna Bresciani | Lucie Gatzmaga |
| 24/10/25 | Blowing up Exercises | Calum Spicer | Adam Baranski | Patrick Luo |
| 31/10/25 🎃 | Symplectic geometry Notes with exercises | Dima Panov | Oliver Sokvari | Zhaoyang Liu |
| 7/11/25 | Morse theory
Exercises | Old notes with exercises | More old notes with exercises | Selim Ghazouani | Oliver Seaman | Silvia Gangeri |
| 14/11/25 | Hodge theory | Heather Macbeth | Ivan Noden | Sasha Novik |
| 21/11/25 | Minimal surfaces Notes with exercises | Mikhail Karpukhin | Edison Xie | Natasha Diederen |
| 28/11/25 | Mapping class groups Notes | Exercises | Mehdi Yazdi | Zhengyang Cui | Fulin Zhong |
| 5/12/25 | Moduli spaces Exercises | Soheyla Feyzbakhsh | Edward Young | Ashesh Bati |