Welcome to the LSGNT Topics in Geometry course for 2024/25.
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 and videos of talks on the website for last year's course which was run by Yankı Lekili. Also see the 2019 course for words of wisdom from Richard Thomas.
Term 2 lectures are in room 642, Huxley building, Imperial College. Wrap-ups remain in Huxley 408.
Lectures are on Fridays 3pm-5pm. Wrap-up sessions are on the following Friday, 11am-1pm.
| Date | Topic | Lecturer | Owner | 2nd year |
| 24/1/25 | Dynamical systems Notes with exercises | Nattalie Tamam | Silvia Gangeri | Samuele Ciprietti |
| 31/1/25 | 3-manifolds Exercises | Selim Ghazouani | Xander Povey | Parsa Mashayekhi |
| 7/2/25 | Geometric Representation Theory Exercises | Notes | Travis Schedler | Chingun Erdenebileg | Yiannis Fam |
| 14/2/25 | Toric varieties | Alessio Corti | Patrick Luo | Calle Sonne |
| 21/2/25 | Cancelled | Simon Salamon | Yichen Zhang | Paul Lezeau |
| 28/2/25 | Calculus of variations Exercises | Costante Belletini | Natasha Diederen | Alberto Acosta |
| 7/3/25 | Mapping class groups Exercises | Mehdi Yazdi | Fulin Zhong | |
| 21/3/25 | Bend and break Notes with exercises | Dario Beraldo | Sasha Novik | |
| 27/3/25 | Mirror symmetry Notes |
Yankı Lekili | Andy Yang |
| Date | Topic | Lecturer | Owner | 2nd year |
| 27/9/24 | Spec and Proj Old slides | Exercises | Ed Segal | Simon Alonso | Edwina Aylward |
| 4/10/24 | Vector bundles and Chern classes Notes | Exercises | Selim Ghazouani | Naina Praveen | Brad Wilson |
| 11/10/24 | Complex and Kähler manifolds Notes with exercises | Simon Donaldson | Lucie Gatzmaga | Jakab Schrettner |
| 18/10/24 | Poincaré duality
Notes | Exercises | Steven Sivek | Xander Povey | Maartje Wisse |
| 25/10/24 | Blowing up Exercises | Calum Spicer | Patrick Luo | Sara Varljen |
| 1/11/24 | Morse theory
Notes with exercises | More notes with exercises | Aleksander Doan | Silvia Gangeri | Calum Crossley |
| 8/11/24 | Symplectic geometry and moment maps
Notes with exercises |
Dmitri Panov | Zhaoyang Liu | Dan Simms |
| 15/11/24 | Moduli spaces
Exercises | Soheyla Feyzbakhsh | Ashesh Bati | Abishek Khannur |
| 22/11/24 | Ordinary double points
Notes with exercises | Richard Thomas | Yichen Zhang | Bogdan Simeonov |
| 29/11/24 | Minimal surfaces
Notes with exercises | Mikhail Karpukhin | Natasha Diederen | Catinca Mujdei |
| 6/12/24 | Hodge theory | Peter Jossen | Sasha Novik | Ines Chung-Halpern |