Topics in Geometry

Welcome to the LSGNT Topics in Geometry course for 2025/26.

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.

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.

Location

Lectures and wrap-ups are in Room 658, Huxley building, Imperial College.

Schedule

Lectures are on Fridays 3pm-5pm, except the first one which starts at 2.45pm. Wrap-up sessions are on the following Friday, 11am-1pm.

Term 1

Date Topic Lecturer Owner 2nd year
26/9/25Spec and Proj
 
Ed Segal Haoming Yang Simon Alonso
3/10/25Poincaré duality
 
Steven Sivek Kyaw Shin ThantXander Povey
10/10/25Vector bundles and Chern classes
 
Richard Thomas Julian Huber Naina Praveen
17/10/25Complex and Kähler geometry
 
Aleksander Doan Lucie Gatzmaga
24/10/25Blowing up
 
Calum Spicer Adam Baranski Patrick Luo
31/10/25Symplectic geometry
 
Dima Panov Zhaoyang Liu
7/11/25Morse theory
 
Selim Ghazouani Oliver Seaman Silvia Gangeri
14/11/25Hodge theory
 
Heather Macbeth Sasha Novik
21/11/25Minimal surfaces
 
Mikhail Karpukhin Natasha Diederen
28/11/25Moduli spaces
 
Soheyla Feyzbakhsh Edward Young Ashesh Bati
5/12/25TBC
 
Mehdi Yazdi Fulin Zhong