Topics in Geometry

Welcome to the LSGNT Topics in Geometry course for 2022/23.

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 some notes and videos of talks on the website for last year's course. You should also check out the pages for the 2020 course by Yankı Lekili and the 2019 course for words of wisdom from Richard Thomas.


All lectures and wrap-ups are in the Imperial College CDT space, Teaching Room 3 (402). At least the first few lectures will also be streamed on Zoom (check your email for the link).


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.

Term 2

The lectures for term 2 are divided into two streams, differential/analytic geometry and algebraic 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 very welcome to attend extra lectures if a particular topic appeals to you.


Date Topic Lecturer Stream Owner 2nd year
13/1/23The minimal model program Calum Spicer Alg Giorgio Navone Thamarai Venkatachalam
20/01/23The index theorem
Notes with exercises
Simon Donaldson Diff/An Arne Wolf Nicolo Cavalleri
27/01/23Hodge theory Nick Shepherd-BarronAlg Philip Kaddaj Sebastian Monnet
03/02/23 Einstein metrics
Notes with exercises
Lorenzo FoscoloDiff/An Aleksandra Bozovic Enric Solé-Farré
10/02/23 Moduli of curves Alessio CortiAlg Izzy Rendell Mads Christensen
17/02/23 Gauge theory
Aleksander DoanDiff/An Yifan Zhao Enric Solé-Farré
24/02/23 Geometric representation theory Travis SchedlerAlg Yicheng Yang Martin Ortiz
03/03/23 No lecture
10/03/23 Mirror symmetry Ed SegalAlg Santiago Saez David Angdinata
17/03/23 Calculus of variations and related topics Costante BelletiniDiff/An Mahdi Haghshenas Mel Levin
24/03/23 The positive mass theorem in general relativity Zoe WyattDiff/An Zerui Tan



Date Topic Lecturer Owner 2nd year
30/9/22Spec and Proj
Exercises | Slides (from last year)
Ed Segal Megan Masters Diego Chicharro
07/10/22Complex and Kähler manifolds
Notes and exercises
Simon Donaldson Aleksandra Bozovic Enric Solé-Farré
14/10/21Chern classes
Exercises | Notes
Selim Ghazouani Corijn Rudrum Martin Ortiz
21/10/22Poincaré duality
Exercises | Notes
Michael Singer Arne Wolf Michela Barbieri
28/10/22Blowing up
Notes with exercises
Dario BeraldoAporva VarshneyAmelia Livingston
04/11/22Moment maps and Hamiltonian reduction
Notes with exercises
Yankı Lekili Josh Tilley Daniil Mamaev
11/11/22Birational geometry
Calum Spicer Stefania Vassiliadis Siqi Yang
18/11/22Plateau's problem
Notes with exercises
Giuseppe Tinaglia Mahdi Haghshenas Nick Manrique
25/11/22Morse Theory
Extra exercises
Richard Thomas Harmeet SinghAnanya Satoskar
02/12/22Special holonomy
Slides and exercises
Simon Salamon Yifan Zhao Inés García
Notes with exercises
Mehdi Yazdi Harry Spencer