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

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.

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 |

13/1/23 | The minimal model program | Calum Spicer | Alg | Giorgio Navone | Thamarai Venkatachalam |

20/01/23 | The index theorem Notes with exercises | Simon Donaldson | Diff/An | Arne Wolf | Nicolo Cavalleri |

27/01/23 | Hodge theory | Nick Shepherd-Barron | Alg | Philip Kaddaj | Sebastian Monnet |

03/02/23 | Einstein metrics Notes with exercises | Lorenzo Foscolo | Diff/An | Aleksandra Bozovic | Enric Solé-Farré |

10/02/23 | Moduli of curves | Alessio Corti | Alg | Izzy Rendell | Mads Christensen |

17/02/23 | Gauge theory Exercises | Aleksander Doan | Diff/An | Yifan Zhao | Enric Solé-Farré |

24/02/23 | Geometric representation theory | Travis Schedler | Alg | Yicheng Yang | Martin Ortiz |

03/03/23 | No lecture | ||||

10/03/23 | Mirror symmetry | Ed Segal | Alg | Santiago Saez | David Angdinata |

17/03/23 | Calculus of variations and related topics | Costante Belletini | Diff/An | Mahdi Haghshenas | Mel Levin |

24/03/23 | The positive mass theorem in general relativity | Zoe Wyatt | Diff/An | Zerui Tan |

Date | Topic | Lecturer | Owner | 2nd year |

30/9/22 | Spec and Proj Exercises | Slides (from last year) | Ed Segal | Megan Masters | Diego Chicharro |

07/10/22 | Complex and Kähler manifolds Notes and exercises | Simon Donaldson | Aleksandra Bozovic | Enric Solé-Farré |

14/10/21 | Chern classes Exercises | Notes | Selim Ghazouani | Corijn Rudrum | Martin Ortiz |

21/10/22 | Poincaré duality
Exercises | Notes | Michael Singer | Arne Wolf | Michela Barbieri |

28/10/22 | Blowing up Notes with exercises | Dario Beraldo | Aporva Varshney | Amelia Livingston |

04/11/22 | Moment maps and Hamiltonian reduction
Notes with exercises | Yankı Lekili | Josh Tilley | Daniil Mamaev |

11/11/22 | Birational geometry
Exercises |
Calum Spicer | Stefania Vassiliadis | Siqi Yang |

18/11/22 | Plateau's problem
Notes with exercises | Giuseppe Tinaglia | Mahdi Haghshenas | Nick Manrique |

25/11/22 | Morse Theory
Extra exercises | Richard Thomas | Harmeet Singh | Ananya Satoskar |

02/12/22 | Special holonomy
Slides and exercises | Simon Salamon | Yifan Zhao | Inés García |

9/12/22 | 3-manifolds Notes with exercises | Mehdi Yazdi | Harry Spencer |