Introduction to Smith's Methods
Peter Koymans will visit the University of Bristol from 13th-24th April 2026, during which time he will give a lecture series on the powerful methods first introduced by Alexander Smith to tackle the Cohen--Lenstra--Gerth conjecture on class groups of imaginary quadratic fields and Goldfeld's conjecture on quadratic twists of elliptic curves.
Practical details
Speaker: Peter Koymans
Abstract: See abstract
Dates: Monday 13th April — Friday 24th April 2026.
Location: Fry Building, University of Bristol.
Organisers: Ross Paterson and Happy Uppal.
Please note: for non-Bristol based academics, participation is by application only. Please contact the organisers if you need a link to the application form.
Materials
Please note that the exercise sheets can easily take more than 2 hours (and this is on purpose), no-one is expected to solve all of the exercises during the allotted time slots! Participants may wish to look at the primer and have a go at sheet 1 before the event. Exercise sheet 1 below is an exercise sheet of Matthew Emerton from a course in 2012.
Primer: Galois cohomology primer
Exercise sheets: Exercise sheet 1, Exercise sheet 2, Exercise sheet 3, Exercise sheet 4
Notes: Live notes
Schedule
If for any reason you need a break and would appreciate a quiet space, please let the organisers know and we will find you a private space. Below the weekly schedules, we list some additional booked spaces for quiet working use only.
Week 1
| Time | Monday |
Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| 09:00 - 10:00 | Lecture 2 (2.04) |
Working time (2.04) | |||
| 10:00 - 11:00 | Lecture 1 (2.04) |
Lecture 3 (2.04) |
Exercises 3 (G.07) |
||
| 11:00 - 12:00 | Tea/ Discussion | Working time (G.07) | |||
| 12:00 - 13:00 | Lunch | Lunch | Lunch | Lunch | Lunch |
| 13:00 - 14:00 | |||||
| 14:00 - 15:00 | Exercises 1 (G.07) |
Exercises 2 (G.07) |
Working time (G.07) | Working time (2.32) | Working time (G.07) |
| 15:00 - 16:00 | Working time (G.07) | Working time (G.07) | |||
| 16:00 - 17:00 | Heilbronn Seminar |
Week 2
| Time | Monday |
Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| 09:00 - 10:00 | Lecture 4 (2.04) | Informal talk (2.04) | |||
| 10:00 - 11:00 | Catch-up session (2.04) |
Lecture 5 (2.04) |
|||
| 11:00 - 12:00 | Tea/ Discussion | Linfoot Seminar | |||
| 12:00 - 13:00 | Lunch | Lunch | Lunch | Lunch | Lunch |
| 13:00 - 14:00 | |||||
| 14:00 - 15:00 | Colloquium tea@ 14:30 (Common room) |
Exercises 4 (G.07) |
Working time (G.07) | Open Problems (G.07) |
|
| 15:00 - 16:00 | Colloquium | Working time (G.07) | Working time (G.07) | ||
| 16:00 - 17:00 | Wine Reception | Heilbronn Seminar |
Additional room bookings
The rooms below are for quiet working only.
- Monday 13th April: 1200 - 1700 (G.14)
- Tuesday 14th April: 1200 - 1700 (2.82)
- Wednesday 15th April: 1600 - 1700 (2.32)
- Friday 17th April: 1100 - 1200 (2.04), 1200 - 1700 (2.32)
- Tuesday 21st April: 1600 - 1700 (2.32)
- Wednesday 22nd April: 1500 - 1700 (2.32)
- Thursday 23rd April: 1300 - 1700 (2.32)
Acknowledgements
This event is funded by the Heilbronn International Visitor scheme, hosted at the University of Bristol.
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