Author Archives: xenaproject
2022 Xena Project undergraduate workshop
I have funding to run an undergraduate workshop! When? 26th to 30th September 2022 (the week before term starts for many people in the UK). What? A week-long in person workshop including a bunch of working on group projects in … Continue reading
New year, new teaching material
Imperial College has gone back to in-person teaching so I have 250 new subjects to experiment on, namely the new 1st year maths undergraduates. I’ve spent a few years now trying to figure out how best to teach maths undergraduates … Continue reading
2021 Xena Summer Projects
So I spent July and August supervising mathematics undergraduates who were doing Lean projects in various areas of mathematics. Conformal maps, Euclid’s SAS theorem, nilpotent groups and the Radon-Nikodym theorem are just some of the topics I’ve been engaging with … Continue reading
Half a year of the Liquid Tensor Experiment: Amazing developments
[This is a guest post by Peter Scholze.] Exactly half a year ago I wrote the Liquid Tensor Experiment blog post, challenging the formalization of a difficult foundational theorem from my Analytic Geometry lecture notes on joint work with Dustin … Continue reading
The trace of an endomorphism (without picking a basis)
Did you pick a basis when doing a linear algebra question about finite-dimensional vector spaces? Did you need to? Depends on what you mean. Continue reading
Induction on equality
In type theory, equality has a definition, and basic facts about it such as symmetry and transitivity can be proved from more fundamental principles. Continue reading
Induction, and inductive types.
Induction in Lean isn’t just something which you do on natural numbers. Continue reading
Formalising Mathematics : workshop 8 — group cohomology
A brief description of group cohomology H^0 and H^1, plus links to how to formalise this stuff in Lean. Continue reading
Formalising Mathematics : workshop 7 — quotients
Is a quotient a set of equivalence classes? I think it’s something a bit more general than that. Continue reading
Formalising Mathematics : workshop 6 — limits
I talked about limits of sequences of real numbers in workshop 3, but this week I come back to them, because this week we’ll see that the usual ten-line proof that if and then can be replaced by a two-line … Continue reading
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