#phd posting

This week's been pretty good! I've made decent progress and I'm understanding things a lot more! I did have to take yesterday off and work from home today because I've been to tired to go into uni. However, as I said the progress I've made has been good! My supervisor meeting this week was especially good because I got all my questions answered in a way I understood them. I also felt like I was more having a conversation with my supervisor. Like I actually had decent things to say rather than just listening and absorbing.

Seminars:

The algebraic topology seminar was very interesting and a well given talk. It was about trying to understand BDiff(M) for compact connected 3-manifolds in terms of the BDiff(P₁⊔⋅⋅⋅⊔Pₙ), where Pᵢ are the irreducible manifolds in the prime decomposition of M (except not S¹×S² though, even if the manifold has it as a connected summand I can't remember why). The jist was the speaker (and collaborators) construct a map using some ∞-categorical techniques and are abled to fully describe it's fibre in a nice combinatorial way.

The postgrad seminar was alright. It was a geometric analysis talk about the Plateau problem and results about regularity of solutions. It was a decently given talk, it just isn't my sort of thing.

Summer Project:

The extra stuff my supervisor had me working actually turns out to be a better way of doing the calculations I'd already done. It's a lot clearer what's going on and feels way less hand wavy. Originally he got me to work on a simple case because the goal was to get things done in more detail to allow us to calculate something slightly different. However it turns out the general method was very useful for the general case. Whilst I don't wish to pursue the full case in as much detail it's possible in theory (it just requires multiplying lots of polynomials together and I'm not sure it's worth it and my supervisor agrees).

A fun this is I had to produce a matrix whose entries are elements of ℚ[x,x⁻¹] which is fun! (Actually this part was my idea, when my supervisor was playing around with things he just wanted a matrix over ℚ but thought my idea was probably more fruitful!)