Learning

Geometric Analysis: Day Two

We begin a bit late today, but very well. [22:22:45 5 set 2024.]

First, I thought I'd share what I'm preparing for. The title and abstract for the seminar I plan on attending are as follows:

"'Decay of excess for the abelian Higgs model'

Entire critical points of the abelian Higgs functional are known to blow down to generalized minimal submanifolds (of codimension 2). In this talk we prove an Allard type large-scale regularity result for the zero set of solutions. In the 'multiplicity one' regime, we show the uniqueness of blow-downs and classify entire solutions in low dimensions and minimizers in all dimensions; thus obtaining an analogue of Savin's theorem in codimension two."

What I don't know:

"'Decay of excess for the abelian Higgs model'

Don't know = I don't understand, I know this word but do not understand in context, I don't have a concept attached to these words, I have no significance attached to these words ie. I don't know what you want me to understand or why you want me to care.

So far, I've reviewed yesterday. Today, I will find definitions for all the key words, map them, and explore some of these new terms as well. The general objective, I believe, is to get to a point where I have a concept in mind attached to the abstract as I read it. There is an image in mind, I understand what it means, I understand why it's significant, even if I haven't studied the intricacies. The goal is to sit in a room where this is discussed and be able to follow along, not mathematically, but conceptually.

I've been to lectures and seminars before, but all within science and technology disciplines, and I'm a bit of the expectation that a mathematical lecture is less accessible. I don't know this for sure, but I'm preparing as a result of this expectation.

Anyway, my review. [1:11:15 6 set 2024]

I began by writing everything I could remember without reference. I occasionally had to stop and think a bit longer, but it was a good mental stretch. After reviewing, I went over my recall, highlighting key terms, correcting errors, and filling any blanks. At this point, I was still working without a concept of some of these words, but it made sense. What was being done and studied made a kind of sense, and I had some vague images in my head approximating the concepts I would be learning.

I followed with researching the terms I'd listed. I didn't exactly go in order as they started to circle each other and I learned them as it made sense to do so.

I'm realising I know a lot of these things, or I'm familiar with them. I simply don't know the names and that complicates things (like a child learning physics), but I am familiar and complications can be smoothed. There are many things I'm still curious about and would like clarification on, but I don't know when I will have the opportunity to ask anyone willing to explain. That's okay. I think I can manage well enough for now.

I've realised I lean towards topology. Maybe incidentally. I may end up researching it more because I'm less familiar, so it's most of what I'm interacting with. I think I'm also most intrigued [by topology], but again, maybe it's more difficult to be intrigued by something you feel you completely understand.

The more I researched, the more I came across terms I found easier to conceptualise through image and comparison to what I know. I have no interest in learning mathematical definitions [as of yet] partially due to the time constraint. I just need to understand what you mean, feel it, and have some sense of logic within the world you define.

I did not research all of the terms on my list, nor did I get to most of the terms in the abstract. I will attend the seminar anyhow, research abstract terms in commute, and at minimum, enjoy the experience of watching someone talk about something that matters to them. Something they are learning. That experience is invaluable.

I also have the privilege of no time limit on my general learning. This could last a lifetime if I let it. A seminar is not the end.