The plan for today was to get up to date with research work. What do I mean when I say I want to get up to date? I want to do enough to be able to report to Kasturi on Monday. OK, I feel full, I shouldn’t have had that much root beer. OK, back to work, what will I tell Kasturi? What do I want to tell Kasturi? I will talk about the extension of the bad example to the general case. And I will talk about use of combinatorial methods. I will talk about a) finding the shortest path from x to its infinite exterior and then for each disk on the shortest path finding a shortest path along the belt from one end of the disk to the other. But this is what he mentioned last semester. What is new here? Honestly, nothing. I have to tell him that all I could come up with was what he had already mentioned and that I don’t see any problem going in this direction.

But that is not good as I should have done some work before. Well, I haven’t.

What are his objections likely to be? They are most likely to be that, well, what about the case where the point may be contained inside a disk? Well I want to tell him I want to handle that as a special case and then focus on this one. This is sure not to please him.

There sure was something else that was a gap in what he said last semester. It has to do with figuring out the properties of essentialness etc. of the cycle w.r.t the surface at hand.

So what do I tell him? I definitely feel that for Monday I should focus on presenting to him better rather than trying to do anything new in a rushed manner.

So here are the points I want to talk to him about:

1) Bad example

For the bad example, I want to first remind him of the bad example we discussed. What was it? It was showing that a path $\pi$’ could enter a disk several times. OK, the figure is drawn. The bad example is recollected.

2) Combinatorial Methods

As far as combinatorial methods go, I want to begin by talking about the paper – what paper? – the Jeff Erickson paper. Say I went through it, but the main idea seems to be finding shortest paths from which we go on to find the shortest cycles and then ensuring the essentiality property. Say that I haven’t got the details of this work; but I remember discussing the shortest path approach before we left for break and would want to start off by recollecting what is the void in this particular approach.

3) Also maybe it might be an interesting idea to go home and look at the notes I made in the small pad which had some slightly mathematical content.