Today on the conference Florian Pop gave a wonderful, very inspirational and very enlightening talk on Rumely’s arithmetical capacity theory. I feel a strong desire to abandon all my current projects and start reading Rumely’s books. Last time I had such feeling when I learned the notion of o-minimality and read the book of van den Dries.
By the way, as Martin Widmer remarked during his recent talk in Bordeaux, o-minimality is a very clever way of formalizing the notion of “being non-pathological”.
Vieux Girondin 
April 19, 2013 at 8:34 am |
Generally speaking, o-minimality was devised as a general way to overcome problems with (mainly) roots of univariate functions by embedding these questions into a multidimensional context, and about 10 years ago people where very fascinated about prospects of this approach.
Apparently, the difficulties turned out to be much heavier than initially believed. Thus far (apart some general theory-building), the o-minimality approach is yet to bring its fruits in the area which was a primary potential customer.
BTW, what means 90 at the title?
April 20, 2013 at 11:22 pm |
I am rather ignorant about the original motivation for o-minimality. But what I know for sure is that its applications in the arithmetic geometry are truly spectacular.
April 20, 2013 at 11:24 pm |
no idea about 90…
April 21, 2013 at 7:31 am |
But what I know for sure is that its applications in the arithmetic geometry are truly spectacular.
I am really curious: could you give examples? Or, more simply, do you plan to be in Israel any time soon?
In analysis (analytic ODEs and limit cycles) the work is more on the foundational level, developing tools and sophisticating the language. I’m afraid that if (when?) the original problems will be solved by the logicians, the rest of us would already be unable to understand them.
April 21, 2013 at 11:25 pm |
You may start from my lecture notes
Click to access basel_yaro_chennai.pdf
You will find further references therein.