Madison, Wisconsin

On the left, Lake Mendota, covered in ice.
This just down the street from the Lowell Center, where I stay. On the right, a snow disk above the lake, on campus.

The google map reference for here is http://maps.google.com/maps?oi=map&q=Madison,+WI,
and for home is: http://www.google.com/local?f=q&hl=en&&ll=53.392286,-6.633682&spn=0.024824,0.058966

The meeting on Complex Analysis, in honour of Ahern, Nagle, and Rosay was quite outstanding, with a lot of high-powered folk present, and a very high standard of talk. Madison is an amazingly pleasant place, with all this water-scenery, a tremendous variety of restaurants, and more coffee-houses to the square mile than Amsterdam. Good place to do mathematics.

By the way, apologies to visitors to my blog for the unpleasant ads that appeared in the last couple of days. This was no doubt view to the fact that in my remarks about my delayed luggage I made light-hearted mention of the replacement of my unmentionables, and this provoked, via the wonders of search-engine technology, a spate of ads about precisely those, which were really quite offensive. I'm experimenting with this business of ads, and if there is much more of this kind of thing, I'll pull the plug. In general, the ads that pop up are reasonably-related to my content, and actually informative for me.

Back in the USA

First time since the Spring of 2001. Last time, I visited Webster in Chicago (to talk about involutions), and Kaufman at Urbana (to talk about the Zygmund class).
Apart from those luminaries, the high points were the ride on the City of New Orleans to and from Urbana, with Arlo Guthrie's rendition of Steve Goodman's song playing in my mind, and the amazing Art Institute of Chicago.

Various little things went wrong, mostly due to some rather bad winds in the midwest. My connection from Chicago to Madison was cancelled (that's how I spell that), and my bag went missing for a couple of days, but it all worked out. I found as always, how very easy Americans are to get along with, and encountered much kindness and good humour. Apart from various airline employees and hotel staff who just did their jobs efficiently and with exemplary courtesy, I met Tom and Loretta Dichraff, a retired couple from Madison, who went out of their way to the extent of offering me a lift to the University from the airport.

Funny the things that affect you. I had a plain sugared doughnut at O'Hare yesterday morning, with a cup of weak and gratuitously-sweetened coffee, and the first bite of the doughnut brought a rush of recollection, and tears to my eyes. It wasn't that it was so good (it was fine), but that it was exactly the same as always, and they never make a doughnut just like that at home. You taste it, and you know you're in America.

On the plane across the Atlantic, I sat with a young man from Iran, who was going to San Francisco to get married. Security and immigration at Dublin took me seconds flat. The only intrusion was that they recorded my index fingerprints at immigration. (I recall that they took my thumbprint many years ago, so that's 3 digits down and 7 to go.) They gave him the third degree, strip-searched him, and took about an hour going over his story. They explained that it was required for people from Iran, among other places. He found it harrowing. Being picked out like that always raises hackles. I remember how it felt when the British police used to pull all the Irish people out of the ferry queues, in the seventies and eighties. At first, you had some sympathy, but eventually you got tired of it.

Hackles are feathers, on a bird's neck. I've now become very interested in hackles. They are exactly what you need to make those ruff-like arrangements you see behind the head of a
dry artificial fly. You wind them round the shank and they splay out perfectly.

The only fishing going on here in Madison at present is ice-fishing. They are forecasting snow for this evening.

Website Stuff

I've been studying the circle of protocols and languages useful for web pages: html, xhtml, css, ssi, perl, javascript, php. There is an outstanding site with tutorials on these things, at http://www.htmlite.com. I tried out the stuff on my sites at the Maths Department, and Logic Press.

Cascading style sheets allow you to alter the entire look of a whole site by editing one file. One issue is that the gurus deprecate the use of colour names such as green, magenta, etc, and so you end up learning about RGB descriptions of colours. This has been a bit of an adventure. I keep trying things, and being surprised by the result. For instance, equal red, green and blue, such as #ffffff (that's three 255's in hexadecimal) gives white, as you would expect, but if you drop the red just a little bit, say to #f0ffff, then you get a very pale and dreamy green.

Now there's a funny thing. The blog editor that comes with this site allows me to wysiwig in the html code for the above colour, which I pick from a pallette of 80 colours. It also allows me to edit the html, and change the colour to #f0ffff, but if I do, then the text vanishes in the previewer! Maybe if I go ahead and publish it, your browser or mine will display it; why not? Maybe the previewer is set up to recognise only colours from that pallette. Let's try. The end of this sentence is written in a pale and dreamy green, but if it ends at the comma, then I'm wrong.

Do you see the text after the comma, in very pale green? Aha! It's there, by gum, but I now see that my page has a very pale pink background, and the pale and dreamy green has become an almost invisible slightly yellower shade, and you don't see it at first. It's a special case of a general problem: it's really easy to make stuff invisible on a web page.

Another issue is what it takes to get a server-side include included by the server. I find inconsistent behaviour between different servers. The server running at Maths
handles something like (I had a bit of ssi code here, but it got excluded when I saved it! Blog-editor-side-exclude, I guess.) by sticking the contents of test.shtml into the current file before sending it out to the browser. But the server running at Host Ireland won't seem to do this unless I rename the current file so that its extension is .shtml instead of .html. What is this? Once I have a page up, and people have found it and bookmarked it, I don't want to change its name, nor do I want to go around installing redirects all over the place. Apart from anything else, people get nervous when you redirect them these days: they are afraid you are sending them to a russian mobsite that will hijack their computer and use it to sell porn.

This is not good, because the gurus want us to use server-side includes instead of frames to put stuff such as navigation bars and, well, frames on and around our pages. It seems that frames don't work too well if you are displaying the page on some exotic device, and people are using more and more exotic devices these days.

Logic Press' Site's Up

In the past week I became the owner of the domain name logicpress.ie, and the site is up and running at http://www.logicpress.ie/ . It remains to be seen how this affects the operation of the Press.

The site is hosted by HostIreland, who are easy to deal with, reasonably-priced, and respond quickly and competently to queries. I took the basic Linux package, as this provides ample
storage for me (I believe in lean code) and gives me convenient access using my favourite
operating system.

The online payments are done using PayPal. This was really easy to set up, works like a dream, and the pricing structure compares very favourably with VISA, for a small business.
It's especially attractive for a seasonal business, because it costs almost nothing to set up,
and you pay nothing if you receive no payments.

I allowed ads from Google on the site. I was concerned about some of the ads that popped up at the beginning, as they were for marginally-dodgy stuff that I wouldn't want to have near my site. But Google advised me how to block these, and they seem to have dried up. I'll see how this goes; it may not be worth the trouble.

I've also submitted all the books to the Google Publisher programme. This will allow online search of the full text of each book. The benefit to the Press is that it may promote sales: each page displayed will be accompanied with buy-this-book links, including one to the Logic Press site. Again, it remains to be seen how it works out.

I had to setup a redirect from my old host, and found the site instant-website-tools.com
useful for this and other matters of interest to website controllers.

Playlist for Sick Days

When I set up the blog profile, one of the questions was about my favourite music. Impossible to answer.

On Thursday last, I tore something in my lower right back, and by Saturday I was unable to stand up without crutches, having made it much worse by repeated aggravation. Could not sleep much, Friday to Sunday, as there was only one pain-free position, and the slightest deviation produced spasms. Got a handle on it late on Sunday, and figured out how to move about on crutches without making things worse, and on Monday p.m. Grainne provided a little machine that imparted low-voltage shocks, and accelerated the repair process. Recovered normal locomotion by Tuesday evening, and had a pain-free night's sleep; all's well now.

While it was at its worst, there was nothing to do but lie on the floor of my office and listen to music. Here's the playlist that came off the shelf:

The Christy Moore 81-91 Collection. Many good songs, but the masterpiece is Ride On. This, like many a great song, comes from some place outside the universe. Second-best song: Nancy Spain. Warner. 9031-75351-2

Canticum Canticorum. Settings of the vulgate text of the Song of Songs, performed by Capilla Flamenca. ISBN 90-5826-208-1. Four settings (no less) of Quam pulchra es, five of Tota pulchra es, two of Anima mea liquefacta est, and more. Amazing.

Messe Saint-Leon Le Grand. Collection of fine popular choral pieces, and a mass by Denis Bedard, performed by a Canadian church choir (Westmount, Quebec). Gift from Paul Gauthier. High point: Bruckner, Locus iste. CSTL 100

Arlene Auger. Double CD of soprano arias and songs. Gift from Declan O'Keeffe. Best: some Villa-Lobos. Delos DE 3712.

Jo Stafford. Double CD. 54 songs from 42-52. Incredibly clean notes. Of course the high point is the duet Whispering Hope, beloved since my infancy.
http://www.sanctuaryclassics.com/

The Best of Elkie Brooks. High point the incomparable Pearl's a singer (- she stand up when she plays the piano...). Reissue of the A&M, by Karoussel.

Gypsy Kings. Mosaique. This is up there with the greats. I have no idea how they do it. These guys seem to live in Marseilles, but sing Spanish gypsy, canto jondo. Michael and Anne-Marie gave us tickets to their Point concert last year. It was a very good concert, but the best things they do are the slow, agonised love songs, and they concentrated at the concert on the ecstatic gypsy dance stuff.

Mozart and his Czech Friends. The latter are Jan Nepomuk Vent, Josef Mylivecek, and Jan Krtitel Vanhal. Symphonies for chamber orchestra. Agreeable. Multisonic 31 0399-2

Mozart. Mass in C Minor. Highlights + some extras from the Solemn Vespers, and the Ave Verum. 1994. By our own Maynooth Choral Soc, Gerard Gillen conducting. Private circulation only.

Liszt. Symphonic poems 2&3, Hungarian Rhapsodies 1,3,5. New Philharmonic Orchestra.
Why not?

Great Spanish Mathematicians

A few months ago, my old poker-school confrere Frank Spain came back from Ciudad Real to bury his father, and we renewed acquintance. Later, he sent me a copy of some magazine with an article "Cerebros al cuadrado", by Monica Salamone. It was about the top Spanish mathematicians.

Who are they? Turns out they are:

• Enrique Zuazua Iriondo (at the Autónoma, Madrid), working on PDE (partial differential equations)
• Jesús Sanz Serna, (Rector at Valladolid). Founder of the Spanish Applied Maths Society, now rector of the university, (-- "Así que ya no investiga").
• David Nualart (Kansas) Working in applied probability, especially market models.
• Juan Luis Vázquez (Autónoma, Madrid), working on applied nonlinear diffusion problems, such as the flow of water in a porous medium.

Did I know them, said Frank? No. Would they have been top of my list? No. Is that strange?

No. The list was arrived at by taking the most cited scientists in the world, in all fields, and then looking at the Spaniards. It turns out that there are more mathematicians among them than practioners of any other field, and these are the most cited of those.

Great people, no doubt. But citation-counts, based on ISI and the like, measure something other than an article's impact on its field.

Measuring CO Emissions and the NCT

We took Lise's Opel Corsa Champion for its bienniel checkup on Friday; it's just coming up to its sixth birthday. The car has been a grave disappointment to her, presenting a litany of troubles over the years. For instance:

• The front passenger seatbelt catch failed; eventually, they had a recall on the whole fleet about that one.
• There were a considerable number of flimsy, or flimsily-attached pieces of plastic around the seat area that came off within a short time.
• Several dashboard lights failed, and it turns out that they are so awkward to get at that it costs 100 euros labour to replace them.
• The thing has an idle motor (Why? Can't the ordinary motor idle?). This failed just after the warranty ran out, and again three years later. 300 euro a pop. When it fails, it's a complete shambles; you're there, revving the engine in neutral when you have to stop in traffic, to avoid it cutting out.
• We've replaced the exhaust (US: muffler) five times, no less.
• Last test it failed on the headlight aim, and it took major surgery to get the thing pointing where it should.
• The exhaust came apart once in the middle, and the little car vaulted over the back box, folding over the pipe and jamming the box between the floor and the road to make a first-rate brake. Lise was stuck fast. When I arrived down to see what was wrong, I had to cast about for a log, and jam it under the wheel so the car could drive up on the log and free the exhaust. Driving home without the exhaust was the only time the car really went!
• It often produces an appalling rattle, a bit like one of those old Leyland buses starting up, as you start off.

So we approached the National Car Test with no great hopes, and were pleasantly surprised when they told us that the only thing wrong was the carbon monoxide emissions at low idle, and that this would probably be fine if we got the holes in the exhaust fixed. Never mind that the exhaust was practically new, and we knew nothing about holes. Holes can be fixed, and if not we could always buy a sixth set. I'd been fully prepared to write the thing off and take her back to Toyota.

I was a bit shocked at the reading: 3% CO, but the tester said that with holes you get a false reading.

Sure enough, it turned out that the leaks were at the junctions, and were due to the heroic efforts of our usual mechanic to strap up the exhaust and stop the awful rattle. And as soon as the junctions were repaired, the CO reading came down to something tiny, and the car passed.

The main reason for this post is to ask a question that bothers me: How is that holes in the exhaust raise the CO concentration reading? What is that NCT machine doing? It's supposed to measure CO percentage by volume. As far as I could see, it was attached to the end of the pipe. Was the CO percentage different between the two tests, or is the machine measuring some proxy for the concentration?

Homeland, by Paul Mercer

We went on Monday to the Abbey to see this. First of his plays I've seen. It's
very amusing. I'll look out for more of Mercer.

There is a loose connection to the story of Oisin and Niamh. I forget everthing; I thought it was Oisín mac Conan mac Fionn, but the programme notes told me it's
Oisín mac Fionn mac Cumhaill. It's a long time since I read the story.
Perhaps I'll remember, now.

Fly Fishing for Trout

Yesterday, I may have actually achieved real fame. My photograph has occasionally appeared in the papers before, but always in relation to minority-interest stuff, such as computers and mathematics. Yesterday, January 23rd, I featured on the fishing column of the Irish Times, page 22. holding a big trout. Everyone knows that fishing is the number-one sport, by number of participants, in Ireland; maybe everywhere. There is something deep in the blood that draws us to it.

Michael arranged a trip to Rathbeggan Lake on the Wednesday of Christmas week for Colin and myself.

(Tried to add a photo of Colin here, but I'm doing something wrong.)

Rathbeggan a private fishery, and you can fish there in the off-season. Never did that before; I'm not completely sure it's moral. Anyway, it was pretty cold, and the fish lay low and took a lot of coaxing. We laid all sorts of flies across them, and they ingored the lot.
No-one was catching anything. At the same time, they did regularly break the water, big fins and flukes rolling by, more like little dolphins than trout. There were essentially no flies on the water.

We were impressed by one fellow who rolled up and hauled out four fish in about an hour or ninety minutes. When he caught his first, I went over to have a look. Rainbow trout of about two pounds. He was fishing with a pink Marabou streamer, with a heavy gold head to sink it, and a palmered brown hackle over a pink chenille body. A sinking lure, basically, imitating a small fish; not that we have any fish remotely like that. Lord only knows what trout think about these things, but they certainly went for it. He told me the trout were only surfacing for air. He fished a very long leader on a floating line, and jerked the thing along just off the bottom, which was 6 to 10 feet down.

I had nothing like that pink yolk in the box, and went up to the lodge to see if they did. Sure enough, they were, as Huck Finn would say, plumb out of pink streamers. The nearest thing to our friend's arrangement was a hairy looking thing with a big gold head and a lot of rabbit-fur. I forked over two euro for one, and went back down.

We tried whatever we had that was pink, and then I had a go with this rabbit-fur do-dah.
I cast ahead of a fish that had just broken the water, and seemed to be cruising in an oval pattern, and he grabbed it as it sank, quite high in the water. Mighty fish. Just then the proprietor came down with his camera to get a shot to send to the paper, who had requested something, so he advised my as I brought this animal to Michael's net, and got him out.
Hence the photo in the IT.

Better things happened the following week. Michael got me a book about fly-tying for Christmas, and I worked through it. I made a pink Marabou streamer, and some other stuff, including a red-brown nymph with gold ribbing, and a wet and dry effort. It's a lot of fun, and mighty interesting. These fly-tying folk have preserved a vast amount of lore about the characteristics of natural plant and animal materials, and there is a whole new vocabulary.
We went back up to Rathbeggan the following week, and I hauled in two trout, one on the pink Marabou (after I clipped a bit of weight onto the head), and a truly mighty fish on the gold-ribbed nymph. Funny thing, I wasn't even holding the rod when he took it. It was a warmer day, and people were catching fish. There were a couple of pensioners there, doing pretty well,
and I'd stopped to talk to one of them about his flies, leaving down the rod with the fly in the water. Colin let a yell when the line jerked, and we were in business.
It measured nineteen inches.

So now I've caught fish on my own flies! It doesn't get any better.

Media

"Radio", she said, "is my favourite media."

Latin: There's the adjective, medius, media, medium (mid, etc.), which agrees in gender, number, and case with the noun it qualifies. The derived neuter noun medium (middle, etc.)
is declined medium, medii (genitive sing), etc., and media (nominative plural).
This root gives us:

English: medium, median, mediate, mediator, mediatrix, immediate, etc.
When used for a mediatrix between the living and the dead, medium has usually had the plural mediums. In all other cases, people like me use media. Fowler noted the use of mediums by a minority. Television is a medium of communication, as are radio, the print media, town criers, speech, braille, and tom-toms.
At some point, people started distinguishing the mass media, and then this was shortened
to the media. Then an interesting thing happened.

Latin: Common first-declension feminine nouns end in -a. Most school grammars illustrate this by using puella (girl), but the Christian Brother who wrote my first text (in Irish) didn't want us thinking about girls, and used mensa (table). The nominative singular -a becomes
-ae in the genitive singular and nominative plural: puellae (don't think about them), mensae (tables).

English: Most Latin words carried into English that end in -a are feminines. For instance, formula, patina, patella, villa. Literate people tended to use the Latin form of the plural, such as formulae, although I've never seen villae. (Funny the way these icons for bold and italic work! Not like the usual wisiwig.) The ending -as had its supporters as well. Others, noticing this, aped the practice, and invented a rule (as we are hard-wired to do): "Fancy words ending in -a are singular, and the plural is constructed by changing to -ae if you want to be pretentious, but -as is fine for most purposes". Works well in many cases, but comes to grief on cases such as data - plural of datum, a given thing, from do, dare, dedi, datum (I give, to give, I gave, given); phenomena - plural of phenomenon, Greek, a sneaky one that; agenda - plural of the gerund agendum, thing that has to be done, from ago, agere, egi, actum (I do, etc.); incidentally, the cetera in etcetera is the plural of the neuter ceterum (residue).

Which brings us back to media. Obviously singular, by the "rule"; most commonly used as a synonym for television.

It offends my ear, but the truth is that living language mutates continually. It is quite acceptable now to say this data, or these medias. The only thing to regret, if there is any point in regretting anything about all this, is that educated younger folk are no longer in touch with the roots of our civilization and language. Something lost there, perhaps. Then again, perhaps it was all a burden, holding us back.

It's Cold Today

Here's a picture from warmer days. The Liffey, just below Liffeyhead Bridge, a couple of miles from the source on the flank of Kippure.

The blog will be slow to load with these high-resolution images. I suppose the
thing to do is to give links, and possibly thumbnails. But I don't want the bother of editing photos to size them before posting. I also don't want the bother of copying them from my usual spot to a public area on my server. Ah! I can just upload them to this photos1.blogger.com, and link to a text. For instance, here I just edit
the html to replace the "<" img .... /> bit by the text I want, such as "Here's a picture...".

Maybe I shouldn't worry about stuff like file sizes, storage limits, and download speeds. It's the result of long habit. I started computing in 1965-6, on the IBM 1620, using FORTRAN-2,
punch-card or console input, and punch-card or teletype output. I just missed the end of the paper-tape era. Fr. Ingram (may God be good to him) taught me the rudiments. The thing had 16K (bits?), which were quite large transistors and failed a lot, it output a little faster than a good typist, it had no read-write external storage, no operating system, did one job at a time, and lived in a climate-controlled room, cared for by a roster of pretty girls and a brain surgeon from IBM who came in every few days to replace a failed component. You could do wonderful things with it, but your code had to be efficient, minimising computations and minimising use of memory. This discipline developed habits that stay with me, and make me weep to see the waste that goes on nowadays.

Put Out Their Eyes

We watched the film of Hrabal's book Closely Observed Trains on Wednesday. The bit about blinding a bull to quieten him recalls other blindings: the play Equus , the book From Here to Eternity , and classical cases. It gets your attention.

Hrabal reminds me that there was supposed to be a very good samizdat article by Peter Connolly, God rest him, about the difference between erotic and pornographic work. I don't know whether it's in print. In the old days, it seemed the clergy here in Maynooth hated publishing anything, or even signing a letter. I actually heard the advice: never sign anything! This made it difficult to get some things done.

School Geometry

We are short-changing our students on geometry in Ireland. A recent OECD comparative study showed that our 15-year-olds perform well in general, but are below par in handling problems that involve spatial ideas. We need to get them thinking geometrically. Apart from giving it the necessary time and attention, we need good books, of two kinds:

(1) Texts and extra reading for secondary students that will be mathematically sound, interesting, and challenging. Most of our students hate geometry. If they were exposed to the right stuff, they would learn to love it. see
a typical good geometry resources page.
I recommend the posters on Math in X (where X is a country), if you can still get them.
There are excellent books available, tailored for US school practice. An outstanding example is Harold Jacobs, Geometry: Seeing, Doing, Understanding, 3rd edition, Freeman 2003. Let's have something like this in use here.

(2) University texts for prospective maths teachers. Most younger teachers also seem to hate geometry. The universities should do things to fix this, at least with the new entrants to the profession. Most US universities have courses that aim to meet this need, and there are many texts, at varying levels of sophistication. A sample course is that at Clark University Some examples of texts:

P.D. Barry. Geometry with Trigonometry. Horwood. Suitable for a one-semester course, with modest prerequisites.

H.S.M. Coxeter. Introduction to Geometry. Wiley. A vast panorama. Could be used over three or four courses, over several years.

D. Pedoe. Geometry. A Comprehensive Course. Dover.

D.A. Brannan, M.F. Esplen and J.J. Gray. Geometry.
Cambridge UP. Designed for Open University work; works up from the basics.

J.N. Cederberg. A Course in Modern Geometries. Springer. 1995. Needs mathematical sophistication in the student, to begin with.

At Maynooth, we've used Greenberg. Euclidean and Non-Euclidean Geometries: Development and History. 3rd edition. Freeman. 1994. This has worked reasonably well with 3rd year students of Mathematical Studies.

King Kong

That's Lise and my special friend, Naomi.

Lise and I saw the movie this evening. Great picture, except they
should have cut out about 15 minutes of horrible
gore. Kept tightly to all the classic scenes of the
last one.
Lise says Kong is an allegory of America -- colossal,
brutal, soft-hearted, brave, flawed, lost.

Technically interesting (and touching)
was the effect when the light went out of Kong's eyes
as he died. It's a movie cliché. This time it was very sharp,
or something; presumably this high-definition stuff
and the computerised animation make it possible.
Apart from movies, does it correspond to any reality?
As far as I recall from personal experience of deaths,
the eyes of the recently dead are characterised by
lack of movement, rather than lack of
reflectivity. But my experience is limited, and I was never
emotionally-detached, so my observations are not
reliable.

Maths Teachers should be qualified

Did some work for the registration section of DES
this afternoon, and also read some impassioned comments
by Ted Hurley. He's right. We have reasonable criteria for
registering someone as a secondary maths teacher. However,
there is nothing to stop a principal assigning maths classes
to any teacher, no matter what subjects they are qualified to
teach. Only 20-25 percent of maths teachers qualify in maths.
It has to stop.

Keeping in Touch

I've been using gmail for about six months now. Joel Feinstein convinced me to give it a go, and after a few months I decided to scrap and disable the good old aof@maths.nuim.ie. The problem
was that, having been up forever, i.e. since even before the internet had html and browsers, the address (which was always an alias) is on every single spammer's list, and got about ten thousand messages a week, of which an irritating proportion pierced the filters. The address is now
dead, and I'm gradually letting my real contacts know about the new one.

Today, I was prompted by the fact that Susan Oakes of the LMS could not reach me to import a few lists into my contacts. Turns out I need them in comma-separated-value format. Google help suggests that I put them into Excel first. I'd prefer (since I hate The Evil Empire) if they would just tell me what
csv format is. Probably:
1) lines (separated by c/r at least), and comma-separated fields.
2) First line to give the headings
3) email must be one of the headings (or is it e-mail?)
Is this right?

No. Wikipedia has it at
http://en.wikipedia.org/wiki/Comma-separated_values
Tells me all I need to know.

Business to Consumer search engine

I read about Froogle. looks useful.
It seems that I'll need to
make a separate order page for US dollar customers
in order to meet their requirements.
No time to do that today, or for a while.

Diffeomorphism Groups

I'm interested in groups of maps, and particularly
in the role played by the involutions in such groups.
Right now, I'm concentrating on diffeomorphisms
in one variable. Maria Roginskaya and I have worked
out some things, and we are aware of some work of
Sternberg, Mather, Smale, Robbins, Ahern and Rosay, Calica,
Kopell, Takens, Sergeraert, Young, Afraimovitch, Liu,
relating to conjugacy, normal forms, conventional
multipliers and moduli. I'd be glad to hear of sources.

Starting my Web Log

This is a first test post to my blog.
I'll try a link to my
Home Page:
http://www.maths.nuim.ie/staff/aof/

OK, that worked. I had a bit of trouble with it; it's not quite clear
how the stuff works.

Now a link to Logic Press:

I'm starting to get the hang of it. The first time I tried the
icon for a link, I got a link with no text to click on;
you mark the text, then click on the link icon!