Those of you who figured out what enneadecahebdoversary meant, or caught some other clue I’ve given about timing, or know Hannah and me well and have a knack for dates, will realize that today Hannah and I are celebrating six months together. (Yes, I know “hexa” is a Greek prefix which I’ve stuck on a Latin-based neologism. But I decided a while back that the Greek numerical prefixes are almost always cooler and even more natural-sounding than the Latin ones. “Seximensiversary”? Does that work at all? Plus, it has too many overtones in English.) Honestly, I did more for Valentine’s Day than I’m doing for today, partly because I completely lost track of the dates and didn’t realize this was coming up until yesterday when it came up in conversation. (Right now, all time is measured strictly by the number of days remaining until Hannah comes to visit—three weeks from yesterday—rather than by Gregory’s ancient decree of quotidian nomenclature.) If I were in Ithaca, however, it would be different. We would have gone out to dinner on Valentine’s Day, certainly, and I would have brought Hannah flowers. But today, were I there, I would take Hannah on a walk in the snow, perhaps go down to the Carriage House and have a hot drink and a nice brunch. We’d spend the afternoon inside, keeping warm, perhaps working some because we’re students and there’s always work to do, but we’d take time in conversation to remember how lucky we are to have grown so close and to have the promise of so much more. (We had part of this conversation yesterday, as we recalled our histories. We’ve both changed a lot over this time, becoming more and more suited to each other. But in the days before I left Ithaca, before we were dating, we were desperately trying to make sense of our situation. I didn’t think it would be a good idea for us to start dating; I wanted to give her freedom for the year. But as Hannah has pointed out, I still wanted to be the closest man in her life.) I’d sing her a love song…
Moi je t’offrirai
Des perles de pluie
Venues de pays
Où il ne pleut pas
Je creuserai la terre
Jusqu’après ma mort
Pour couvrir ton corps
D’or et de lumière
Je ferai un domaine
Où l’amour sera roi
Où l’amour sera loi
Où tu seras reine
We’d make dinner together. And we’d kiss each other good night, preparing for the morning when we’d go worship together.
Why should this be any different from how we’d spend any other Saturday? I guess in many ways it’s not. Days can be made special by either event or intent. Six months into a relationship is something of a hurdle; a lot has happened by this point, and while things can remain fresh (as they can throughout a lifetime), the relationship isn’t pristine any longer. Many of the complications of depending on another person and having lost some measure of independence have been brought into relief. Six months isn’t a moment to fear, but it is a moment to mark, and maybe marvel. The work has been done, and will continue. The intent of today is to declare that the decision made half a year ago, in such doubt and anxiety and excitement, is now sure. “Happy six months” doesn’t mean that every moment or even every day of those six months has been happy, because that’s simply not true. We have had pain and confusion and sorrow. It means that today I’m happy we’re still together, and I want to remain that way. It means this time has been incredibly wonderful and joyful, despite the hardships. It means, for us, that when I return to the States and a full nine months will have elapsed since the spurt that pushed us into this, the time will not have been lost. It means thank you for being willing to live this experience with me.
Happy six months, Hannah.
Saturday, February 24, 2007
Friday, February 16, 2007
a tale of two spaces
Well, in some ways this week was spent studying three spaces, but two of them made their way into the title of the conference: outer space and Teichmüller space. Teichmüller space has a long history in the study of Riemann surfaces; outer space is much more recent, and the conference was organized in part to celebrate the 20th “birthday” of outer space: in 1986 the definition and fundamental properties of outer space were published by Culler and Vogtmann (the latter of whom is a professor at Cornell). At Thursday night’s bouillabaisse dinner, the two of them blew out the candles on a birthday cake. The third kind of space mentioned this week was symmetric spaces; the study of these goes back even further than Teichmüller space. Several talks described the fruitfulness of thinking of these three kinds of spaces jointly, to see what analogues and differences there are.
Part of the idea in the study of these three spaces is to link geometric and algebraic objects so that each can cast light on the other. Generally, the algebra comes from looking at symmetries in the geometry. Theorems arise which describe the restrictions one side puts on the other: that is, if your geometric object looks the same in a lot of places, then there are a lot of ways to move the points of the object around on itself while keeping the same structure, and vice versa. (Think of how a sphere can be rotated around any axis through its center by any amount to give the same sphere, because it looks exactly the same at every point. A cube, while it has lots of pretty symmetries, is less symmetric than the sphere, which you can see by the severe restrictions on which axes you can rotate around and by how much to leave the cube looking as it did before. A highly irregular object looks different no matter how much you rotate it in any direction; this is called having a trivial symmetry group, which is an algebraic way of describing a geometric property.) The basic geometric objects in Teichmüller theory are surfaces with metrics, i.e., ways of measuring distances on the surfaces. The distances can make little patches on the surface look either flat or curvy (for an explanation of what “curvy” means here, see Tim’s entry about bugs on a hotplate). The symmetries of such a surface can be described roughly (almost always) as ways to cut the surface up and glue it back together so that it looks the same. Outer space looks at graphs, which in this context means not plotting a function or the year’s earnings, but taking points and connecting them with edges of various lengths. (A common example here is a single point with several curves that leave and come back to it; this is called a rose.) The symmetries come from ways of exchanging pieces of the graphs. But whereas Teichmüller space interests itself mainly with the geometry of the surfaces, outer space was created specifically to study the ways of moving the graph around—that is, the focus is on the algebraic aspect. This means the study of outer space falls under “geometric group theory,” using the geometry of an object to glean algebraic information about the associated symmetries. (Indeed, it is called “outer space” because the ways of moving things around form the outer automorphism group, an algebraic object that was studied long before the introduction of outer space.)
This was a fantastic week to be in Marseille (or more properly, in Luminy where the conference center is). For those interested in the conference webpage itself, you can find it (containing a description of the week, a list of participants, and summaries of the talks) here. I could throw around the names of some of the top-notch mathematicians who were here, but everyone who cares probably already knows. I made and strengthened a number of good contacts, and got some good references and discussion for the projects I’m currently working on. Congratulations and thanks to the organizers, and to all the speakers, and to my colleagues with whom I met. I look forward to continuing in this field, at the intersection of so many interesting parts of mathematics and drawing on the skills of so many generous and talented mathematicians, for many years.
Part of the idea in the study of these three spaces is to link geometric and algebraic objects so that each can cast light on the other. Generally, the algebra comes from looking at symmetries in the geometry. Theorems arise which describe the restrictions one side puts on the other: that is, if your geometric object looks the same in a lot of places, then there are a lot of ways to move the points of the object around on itself while keeping the same structure, and vice versa. (Think of how a sphere can be rotated around any axis through its center by any amount to give the same sphere, because it looks exactly the same at every point. A cube, while it has lots of pretty symmetries, is less symmetric than the sphere, which you can see by the severe restrictions on which axes you can rotate around and by how much to leave the cube looking as it did before. A highly irregular object looks different no matter how much you rotate it in any direction; this is called having a trivial symmetry group, which is an algebraic way of describing a geometric property.) The basic geometric objects in Teichmüller theory are surfaces with metrics, i.e., ways of measuring distances on the surfaces. The distances can make little patches on the surface look either flat or curvy (for an explanation of what “curvy” means here, see Tim’s entry about bugs on a hotplate). The symmetries of such a surface can be described roughly (almost always) as ways to cut the surface up and glue it back together so that it looks the same. Outer space looks at graphs, which in this context means not plotting a function or the year’s earnings, but taking points and connecting them with edges of various lengths. (A common example here is a single point with several curves that leave and come back to it; this is called a rose.) The symmetries come from ways of exchanging pieces of the graphs. But whereas Teichmüller space interests itself mainly with the geometry of the surfaces, outer space was created specifically to study the ways of moving the graph around—that is, the focus is on the algebraic aspect. This means the study of outer space falls under “geometric group theory,” using the geometry of an object to glean algebraic information about the associated symmetries. (Indeed, it is called “outer space” because the ways of moving things around form the outer automorphism group, an algebraic object that was studied long before the introduction of outer space.)
This was a fantastic week to be in Marseille (or more properly, in Luminy where the conference center is). For those interested in the conference webpage itself, you can find it (containing a description of the week, a list of participants, and summaries of the talks) here. I could throw around the names of some of the top-notch mathematicians who were here, but everyone who cares probably already knows. I made and strengthened a number of good contacts, and got some good references and discussion for the projects I’m currently working on. Congratulations and thanks to the organizers, and to all the speakers, and to my colleagues with whom I met. I look forward to continuing in this field, at the intersection of so many interesting parts of mathematics and drawing on the skills of so many generous and talented mathematicians, for many years.
where to go part 4
I don’t know what to say. Things have gotten worse in Guinea. Conté has declared the country to be in a state of siege, and is entirely ignoring the fact that it is his appalling leadership, self-absorption, and reliance on sycophants that have provoked the violent unrest. Martial law has been in effect since Monday. The International Crisis Group has issued a strongly-worded assessment of the situation and list of recommendations for all parties involved, including ECOWAS (the Economic Community of West African States), the African Union, and the international community (the U.S. and France in particular). Anything more I could say would just be repeating the Friends of Guinea reporting, so I recommend you look there for a summary of news reports.
I never imagined this happening. But I guess the potential has always been there. Where do we go from here? What possible recourse do we have other than to pray the demonstrators, the looters, the government, and the military will shore up what’s left of decency and find a better solution than ceaseless turmoil?
I never imagined this happening. But I guess the potential has always been there. Where do we go from here? What possible recourse do we have other than to pray the demonstrators, the looters, the government, and the military will shore up what’s left of decency and find a better solution than ceaseless turmoil?
for all you literary types
Hannah has begun a blog of her own: Poesy and Poetics. The idea is to share poems she likes and finds interesting to analyze. Ask her about her philosophy on analyzing poetry sometime. It’s one of those things she’s happy to talk about just about any time, and you’ll get a taste of the vibrant way she approaches many academic subjects. She started on Wednesday, which was Valentine’s Day, which of course meant a discussion of one of Shakespeare’s love sonnets. It’ll definitely be worthwhile just to see what selection she makes as she goes along.
Thursday, February 08, 2007
where to go part 3
This isn’t about the strikes in Guinea (which look like they may begin again, incidentally). It’s about the strike happening here in Marseille, with a parade of protesters marching at this moment down the Boulevard d’Athènes and the Cours Julien, starting from the train station, and going presumably all the way to Castellane, if not further. I would have remained entirely oblivious to it had I not gone out to do some errands this morning. On my way back, I noticed the strange traffic flow and the red flags with yellow symbols flying and the early rumblings of a voice on a loudspeaker. So instead of taking a shortcut home, I walked up to the Place des Capucines, where the head of the parade was just about to get underway.
Protest rallies are great places to obtain flyers about all sorts of causes. I got four, and I don’t think I got everything available. The principle one is entitled 8 février : Toutes les raisons d’être dans l’action et la grève (All the reasons to be in action and on strike). The umbrella organization in this activity is the CGT (Confédération générale du travail) of the Bouches-du-Rhône. You can find “Toutes les raisons” as a Word document on their website. Today the call was sent out to all public employees to join in the strike and demonstrations. And, as you can see from the pictures below, many different groups are represented.
If you go to the main CGT page for all of France, you find that this is in fact a nation-wide campaign. The complaints are both that salaries are insufficient (the demand is that the minimum be raised to 1500€, presumably per month) and that jobs are being destroyed, not created, while the population (especially here in Marseille) is growing. The unions are addressing the European Commission, seeking increased security, increased salary, and increased availability of public services.
You might also notice what is marked on those red flags that caught my attention. The Jeunes Communistes took the occasion to make an appearance, which is where my second flyer came from. The header on one side declares “Avec les communistes : unir, lutter, vaincre!” (“With the communists: unite, fight, vanquish!”) I was particularly interested by their discussion, in a single sentence, of contemporary French politics: “By imposing, with incessant propaganda, the rivalry between Nicolas Sarkozy de Naguis-Bosca and Marie Ségolène Royale as the political issue, they leave us to believe that we will have no other solutions except to choose between a dangerous reactionary and a pale conservative. LIE!!!” And they present their candidate, Marie-George Buffet, along with their demands: the sharing of wealth, power, and information. Not a bad presentation, overall. Sufficiently and simultaneously indignant and informed.
The third flyer came from supporters of Roland Veuillet, a teacher and active union member who has been on a hunger strike for 47 days. From what I can gather, in 2003, during a proctors’ strike in Nimes, he “opposed” the school’s (apparently illegal) practice of placing older students in charge of watching the exams. (I haven’t found exactly by what means he opposed this.) Soon afterwards, he was sanctioned by the minister of education De Robien, and was relocated to Lyon. I’m taking all this information from the materials of Veuillet’s supporters, so I have no idea what the other side of the story is, but the hunger strike is real. Several students and other teachers have joined this strike in solidarity at one point or another.
The remaining flyer was less ambitious. Just half a page, printed on one side only, it declares, “Housing is not just the problem of the homeless!” Then it speaks of drawing on public funds to build “social housing” (“logements sociaux”) and improving rights of tenants. The language of this flyer catches my attention; they use the phrase “Exigeons” rather than “Nous exigeons”—that is, “Let us demand” rather than “We demand”, effectively supporting their claim that solving this problem shouldn’t be left to those we’d like to believe are the only ones it affects.
Strikes are painful. They wouldn’t really be effective if they weren’t. France is well-known for frequently having strikes of one form or another. Somehow, in the States, we’ve avoided most of the pain of these events in recent times. (I’ve heard some opinions on why this is the case, but I don’t think I should bring them up here.) I know I’ve been traveling at times when some part or another of an airline’s necessary workers were striking (I think it was the luggage handlers), and I hardly noticed any difference at all—the main thing was the flyers that appeared. But a well-managed strike can bring everything to a standstill. They’re a method of either asserting power or trying to grasp it. Such power may well be merited, and I suspect the causes are usually just. I doubt I’ll ever be in a situation where I’ll have to go on strike with a union. Before today, I hadn’t thought about it. But I believe if the time came, there are conditions under which I would join in approvingly, either for the sake of ameliorating the state of my fellow workers or in protest of an outrageous policy or action. I wish these times weren’t necessary. But that goes back to how the world doesn’t really change, injustice remains, and we have to keep fighting collectively and individually to stamp it out.
Protest rallies are great places to obtain flyers about all sorts of causes. I got four, and I don’t think I got everything available. The principle one is entitled 8 février : Toutes les raisons d’être dans l’action et la grève (All the reasons to be in action and on strike). The umbrella organization in this activity is the CGT (Confédération générale du travail) of the Bouches-du-Rhône. You can find “Toutes les raisons” as a Word document on their website. Today the call was sent out to all public employees to join in the strike and demonstrations. And, as you can see from the pictures below, many different groups are represented.
If you go to the main CGT page for all of France, you find that this is in fact a nation-wide campaign. The complaints are both that salaries are insufficient (the demand is that the minimum be raised to 1500€, presumably per month) and that jobs are being destroyed, not created, while the population (especially here in Marseille) is growing. The unions are addressing the European Commission, seeking increased security, increased salary, and increased availability of public services.
You might also notice what is marked on those red flags that caught my attention. The Jeunes Communistes took the occasion to make an appearance, which is where my second flyer came from. The header on one side declares “Avec les communistes : unir, lutter, vaincre!” (“With the communists: unite, fight, vanquish!”) I was particularly interested by their discussion, in a single sentence, of contemporary French politics: “By imposing, with incessant propaganda, the rivalry between Nicolas Sarkozy de Naguis-Bosca and Marie Ségolène Royale as the political issue, they leave us to believe that we will have no other solutions except to choose between a dangerous reactionary and a pale conservative. LIE!!!” And they present their candidate, Marie-George Buffet, along with their demands: the sharing of wealth, power, and information. Not a bad presentation, overall. Sufficiently and simultaneously indignant and informed.
The third flyer came from supporters of Roland Veuillet, a teacher and active union member who has been on a hunger strike for 47 days. From what I can gather, in 2003, during a proctors’ strike in Nimes, he “opposed” the school’s (apparently illegal) practice of placing older students in charge of watching the exams. (I haven’t found exactly by what means he opposed this.) Soon afterwards, he was sanctioned by the minister of education De Robien, and was relocated to Lyon. I’m taking all this information from the materials of Veuillet’s supporters, so I have no idea what the other side of the story is, but the hunger strike is real. Several students and other teachers have joined this strike in solidarity at one point or another.
The remaining flyer was less ambitious. Just half a page, printed on one side only, it declares, “Housing is not just the problem of the homeless!” Then it speaks of drawing on public funds to build “social housing” (“logements sociaux”) and improving rights of tenants. The language of this flyer catches my attention; they use the phrase “Exigeons” rather than “Nous exigeons”—that is, “Let us demand” rather than “We demand”, effectively supporting their claim that solving this problem shouldn’t be left to those we’d like to believe are the only ones it affects.
Strikes are painful. They wouldn’t really be effective if they weren’t. France is well-known for frequently having strikes of one form or another. Somehow, in the States, we’ve avoided most of the pain of these events in recent times. (I’ve heard some opinions on why this is the case, but I don’t think I should bring them up here.) I know I’ve been traveling at times when some part or another of an airline’s necessary workers were striking (I think it was the luggage handlers), and I hardly noticed any difference at all—the main thing was the flyers that appeared. But a well-managed strike can bring everything to a standstill. They’re a method of either asserting power or trying to grasp it. Such power may well be merited, and I suspect the causes are usually just. I doubt I’ll ever be in a situation where I’ll have to go on strike with a union. Before today, I hadn’t thought about it. But I believe if the time came, there are conditions under which I would join in approvingly, either for the sake of ameliorating the state of my fellow workers or in protest of an outrageous policy or action. I wish these times weren’t necessary. But that goes back to how the world doesn’t really change, injustice remains, and we have to keep fighting collectively and individually to stamp it out.
Tuesday, February 06, 2007
moving along
I gave my first seminar talk in several months last Friday. It was on work contained in a preprint which isn’t my own, but which is closely related to some of my work, and which I could enlighten relatively well for the seminar attendees. Both Dr. Hubbard and Pascal, who organizes the seminar, seemed quite pleased with the exposition.
I’ve been spending most of my time lately working, not going out much. I’ve started tutoring three daughters of an Egyptian family in math and English. This week, a number of Cornell folk are in town for a conference at the CIRM in Luminy, which is where Dr. Hubbard’s birthday celebration was held in summer 2005 (our first time to come here). Melanie (co-creator of Abstractionary) came early to visit over the weekend, which was nice. Unfortunately, I’ve managed to get sick (from all this excitement? not sure) and am trying to both heal myself and get more work done. Next week CIRM hosts a conference on outer space (not what you think) and Teichmüller theory, which will bring lots of interesting people to talk with.
I have ideas for a couple more long essays, hopefully to come along soon. Hope y’all are well.
I’ve been spending most of my time lately working, not going out much. I’ve started tutoring three daughters of an Egyptian family in math and English. This week, a number of Cornell folk are in town for a conference at the CIRM in Luminy, which is where Dr. Hubbard’s birthday celebration was held in summer 2005 (our first time to come here). Melanie (co-creator of Abstractionary) came early to visit over the weekend, which was nice. Unfortunately, I’ve managed to get sick (from all this excitement? not sure) and am trying to both heal myself and get more work done. Next week CIRM hosts a conference on outer space (not what you think) and Teichmüller theory, which will bring lots of interesting people to talk with.
I have ideas for a couple more long essays, hopefully to come along soon. Hope y’all are well.
where to go part 2
The strikes in Guinea were ended at the beginning of last week. The union leaders apparently felt the government had met sufficiently many of their demands. But the news stories since then tell that Conté has not named a new prime minister to start taking some responsibility for the nation, as he had agreed to do. Peace Corps Volunteers’ blogs tell of hanging out in Bamako, waiting to hear if they’re going to get to go back. I still doubt it. I briefly hoped when the strikes were over, but I’m back to my skepticism.
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