The weekend and Monday, Tuesday, Wednesday..

Well.. I didn't really feel that I have had time to post anything new on my blog during the last couple of days. I have been studying really hard.

My courses are really advanced, and all of a sudden we started using K-theory and Vector Bundles in Noncommutative Geometry. Taking three courses is a lot of work, but I think I'll manage...somehow. ;P Time to remind myself that I'm awesome. ;)

Friday evening, I needed a break from quivers, Lie groups, Gelfand transforms... So I went down to the common room and played my first game of Foosball. After an intense match I and my Italian friend stood victorious. =)

After that we started talking about getting the crew together and go to a pub or a club (assuming that Fredericton had one.. haha :P). So the "Math gang" headed downtown. Here are some pictures of some of us.

As you can see I am drinking a Gin and Tonic, for as I have said before, beer taste like piss.

After that we headed back, I taught them how to dance (Salsa, Swing...) in the common room, and then I went to sleep..

Next morning, some of us were going down to check out the "famous Saturday Market". It was supposedly a great place to go to, and they were supposed to have lots of good stuff.

As you might have guessed, this place was not my kind off place to be at... It was too crowded, small, sold junk, and even smelled bad. (Sorry Fredericton) :(

After that I headed back and studied some more.. Sunday was just really stressful, because there was a lot of things to finish for the Noncommutative Geometry lecture on Monday. So I sat down and proved Heisenberg's uncertainty principle (awesome proof by yours truly), or rather showed that there is no unital Banach Algebra that exist, such that the quotients cancel. =)

After that, I went out for an evening walk, cleared my mind and watched the stars. It was really nice to not think of things that are not Noncommutative (or at least not in an obvious way).

Monday, Tuesday and today have just been full of stuff to do, still I've managed to go for a walk every day. The only bad thing is that I am reminded as soon as I leave Campus, how polluted the air is.. :( You can really smell the cars, even in this small town. :/

A couple of my friends here and I were talking about renting a car and go down to Saint John. We haven't really decided if we are really going, but if we are, then maybe next weekend. I have also been looking into taking a two day trip from Toronto to Ottawa, so I get to see the capital, but haven't decided yet.. Figured I might be able to take two night buses, so I don't have to pay for a hostel two nights, then it could fit into my budget. But haven't decided yet..

Swimming

Today was yet another day here. It was basicly the same as other days, except from the fact that it was sunny. :) After class, I went with one of my friends to the swimming hall on campus, and swam for an hour. I got to use my special guest card from the AARMS. :)

Awesome! =) They've got several sports halls, which are always free for me with this card, so why not use it? My next project is to find someone to play badminton with..

After swimming and having supper, I got back to my room and continued with my studies..

I realized that I am kind of taking 3 courses, which is supposed to be an impossible amount of work as the director of the summer school said. But if I find NCAG too difficult, then I'll drop it. :P I might only get this chance once, so why not go for it?

Not much really...

Today was yet another day. It is basicly like most days are here; wake up, shower, breakfast, Riemannian Geometry, Noncommutative Geometry, lunch, power nap, read some, Noncommutative Algebraic Geometry, read some more, have supper, study and do homework, sleep etc... Because of this there isn't really that much to write about, so don't be surprised if I don't write that much while I'm here..

One interesting thing though, one of my Polish friends here and I were talking about going to swim, since there is a swimming hall on Campus, and we can go there for free through the university. Maybe tomorrow? They were open really strange hours..

Today in Noncommutative Geometry we introduced the Gelfand transform and showed that it has the same basic properties as the Fourier transform. This is nice, since I am quite familiar with the Fourier transform. :)

In NCAG (abbreviation for NonCommutative Algebraic Geometry from now on) we introduced quivers, which is really just Directed Graphs with a defined Algebra over it. For some reason, algebraists seem to like to take simple things, rename them, and then use them (I am very aware that there are purposes for this but still). Anyways, quivers will enable us to go from the Noncommutative Algebra to the Algebraic Geometry and vice versa, so that we will be able to use methods directly between them. The name quivers is quite ingenious though, because a quiver is the container that holds the arrows for an archer, and directed graphs basicly look like arrows, so a quiver becomes in the same sense the thing that holds the arrows.

I found out something interesting as well between classes, when I spoke briefly to our professor, Massoud Khalkhali. I asked him if we were going to cover the Non-Hausdorff spaces in the course, and his response was that we weren't. All that we will cover is the spaces that can fail to some extent to be Hausdorff (wikipedia it you are wondering what a Hausdorff space is). That is an interesting case, but I don't think that is where we will find the answers that explain the universe. I think that the Geometry and Algebras that will explain most of Physics and Mathematics are actually contained in the abstract spaces which are not Hausdorff at all. But as it seems, there isn't much progress in that field, because well it doesn't really make sense..

The first days.

Monday morning (yesterday) at 8.30 am we had our first lecture, in Riemannian Geometry. The first part of our course is devoted to developing some concepts from Differential Geometry (which is my major field) so it hasn't been so challenging. :)

The thing about his lectures is that he keeps saying these things, which made me think that Riemannian Geometry (or rather Differential Geometry) isn't his actual field. His approach towards proving properties of curves, by finding a frame, was purely analytical and, for me quite strange, because it got rid of almost all geometrical interpretations whatsoever. Curves are not really that interesting to study anyway, but then he went on and said something about that the real point of Differential Geometry was to use the properties of the embedding functions, which is not true at all. From what I know (I don't know anything really about anything, ask me in 10 years and I'll say the same thing) the point of Differential Geometry is just to make way for the Riemannian Geometry (which works for an arbitrary number of dimensions) unless you are in fact interested in studying curves and surfaces in 3 dimensional spaces. The biggest point of Differential Geometry, I would say, is to find that several properties are independent of the embedding in space (the opposite of what he said), like the Gaussian Curvature, and it is in fact these ideas that gave Riemann the idea of developing a Differential Geometry for arbitrary spaces which are purely based on these intrinsic properties that are invariant of the embeddings.

The second lecture I had that day was in Noncommutative Geometry. We started by showing the correspondences between Noncommutative Algebra and Noncommutative Geometry, and then stated that the Noncommutative Geometry is really what justifies the Noncommutative Algebras. The professor is an expert in his field, and seems very intelligent. What is even more impressive is that he doesn't use lecture notes, instead gives theorems and proofs of very abstract concepts just out of his head. That is basicly the level of understanding that I one day hope to achieve.. Even though the course seems very good, it is 2 or 3 years above my level of understanding. But I'm reading a book right now, on Algebras and Categories which might give me the knowledge I need. :)

Since I got the chance of coming here and I really want to learn, I am also sitting and listening to another course, called "Noncommutative Algebraic Geometry" by a professor from Oxford. That course uses a more algebraic approach toward Noncommutative Geometry, and even if it is a bit over my head, like the other course, I'm hoping that some things might stuck, even if the whole picture will elude me for some time in the future.

After that, me and some friends went to Walmart and I bought some Coke to drink while studying and some Shower Gel. After that and after we ate in the cafeteria, I locked myself in my room and started to read some Abstract Algebra.

This morning I woke up, showered, had breakfast and then went to class. It is amazing how much fried food they seem to eat here. Every meal here since Sunday morning has had something fried, eg. Potatoes, Chips, Fries, something that looks like the Swedish "Rösti" etc. Fortunately it is somewhat like a buffet, so there are plenty of different kinds of things to eat, so I have been able to avoid the fried things. Another thing that I noted is that there are always sweets to have as dessert with the meals. I have been avoiding it so far, because that amount of sugar is just not good for you. And most people drink soda with their meals (sometimes I drink the diet Pepsi), but that has to give them a lot of extra sugar.. Well what can you say? North Americans...

Apart from my classes today I have mostly isolated myself in my room to read. I hang out with the people the minutes before and after the lectures and in the dining hall, but apart from that I try to study as much as possible, because well... In a month, I'll most likely never see most of them again, while my knowledge is forever (or until I get senile or die ;) ).

Orientation

Today was a very dull day.. As yesterday, it was raining heavily. So after having had breakfast and met some of my course mates (which are very nice people) :) I decided to read some on Topology (mostly Algebraic Topology) and catch up on some sleep that I've missed on the flight, the bus trip and from the heat in Toronto.

Later in the evening, me and one of my new friends here from Boston, decided to go up the hill to go to WalMart to buy notebooks for the classes tomorrow. We walked and walked, and couldn't find it. :/ Instead we found a small Delhi called "Mail Mart" (kind of ironic?) and bought some notebooks. Then we headed back to the orientation around 7pm, where they were giving out notebooks... :/

I introduced myself to the professors, had some cake and soda, talked to my course mates, and then headed back. Now I'm going to sleep. Tomorrow the courses begin..

Today, from my own reading, I've learnt some things about what is called the Fundamental Polygon in Topology. It is constructed by taking a closed surface, cutting it vertically to its orientation lines, and then identifying the edges of the polygon to identify the surface. Some examples of simple surfaces that it can easily be done for, are the Sphere, the Torus (Donut-shaped surface) and the Möbius strip. If you want to know more about this, check the wikipedia site on the fundamental polygon.

Fredericton

Fredericton can be described by one sentence, "don't go there" (unless you are studying Noncommutative Geometry, which the university seems to offer some really good courses. :/

Above is one picture of what the buildings on campus (the university area) looks like. I live in a two person dorm room in one of them. But because there are so few people studying here, I have the room for myself. This is what it looks like.

After having "established a base" I decided to go down into town ("meals weren't provided by the AARMS (Atlantic Association for Research in the Mathematical Sciences) and look around and have dinner.

The town looks like the basic North American small town.

And what gives it a bit of a creepy feeling is that there are lots of churches everywhere. The rain adds a bit to the creepy feeling of the picture.

Anyway I went downtown. Downtown Fredericton is basicly only one street. In any case, I went down there, found a Korean restaurant and had supper. Then I went back and wrote this...

The advantage however is that if there are very few things to do, then there are very few things to interrupt my studies. :) Now I'm going to read some Algebraic Topology and then call it a day.

Niagara Falls

Had yet another awesome day in Canada. Today I went to Niagara falls on a bus tour. Unfortunately, the weather wasn't as nice as before..

It might be difficult to see on this picture but it was pouring down. Anyway, I got on the bus and we headed off towards the Niagara falls.

We arrived around 11.30 and started with going on a little boat tour into the falls called "Maid of the Mist". As we got on that everyone was already soaked from the rain, so the plastic rain robes didn't do so much for us. As can be seen, even I got one of these sexy see-through plastic bags to put over my clothes. ;)

The Niagara falls are very beautiful, and I really like the whole nature thing about Canada. I like it a lot. :) The falls, made me think about the idea I have been sketching on, the "Theorie Egregium" and how the equations for it should be somewhat similar in 3 dimensions to those of flowing water...

After walking around in 3 hrs in pouring rain around the area of the Niagara falls, we went on the bus again and stopped first to see the Niagara Whirlpool (which wasn't much to see really so I'm not going to bore you with some pics of it). Then we continued on to the small town of "Niagara-on-the-Lake". It was a beautiful little town (looks something like Alabama in the film "Sweet Home Alabama"), and we got to walk around there for 1 and a half hours.

A beautiful small town and as everywhere (or at least that I've been to) everyone in Canada is super friendly and nice. :) If I were ever to get married, this is definitely a place I would go to.

And here's a picture for Helen. A small, but still quite big boutique selling only Christmas decorations. It was really nice! :) I also went into the local chocolate store and bought a chocolate dipped Belgian Waffle. Tasty! :D

After Niagara-on-the-Lake we headed towards our final stop before going back to Toronto, a wine yard, where we had free wine tasting. I generally try to avoid wine because it often just tastes cheap, and makes my lips purple (from red wine). But now we got to try three different Niagara produced wines, a red wine (Dark Noir), a white wine (Riesling) and a real Canadian Ice wine (Riesling). The red wine wasn't that good, tasted a bit like the regular Merlot wines, and the white wine like a german Riesling wine (eg Wild Boar), but the Ice wine was really good.

Ice wine is generally more like a desert wine, invented in Germany (probably somewhere in the south) and is produced in a different way than regular wine. The trick is to let the grapes freeze for at least three days in a row before picking them. The water in them then separates from the sugar, and by then picking them in the middle of the night and pressing them at a low temperature, you can extract only the sweet juice from them and get rid of a lot of the water. They also have to make sure that the alcohol percentage in the wine doesn't get to high, as it would remove a lot of the sugar in it and thereby the sweetness. The wine was, very good, and if I had the money and knew I could bring it on the flight, I would have bought a bottle. (Ice wines are more expensive than regular wine, because you filter away so much water in the process, you need more grapes, and the amount of grapes needed for one bottle of ice wine is equal to the amount needed to make 30 bottles of regular wine.

Tomorrow morning I'm heading to Toronto Pearson International Airport to fly into Fredericton and on Monday, the studies begin.. Just hope I'm ready. ;)

First day in Canada

Well, I got on the bus last night to Toronto, and did my best to try to sleep. The problem was that every time I started to fall asleep the bus hit a bump in the road and I hit my head against the window (Thank you US for have so great roads ;) haha) But around 9 this morning we reached the Canadian border and without much effort I entered Canada.

It didn't take long before you started to notice the contrast between the two countries. The road in Canada was much better paved, and instead of boring little farms everywhere along the road, there were instead forests and wilderness. In other words, Canada is more like Sweden.

When we entered Toronto, I noticed how much cleaner it was than NYC, and that the air was much less polluted. Still Toronto has 2.5 million citizens and a lot of cars. I walked around trying to find my hostel, and noticed how beautiful Toronto is. There were flowers planted everywhere and parks, and there weren't beggars and homeless people walking around everywhere (Later I saw two). Here are some random pictures that I took when walking around.

When I finally found my hostel at Clarence Square, I took a shower and slept for a couple of hours. (It takes a lot of energy to be this awesome) :P After that I went out and decided to go to the CN tower.

The CN tower holds the record of being the tallest "single" building (Only surpassed by the towers in Malaysia, which are not a single building per se. I bought the ticket and started exploring. The first thing I did was to see a Ride Motion Film (called 4D-cinema in Sweden), about, believe it or not, how it would feel like to be a bit of timber in the year 2020! Only in Canada. It was awesome though. :D Then I saw a real 3D-film (not the usual depth picture 3D that we usually have) about surfing on Tahiti. It wasn't really that exciting, but they had some incredible effects! Last of all I went to the observation deck of the CN tower and took some really good photos of Toronto. They have glass floor in the tower as well, so you can see a couple of hundred meters down from your feet. Awesome!

I ended the day with some (disgusting) really cheap Canadian pizza. Can't believe if someone manages to eat a whole of these. :S This is how much I managed to eat. But now I've got food for...Two more days? :P

Walking down Manhattan

So far today, I walked down Manhattan, passing through several parks went into the big grocery store at Union Square and ended my trip in China town. The day is not over however, and soon another great adventure begins, my trip into Canada.

But in more detail, I woke up after 7hrs of sleep around 8 this morning. After writing the entry of yesterday's adventure I went out on yet another trip. This time I had my heart set on Canal Street and Chinatown. I started walking on Sixth Avenue (Avenue of America), down to Madison Avenue, and had Taco Bell food (as I promised Jess).

It was disgusting (sorry Jess). It had a dreadful taste, and now I feel disgusted about the fact that I ate it. :(

Anyways I continued walking and saw a great deal of buildings. New York truly is amazing in that way, even if it sometimes just looks weird. They have built so many buildings, so close together and each building has its own architectual style. It is really amazing.

When I got to Union Square I needed something to drink (it was really hot today as well) so I went into the store at Union Square (the store to the right, the left one was for you Marika; 3 floors of shoes :P haha). So I bought a gallon of milk and some water.

Then I continued on walking, and ran into a friendly little Greenpeace activist around Washington Square. We talked for a bit, and when I explained that I was from Sweden, things got a lot more interesting. She said that she knew that the US was a bit behind on the environmental issues, but apparently not how much. When I started telling her about Stockholm, our environmental policies, gas prices and all the research on Green Energy our government is financing, she went quiet. I even showed her some pictures I had on my cell phone of what the inner part of Stockholm looks like, and then I think she realized how far behind they are here on those issues.

Washington Square Park is really beautiful. I have to come back here again. You could just sit and relax, as the time flew by. I heard a guy play and sing the song Wonderwall, which is one of my favorites, which was a big plus to have in the background. :)

Then I continued south, and came to Soho, and then Canal Street and Chinatown. That was a more interesting story. After having walked for 5 hrs in strong sunlight, I felt really tired and almost a bit dizzy, and drinking more milk or water didn't seem to help. So I wanted to go home, but the machine at the train station wouldn't take a 20 dollar bill to buy an 8 dollar ticket, so I needed change. Therefore, I walked back up on Canal Street and looked for something small and cheap to buy. Then I saw a green dragon (plastic), that they wanted 4 dollars for. So I pointed at it and said to the man "one fifty". He looked at me, a little bit shocked and said, we don't haggle in here, and this is worth at least 3 dollars. So I said "one sixty" dollar, and then he caught on, and we finally agreed on 2.50 $. :) After that I was walking outside, and just around the corner a little Chinese lady was walking and walked right into me. I said, sorry didn't see you but she muttered something at me and looked pissed. I didn't have the energy for this so I said "pokgai" which is Cantonese and means something like "Fuck off"(thank you Mabel for teaching me that). She looked really shocked that me the White Scandinavian Giant could insult her in Cantonese. Haha. I just turned and walked away. The rest of the Cantonese is basicly "Lay Ho Lang" (you are very beautiful) so I'm glad that conversation didn't continue. :) And now I'm here writing, preparing to go to Canada. :) Awesome! :D

The journey begins

It was now time to leave good ol' Sweden and set sail for new horizons. After my grandfather dropped me off at the airport, I was on my own. Checking in and getting through security was not as much effort as some people told me, and soon enough I was on the plane.

After an 8.5 hrs flight (which wasn't so bad, and call me weird but the food was really good) I was finally there, in the United States of America. The first difficulty was figuring out a way to get from Newark Airport and into New York City. This was actually kind of tricky, because it didn't say anywhere where the buses went, and it was really hot outside. 90 degrees Fahrenheit (32 degrees Celsius, I think) and the air was really humid. But after asking around I finally found a bus that went into NYC.

The bus ride was very interesting, especially since I could recognize a lot of the areas from the Video game "Grand Theft Auto IV" (thanks Leffe. ;) I posted some pictures of some areas I remembered.

I jumped off the airport bus at an arbitrary stop (it didn't say where we were, and I had already been stupid enough so I didn't dare to ask. But somehow Lady Fortuna smiled at me, and the stop I chose was right next to the Grand Central Station. It really was a grand sight to behold, and from there I could catch the metro to Jerrod's place (where I was staying the first day). I didn't have that much difficulty getting there, and Jerrod's flat mate let me in.

After leaving my stuff there, I could finally go out exploring and get lost...

The plan was to either take the ferry to Staten Island or go to the Empire State Building. It was too late to take the ferry so I figured I should just do Empire State, eat something and go back, that's not exactly how it turned out. When you're walking around in NYC, it is much bigger than it may appear on a map. Because of all the car, it also takes a lot longer to go somewhere. And I was basicly just looking around, taking some pictures of things and it wasn't long until I lost track of where I was heading. So I walked, and walked...

After a while I got tired of just randomly walking around and decided to look at a map. I think it said that I was in the wrong part of town, so I decided to skip the Empire State Building for now. But two streets down I found someone who was trying to sell tickets to the Empire State, and as it turned out I had read my position wrong and walked right to it. :D

In Sleepless in Seattle they meet on top of the tower in Seattle, this is actually based on a story by Jeff Arch, that was originally set in New York, and the tower was originally the Empire State Building. They met there, because it's the closest place to heaven (which is incredibly beautiful), and after being there, I can say that (in NYC at least, it is the place closest to heaven). The view is amazing, and it is almost like an oasis in the otherwise stressful "City that never sleeps".

I was up there, on the 86th floor from 6 until 9 pm, and watched how NYC, went from being the classical picture of it, to becoming the city of light.

This turned into this..

New York is really beautiful, and I think that everyone has to have been here at least once. It is very different from Europe, and you can barely understand how much, until you've actually been there.

Anyways, after being up there, my friend Jessica looked up where there's a Taco Bell on Manhattan, and I walked there, but when I got there it was already closed. Sorry Jess. All restaurants were closed, and while walking around I got lost. All I knew was that at some point I was in Little Korea, and at a street with three police cars. Then I turned around and walked the other way, because that's not the neighbourhood I want to be in. :S

When I finally found the metro, I went the wrong direction, and it took me two hours to get back to the place where I was staying. When I got there, I took a quick shower, and then I was so exhausted that I just crashed on the bed. Haha.. Not bad for a first day, eh? ;)