At 8:11 the train to Uppsala left Stockholm Central Station. Everyone was waking up with the beautiful views of the woods of Sweden. They work very therapeutic. After a while we arrived in Uppsala and then we could start our first lecture.

The first lecture was held by Maciej Klimek, a professor at Uppsala University in the Financial Mathematics department. The lecture was an introduction to financial mathematics and was split into two parts. The first part was contextual and was more like a history lesson, the second part went a bit in depth. He first introduced the start of financial mathematics, namely in the early era of Mesopotamia. There were clay tables found with scratches indicating loans, contracts and debts, which were neglected since the archeologists did not understand mathematics. This went on for ages until the financial world with call options and stock as we know now. It is noticeable that in cases of financial collapse the politicians always blame to the scientists. The only way that changed between Mesopotamia and now is the culture in which the blaming happens.
Then he discussed some tools used in financial mathematics, including the controversial ones like short selling and value at risk. His conclusions were the following: if one wants to excessively control the financial system, it nearly always leads to disaster. In the right hands, financial mathematics are a beautiful tool that will lead to great human advancement, but in the wrong hands financial mathematics will destroy our society. The most important take-home message was that financial mathematicians do not always know economics and economists do not understand mathematics. Thus if you read an article with someones opinion on the economy, be very critical.

The professor Takis Konstantopoulos (link to his blog) gave our second lecture about discrete stochastic processes with a focus on 1- and 2-dimensional random walks and Brownian motions. Imagine a person that is extremely drunk and stays drunk forever. Every minute there is 50% chance to take a step forward and 50% chance to take a step backward. Will the person always get back to his starting point? The answer, after a few surprisingly insightful computations, turned out to be yes. In particular, if the drunk person walks on for forever, he will visit his starting point infinitely many times.
The next case was a drunk person in Manhattan. At every crossing, there is a 25% chance to move in any direction. If your husband leaves his home in Manhattan drunk, will he ever come back? The computations were not much different from the previous case, so the conclusion was that you not have to worry, your husband will come back. It can still take a very long time, but if he leaves your home infinitely many times, he will all the times come back. Imagine you want be drunk in space. We calculated that this would be incredibly stupid as it is highly likely you will never get back to your space station if you fly away in the wrong direction.
He concluded the lecture with Brownian motion. Place a pencil on a sheet of paper and randomly scratch in any direction you like in this way. The result is every continuous but you can not calculate the direction of your graph in any point. This is quite surprising, since you can feel there is a sort of direction the motion is going to. However, if you know the direction, the motion would not be random and this is impossible.

After the lunch break we joined the physicists and astrophysicists in their program. Alex will write about that soon.

In the afternoon and evening students from study association FYSKAM organized an activity with us. They brought soda, beer, burgers and two typical Swedish games and we met the whole afternoon and evening in the shining warm sun. One of the typical Swedish games was Kubbe, where you need to throw wooden sticks to the blocks of the other team while avoiding the Kings block. If you throw over the Kings block before throwing over the other blocks, you lose. If you first throw over the Kings block after throwing over the other blocks, you win. In such a meeting I’m always amazed by how similar Dutch and foreign students are. The saying “you can sleep when you are dead”, the item “toilet duck” and stealing certain artifacts from your host, to alert them that they need to be guarded, came to me as very familiar.

Until the departure time of the train (10 pm), we all had the time to explore the city of Uppsala. We discovered a nice overview and got something to drink at the old station of Uppsala that was renovated to a luxurious restaurant and cafe.

All good things come to an end, as well as to this day and this blog. After a train drive back to Stockholm, we posted this blog to let you enjoy our day further when we sleep.

The quotes of the day are made by Sebastiaan and Jelco:

Sebastiaan: “Upps, a la did it again!”

Takis Konstantopoulos: “If an extremely drunk person starts randomly walking, when will he come back?” Jelco: “When he is sober again.”

Signed by Mathijs Kolkhuis Tanke & Kevin Oost

We arrived at Lund, again facing the difficult logistics within Denmark and Sweden in general. But Danish and Swedish people speak fluent English and within a short time frame we had two JOJO cards which enabled us to go to the MAX IV Laboratory (yes, named in order after previously doing research in lab 1, 2 and 3). Fun fact about the bus ride was that the bus driver gave us a small tour around Lund. He talked about new buildings planned to be constructed soon and how these would fit in the area (“How” he said, “I don’t know!”). His other major joke made the quote of the day, visible below.

Leaving the bus with applause, we saw a large shiny building. The computer scientists and mathematicians started the visit in this brand new radiation lab, which isn’t even fully updated on Wikipedia and Google Maps yet, with a tour. This laboratory is so new that the official opening of their greatest particle accelerator is at the 21st of June. The tour went through the small ring, which is now in its testing phases. Not only do they need to provide reliable access to tens of thousands of devices, but also allow complex automation and ensure sustainability. Especially Computer Scientists were amazed by the enormous IT environment. The main purpose of MAX IV is to allow the scientists to do their experiments in a flexible and user friendly environment. Vincent Hardion described the architecture of the distributed environment and the tools used for data acquisition and data management. After that Galina Skripka talked about the program to derive accurate atomic reference data for astrophysical applications, including experiments and calculations.

Now, we’re not even halfway the 6 hour ride towards Stockholm. There we will be staying at hostel Lodge32, which is at walking distance to the Stockholm Center. Tonight everyone will explore Stockholm to their own liking. Everyone heard many stories about Stockholm, so we are excited to what this city has to offer. Everyone caught up with their sleep during this train ride, so we are fresh and rearing to explore.

Public transport bus driver while riding us to MAX IV: “At your left you can see the main buildings of Ericsson and Sony.” Then while making a turn around some empty land: “And to your left you can see — nothing.”

Signed by Kevin Oost and Mathijs Kolkhuis Tanke.

After lunch, the Computer Science group went off to visit Penneo, a company which started back in 2011 in a basement with 3 people. Now, it does consulting for over 400+ companies in Denmark. Penneo has developed an electronic signature solution that enables companies sign legally binding documents online in a quick and secure way using the so called nemID (can be compared to a DigiD in the Netherlands). Three cofounders of Penneo talked about how to start and develop an IT-company. They told us about all the mistakes they’ve made as a startup, and how they are now building product/systems/teams to enable them to scale across Europe. In the late afternoon Balder Onarheim gave us an introduction to neuroscience and his company mindsettr.com, which they aim to implement to stimulate the brain in a safe and simple-to-use manner.

The mathematicians had their own program in the afternoon. The first lecture was from Sho Tanimoto. The lecture was titled ‘rational points on algebraic varieties’. An variety is a space that looks like a line, surface or a higher dimensional equivalent object. One example is the sphere which locally looks like a surface, an other example is the circle that is locally a line. An algebraic variety are the zeros of some polynomial equations like x^2+y^2-z^2=0. Then there are three questions one can ask: are their rational solutions to such equations, how many rational solutions to such equations are there and how are the rational solutions distributed on the variety? Sho Tanimoto further explored those questions and in particular the third since that question coincides with his research area.

After a short break we had a talk from Dustin Clausen about the Hopf map. The Hopf map is in his own words ‘a very complicated way for the sphere to give the circle a hug’. He first started building spheres while making hilarious puns and comments along the way. One way to build a sphere is to cramp the edge of a surface together, like making a ball from a piece of paper. Then he showed how many really different ways there are to build a map from a sphere from one dimension to a sphere from the other dimension. In most cases all maps are essentially the same, but for dimension higher than 1 there are countable infinite amount of really different maps. The Hopf map is a map from the sphere to the circle and is really different than just bringing every point to the equator. This map is a very recent result of topology and was the first example that showed a fiber bundle existed.

The last lecture was from Jérémy Sok, a French postdoctoral researcher. Jérémy gave an introduction to mathematical physics. He started with the famous equation of Newton, namely force equals mass times acceleration. He then rewrote the equation in Lagragian mechanics, which gave a huge integral. After working out the integral, he showed that the complex computations were a generalization of the famous equation. Afterwards he gave many examples of mathematics applied in physics.

In the evening we enjoyed an unlimited pizza buffet at the study association Science RADET of Copenhagen together with the physics and astronomy group. Afterwards most went to the local student bar StudentenHuset in the centre of Copenhagen. A nice thing to notice is that the Copenhagens metro is fully automatic without any driver. This enables the metro to run the entire night, since a driver is not necessary anymore. See the featured image.

Quotes of the day:

After Nicolai, investor in Penneo, recieved his presents consisting of various Dutch sweets, he said: “You don’t have this candy for us?” while pretending to hold a joint.

Dustin was lecturing while Sho brought new markers for the whiteboard. Later Dustin said: “Was Sho here for the markers? So he did Sho’d up!”

Signed by Kevin Oost and Mathijs Kolkhuis Tanke

Inside the planetarium we went to a huge IMAX theater, where a beautiful 3D-show about the vast universe and global warming was viewed. Afterwards everyone was off to enjoy the nice sunny weather and the city of Copenhagen. Now we give an excerpt from the day of two groups.

Very close to the Planetarium is the Trivoli amusement park situated, where one group went off to. Fairy tale writer Hans Christian Andersen visited the park, as did Walt Disney and many other celebrities, who all fell in love with the gardens. After this lovely scenery, we traveled by metro to the famous Nyhavn, shown on the featured image. The area was packed with people enjoying their drinks. Nyhavn was originally a busy commercial port where ships from all over the world would dock. Then we walked further to visit the famous Little Mermaid, who concluded our day.

The other group chose to first walk aimlessly through the many streets of Copenhagens centrum. They decided to discover Copenhagen in a unique way, namely by boat. One person has a boat license valid in Copenhagen, one other has much experience on the water, so they found a rental and rented a boat. Their plan was to visit the Little Mermaid by boat, however the currents of the canal were too strong in that area. Instead they sailed through the canals of Copenhagen. Sailing into Nyhavn was not permitted, but they could not resist to sail a little in the port and place a nice rectangular De Leidsche Flesch sticker among many other on the bridge there.

We conclude this blog with best two quotes of the day, which are written in Dutch to preserve humor:

Alex tegen Mathijs over de portofoon: ‘Kun je aan Kevin vragen welke richting we lopen?’ Mathijs: ‘We lopen richting zuiden’. Alex: ‘Ow, ik dacht dat we “Oost” gingen’.

Vera over Paul en Mathijs: ‘Samen kunnen jullie ongeveer alles’. Paul: ‘Nee, we kunnen geen kinderen krijgen.’

Signed by Kevin Oost and Mathijs Kolkhuis Tanke