General Information
| Student: | Radim Předstíraný |
|---|---|
| School: | Computer Science Institute and the Faculty of Applied Mathematics of Charles University in Prague |
| Advisers: | Periklis Papakonstantinou, Bhargav Peruvemba Narayanan and some others unrelated to REU |
| Project: | Breaking the Limits of Standard Theories |
About Me and the Hyper-Bridge Project
I have been in love with mathematical forms and problem solving since I can remember. Currently I am interested in trying to develop whole new area of tools building on new theoretical results bridging topological theories, probability spaces and discrete algebras through exciting new ides of category theoretical flavours.
We are about to receive a very prestigious and generous grant to allow us to connect a dozen best people around the world to help in making this happen. Our aim is to give new insights into cryptography, theory of communication, quantum computing and integer programming, all in one package. It is not our goal to get hard results in these fields, but to create a net of theoretical bridges in between these theories and many others that will allow countless results from any of these fields to be transferred to all the others.
the Czech Group
My stay here is made possible due to other wonderful people being here, and here they are:
Pavel Koblich Dvořák, Andrej Dedík, Aneta Šťastná, Jakub Pekárek, Jan Petr, Jan Soukup, Lukáš Ondráček, Mikhail Beliayeu, Petr Chmel, Petra Pelikánová,
Progress
Due to a series of serious accidents, the work has not been progressing as we'd like to. Most notably there was an injury which prevented me from entering the US on schedule and because of my unsuccessful entry into the US way back, the authorities gave me a rough time going through all the hoops before I was issued new documents to change my travel plans. A real pain in the research department.
In the time I was waiting for everything to clear up, I have spent the first week visiting a few researchers in Bordeaux and Strasbourg. Though our time was limited, we still managed to make some insight about slightly extending the reach of our Hyper-Bridge Theorem. Hopefully next week I will be able to catch up on the schedule now that I can finally get into the US and get the US people and the Czech group involved in person.
Week 1
I have now successfully arrived at Rutgers. The first few days have been mainly filled with necessary bureaucracy, but now I can finally start with my work on adding other important mathematical areas to the Hyper-Bridge Theory. First, I talked with Mikhail, Honza and Petr on Friday as they were the only complete team.
Random walks on graphs haven't been connected to the Hyper-Bridge Theory just yet, but I was determined to work on that. However, when I tried to go to New Brunswick to discover my surroundings, I got lost in thought and circled in the bus for two hours. Then, I got kicked out of the bus and had to call the Knight Mover. The wait wasn't that short either, but during all the time, I managed to find a connection between Markov chains and the bus system, as it seemed to behave quite randomly! More research on that will be needed, but I decided to leave that to Mikhail, Honza and Petr.
Week 2
It turns out that the guys managed to process everything we talked about and create an elegant construction solving most of the issues with random walks becoming part of the hyperbridge. That's the good news. The bad, bad, news is that we have discovered part of our results already being published. It is bad news because our team did not publish anything just yet. We have got hit by someone's plagiarism right when it hurts the most, mere weeks before publishing our main results. We have alerted some of the key journal comitees to try to contain the situation. Unfortunately the bastard(s) were publishing in a totally low-level journal where it is fairly impossible to contain anything. It is really painful to see such beautiful results disgraced by a predator journal. We will look into the already published piece to compare it with our work to see where and when it was stolen. I will find the bastard(s) who did this and make sure they pay for it.
Week 3
Though the hunt for the mole did not conclude last week, this week at least seems promising. I talked with Andrej and Honza. They have really managed to do some impressive work adapting the Hyperbridge methodology to somewhat connect other areas of Ramsey theory via game interpretations. Admitedly, it is a bit weaker connection than one might want (only giving the weaker standard results by projecting infinite group theory), but still it was most pleasing. The whole piece was inspired by our trip to Philadelphia. The game is similar to the problem we have encountered in the Eastern State Penitentiary: there are some cells, and every day, a group of three prisoners would would be tasked with cleaning the prison. However, only those triples, from which any two haven't worked together yet would be selected, as otherwise they could supposedly conspire against the guards.
The guys and me also went to visit Nokia Bell labs. I was late, as usual, and had to catch up with the rest. So as they were at talks, I took the elevator, and sudenly darkness. I did what most rational death-unwelcoming people would do and tried to save myself. To make the story short, it took a few technicians to get me out once they managed to get the the cabin into the 6th floor, where the engineering access is (the elevator does not normally go there, apparently). They said that it had something to do with the elevators having been used over capacity and something broke in a regulator earlier that day. That in itself is fine, but the safety features just shut everything down with me inside. Thank you, safety features.
As I was trying to find my way to the stairs, a few loudly clicking doors later I found myself cut of from the technicians, as well as the locked stairwell. I must have tried every door, like the stupidest version of DFS search, until I came across an unlocked office. There was some really impresively looking hardware behind a glass wall. My guess? Quantum annealing, or something even better (judging by the ridiculously complicated cooling and laser systems). The central part looked pretty much as a tesseract. I could not see it from too many angles, but as it is, I have no trouble believing it is a real tesseract in there.
Why didn't I get to see it from more angles you may ask? There was something else in the office apparently, a face-recognition security system. A sharp looking guard appeared in the door a mere moment after my arrival. Was he glad to see me? Very much the opposite. So my plans for the evening were unfortunately set for me. At least, while waiting in handcuffs (why these things always happen to me? Seriously?), I had a time to reduce the problem with Ramsey games up to a modest problem with $\R(6,6)$, which is now the task for Andrej and Honza to solve. Not a very productive way to start the week, but at least something new came out of it.
On Tuesday, I was discussing our work with Jakub, Lukáš and Koblich. As Koblich had a prior commitment in the Czech Republic, I decided to take his place for the rest of the week to let a bit of steam off. They have been trying to crack open a rather tantalizing problem surrounding interchangibility of space and time. Naturally, computation theory was one of the first connected to the Hyperbridge due to its strong relevance to logical expressability. However, guys have presented me with a rather sneaky usage of some of the existing theory to strenghten lots of existing connections, if what they are trying to do works. On the other hand, the Hyper-Bridge seems be helpful in achieving their results, so it would seem we might be close to a first major previously unknown breakthrough arising purely from the Hyper-Bridge.
Our effort culminated on Thursday night, when I took part in a public observation at the Serin Observatory. Many of the celestial bodies were truly a sight to behold. Apart from the guys and me, we were also joined by a colleague of mine from Princeton IAS. While watching the stars, we discussed various stuff surrounding our research, and he pointed out that the computation theory, if viewed as an information problem, is already known to translate to quantum physics problems. Although the spaces and times in question are of course not the same concepts, the information is a common ground. I have never been more excited into a complexity type research. If we can actually establish a tangible Hyper-Bridge connection, the possibilities are practically endless. It is very questionable whether a direct Hyper-Bridge connection between physics and informatics would be useful on either end, but just the very concept leaves me almost speechless. I have checked, and there are quite a few physicists who'd be willing to work on this idea once I am done here, so there is a lot of excitement.
Week 4
This week, I decided to work with Petra and Anet on their problems regarding the existence of rainbow cycles in graphs. The connections to the Hyper-Bridge theory are surprisingly weak, especially as the basic idea seems to form one of the core ideas Hyper-Bridge was build on.
The work on connecting the cycles was going rather slowly for the whole week, as the current machinery wasn't developed enough to hide all the technical details. However, this changed on Sunday, as I visited the Pride Parade in New York, NY. All the rainbows of the paraders formed a mesmerizing dynamic structure, which was the last piece of the puzzle we were trying to solve. Staticity was not enough! The system had to have some change implemented. Then, everything fell into place and the connection was finally finished.
Week 5:
For the week, I changed my place of stay from Rutgers to MIT in Cambridge, MA. The main reason for the change was the invitation of one of my colleagues I knew from my studies. Although most of the time we worked on other, simple connections such as symbolic computations on non-Abelian asymmetric non-trivial nilpotent groups. However, this was determined to be impractical, so we added the condition for the group to be a semidirect product of two other groups with the above properties acting faithfully.
Ẃe still had enough time to honor the same MIT tradition, that Richard Feynman liked to take part in - hacking. The hack itself was a simple one, but the result was eye-opening. During the hack, I managed to get into the MIT TOY LAB in the MIT tunnels. Of course, one would guess that there are just toys for children, but the truth was much more surprising.
Admittedly, I got lost in the lab, so I searched along the lab to find an exit. Instead, I found a randomly placed lever, which opened a hidden door. Obviously, I entered the door. What else could I do? Just leave it be? That's mindset which is really different from mine.
Luckily, I tried to sneak, so the people inside the room did not hear me. A single look inside the room was enough. What I saw was definitely a convention of the Illuminatí. I did not hear much, as they spoke quietly, but the few words I understood were a strong enough signal for me to walk away as fast as I could without alerting them to my presence. Apparently, the Loch Ness monster exists, but had to be relocated from the Loch Ness to a much safer location in Amsterdam, as the sightings there could be just dismissed as illusions of pot users. These guys really knew what they were doing.
Anyway, they caught me and almost sent me to Idaho, but after I explained why did I crash their meeting and mentioned that I am from the Czech Republic, they decided that it would be easier for them to let me return, as noone would believe a conspiracy theorist from the Czech Republic (that is, if you believe in the Czech Republic). From then on, they were great company and I learned a lot from them. Also, thanks to brother Lazaros (what a coincidence!), I connected trigonometry to the Hyper-Bridge theory.
References
Haha, no, seriously, no one has ever done something like this before!