The topic of my Ph.D. lies in the domain of Computational Geometry. You can have a look if you want, but I warn you, it's quite technical. I was drawn to this topic mainly because of its strong practical component -- it was planned from the beginning that the resulting code would be a part of CGAL, and this was extremely exciting for me. The experience that I gained from this process is unique, having the chance to work with so many bright people is quite enlightening.

Aside from that, I learned French, I collaborated with people from different backgrounds on something completely new for me, and I failed multiple times. I want to believe that I have learned through this experience, and hopefully my work will help someone else do something even nicer. One can only hope, right?

I actually left my job at 01S to go back to Greece and continue my studies. During the entry interview, one of the examiners thought I was joking, they couldn't believe I actually did that. But I did, and I would do it again.

The reason for me returning to Greece for my Master's studies is that I wanted to work with Prof. Karavelas, with whom I also worked during my Bachelor's thesis. I was inspired by him and wanted to continue in the same line of work, which ultimately led to my Ph.D. so I would definitely do it all over.

For my Master's thesis, I worked on something that I find very interesting -- cubic splines on the sphere! The splines that we worked with include a "tension" parameter and by varying this parameter, the spline becomes more or less smooth. The goal is to find the optimal parameters such that the shape defined by control points is preserved by the spline. There's a whole discussion on this, the manuscript is here. If you're up to it, you can also play around with the code.

Right, that was a long one. The thing is, I interrupted my studies from 2007 to 2009, that's when I switched countries and was working at Erbamea. There was a family emergency that I needed to take care of, so I needed that time off. Looks bad on résumés, but family comes first.

When I started my studies, I was feeling quite disappointed because I always wanted to be a programmer. I felt like I would miss out on so many things, studying Applied Math instead. Well, it turns out that I was bitterly mistaken -- there's actually a lot of coding, and it's actually not just mindless coding, there is a lot of thought behind it. I feel like this has given me a unique perspective not only on problems and solutions, but on life itself. It might also be the reason why I'm overthinking everything, but that's a discussion for my therapist. Note taken.

It was not obligatory at my University to submit a thesis at the Bachelor level, but I wanted to do it anyway, it sounded like a fun final project. It was one of the best decisions I've ever made. I had the chance to work with Prof. Karavelas on a topic that was ultimately related to my Ph.D. Funny how life does that, right? Anyway, the thesis is here, but I must say that I myself cringe when I read it now, it feels so badly written... so please excuse undergraduate me.

STOP. Please stop for a second, and consider this -- why would I write my own name with a lowercase letter? Right, it's IORDAN, or iordan if you prefer. Sorry for the confusion, I went with the writing in my passport (although I do think that the Yordan version looks a bit weird so I'm quite happy with Iordan).

I get that a lot. The answer is yes and no.

I was born in Bulgaria, my parents also, I have a Bulgarian nationality, for all intents and purposes I am a Bulgarian national. However, I belong to a tribe called Boyash. We have many names -- Ludari, Rudari, Linguri...

We are a nomadic tribe that would survive either by performing (think like street performers), or by making and selling utensils from wood and other natural sources (spoons, brooms, these large wooden bath tubs even). I myself am an expert broom-maker and broom-salesperson.

We have our own language derived from Latin (perhaps Romanian?) and mixed with some elements from Bulgarian. I guess because we live in Bulgaria. Our language doesn't have a written form, but we do speak it actively within my family. What I find fascinating is that I've found Linguri people in Greece, in Italy, and in France, and I can kind of understand what they say. Mind-blowing, really.

Another one I get quite often.

Let's count, shall we?

English, Greek, Italian, French, Bulgarian. That's 5. I also speak my own language (see previous item), which is not official, so I don't count that one. As for Japanese, I can only communicate basic stuff, so that one doesn't really count either. Therefore, 5.

I really need to work on my Japanese.

We're talking about mathematical and/or programming problems, of course. These are easy to solve, the other ones are more complicated.

So if you're looking for a way to spend your free time, you can head over to Project Euler and have a look at the very large set of problems they have. Some of them are quite frustrating, but they will keep you busy, for sure. Have fun!

It's hard to imagine how Hyperbolic Space works. It's mind-bending, really. Fortunately, there are some very smart people like Vi Hart, Andrea Hawksley, Elisabetta Matsumoto, and Henry Segerman who have done something very cool for us common folks.

These people have created a Virtual Reality model of 3D hyperbolic space, and you can try it our in your browser right now. Try it out if you click here, and you can see the paper here. Once you open the window, you can use the W,A,S,D keys on your keyboard, or the arrows to navigate; use E,Q to rotate. It's like a game!

If you're up to it, you can also try the product of a 2D hyperbolic space and a 1D Euclidean space. It can cause vertigo. Yes, I know this is not how vertigo works, but trust me, in VR it can actually cause vertigo. Here is the paper, if you want to see how it works.

I did. Since I worked with these wonderful curves during my Master's, I wanted to see how they would work in the hyperbolic plane. So I made a simple widget on GeoGebra when I was playing around in my free time.

You can play around with the widget directly in your browser on this link. The implementation uses De Casteljau's algorithm, but it's implemented using circular arcs instead of linear segments (since, you know, in the Poincaré disk model geodesics are arcs of circles).

At some point I came upon this super cool interactive animation based on Game Theory (one of the fanciest things of the past few years, for some reason) that shows how trust evolves. If you've got a few minutes to play around, go for it!

John Horton Conway was an English mathematician who had the inspiration for this simple, but extremely powerful idea. He modeled the way a system of cells would behave with four simple rules. Wikipedia can tell you more about this.

I thought it would be a nice way to spend a weekend afternoon, so I made a tiny implementation in JavaScript. Since I was working with periodic things at the time, I made it so that the left-right and top-bottom boundaries are "glued" together (at least in the code). That makes it into a flat torus! You can see the page here. If you refresh the page, you'll get a new board! ;)

MIT's Moral Machine is an incredible project that will put you in crisis mode within two clicks. The idea is that you get to choose who lives and who does.

You see, everyone (well, at least some people, I guess) is thinking about the future when we will have self-driving cars. The thing is, no one thinks about what would happen if we actually got them. These cars will not exist in a vacuum, so it is highly probable that situations will arise in which a human life will be lost, no matter what the car chooses. The question then becomes, who should die, and who should live?

This is a version of the trolley problem, and it becomes highly relevant in the context of self-driving cars. This is what the Moral Machine does -- it makes you decide the fate of people and animals in such situations. Very thought-provoking, might cause some soul-searching.