Lectures and Workshops

From Bezier curves to animated movies - Karla Ferjančič

In the second half of the 20th century, P. E. Bézier (at Renault) and P. de Casteljau (at Citroen) independently developed curves that enabled the precise definition of the shape of the car body. These curves were called Bézier curves, and with the development of computers they became incredibly useful and are now indispensable in the automotive, aviation and shipping industries, for controlling robots, modeling, creating animations and many other fields. In the course of the lecture, we will first learn about the basic principles of animation and how we can move virtual objects in computer graphics with the help of various curves. Next, we will explore Bézier curves and some of their interesting properties. As an example of use, we will try the basics of 3D modeling and animation with the free Blender tool.

 

The consensus problem - Matjaž Krnc

Frequently we are in situation where, together with some group, we need to find a consensus. "Which movie for the movie-night?" or "Where to go for spring break?" are just two examples which illustrate that without a centralized authority finding a consensus may be a challenge. Nonetheless, most changes in politics, the economy etc. are conditioned on reaching a consensus. In addition, consensus represents a cornerstone of decentralized technologies such as Blockchain.
Together with participants, we will experience the algorithmic challenge of finding a consensus. We will walk through the historical development of the problem, mention several interesting applications, and give an overview of the intuition for a couple of fundamental mathematical ideas that play a role in modern consensus algorithms. For these ideas, we will show our computational experiments on large networks. A small emphasis will be made on the role that consensus plays in Blockchain technology.

 

Human brain and mathematics - Rok Požar

When understanding the interactions in our brain, it is necessary to know how coordinated the individual parts of the brain are - the more similar the pattern of activity they show, the more functionally connected they are. Although different parts of the brain are specialized for a particular function, the entire system is involved in the performance of most cognitive tasks; like having a bunch of experts who are good at certain things, but in order to do something useful, they have to cooperate with each other. That is why we are interested in how individual parts of the brain are organized with each other. Graph theory helps us in this, which allows us to consider the brain as a network. This consists of points representing the basic building blocks of the system and links representing the relationships between the building blocks. In a brain network, points represent individual parts of the brain, and connections describe how strongly two points are functionally connected. In the lecture, we will learn about the basic concepts of graph theory for the analysis of brain networks and illustrate their applicability using examples of identification of neurological disorders.

 

 

Shortest distance on surfaces - Jasna Prezelj

The problem of finding the shortest distance on a given surface has been around for a very long time. We all know that on a plane, the shortest distance between two points is given by a straight line connecting them. But if we try to find the shortest distance on some uneven surface, it is no longer so easy - for example, if we are looking for the shortest route between two places in Slovenia (and we assume that we can cross all the rivers and climb all the mountains anywhere). We will try to find the shortest paths on the surfaces of Platonic solids and on some other surfaces that can be described or modeled simply enough.

 

 

 

 

Rubik's cube: from group theory, through algorithms to speed solving - Branko Kavšek

We all know the Rubik's Cube, right? It is said to be the best selling toy in the world. Ever since it was invented by the Hungarian inventor, sculptor and professor of architecture Ernő Rubik in 1974, a total of over 300 million cubes have been sold worldwide (including its derivatives). The Rubik's cube reached its peak of popularity in the 1980s, when it became the subject of study by mathematicians, computer scientists, and all lovers of this puzzle in general. At the workshop, we will learn what the Rubik's cube is, how it is built, what a permutation of a Rubik's cube is, and how permutations can be described using the mathematical theory of groups. We will touch on the algorithms on the Rubik's cube, find out what "God's number", "God's algorithm" and "sexy move" are, and briefly outline the basic process of solving the Rubik's cube. At the end, we will venture into the waters of fast-solving the Rubik's cube or speedcubing and get to know the so-called "speedcubes". We will see that the basic procedure is not sufficient for a speedy solution, and thus we will get to know Friedrich's (or CFOP) method. Of course, just knowing the methods and algorithms for solving the Rubik's cube is not enough for speedcubing either. So, we will touch on all the other "little tricks" that can ultimately allow us to solve the Rubik's cube in less than a minute, 30 seconds, maybe even less than 10 seconds.