Sorting algorithms are some of the best-studied in the field: so imagine the surprise when a new, faster-than-anticipated sorting algorithm was introduced for Java in 2009. This lecture reports on a current study (with Aumüller, Dietzfelbinger, Krenn and Prodinger), in which dual-pivot Quicksort is analysed precisely for the first time, and presents an outlook on multi-pivot Quicksort (work-in-progress with Daniel Krenn).

When encrypting sensitive data (for example online), one-way functions are often used; these are functions that can be quickly calculated, but the reversal of which is extremely difficult for attackers to calculate. In order to increase security, larger parameter values must be chosen, but this must not increase the calculating time excessively. One approach to speed up the calculations involves digit expansions with negative digits.

When entering a long series of numbers such as an ISBN, EAN or IBAN, it’s easy to make a mistake. The numbers can be mixed up or perhaps left out altogether. For this reason, these series of numbers usually contain one or more “check digits”, which are able to identify these sorts of errors. Similar processes are also used when saving data on hard disks or USB sticks, in order to protect against technical defects. In this workshop, the mathematical procedures that are used for these types of check digits are presented, and these are then tried out in practice with the help of examples.

Abstract: Satalia (NP Complete) is a successful British technology company with a focus in the fields of mathematical optimisation and artificial intelligence. Satalia is currently financing a long-term research project with the Department of Mathematics at the Alpen-Adria-Universität Klagenfurt. Within the framework of this project, Philipp Hungerländer and his team are working on various projects, including with one of the world’s largest supermarket chains and one of the world’s biggest auditing companies. This involves the implementation of their mathematical research results for the improvement of a wide range of economic processes in the fields of logistics and personnel planning.

In various technical and medical applications, acoustic waves are used, for example in ultrasound images from inside our bodies. Acoustic noise can, however, also become very unpleasant. Inverse problems, which are practical problems in which the causes for desired or observed effects need to be calculated, appear in a variety of acoustic applications, from the optimal design of medical ultrasound devices to the reconstruction of noise sources from indirect microphone measurements. In this lecture, we cover a wide variety of topics, from applications from our current research to relevant brain teasers for school pupils.