This course covers recent theoretical and algorithmic developments in combi-natorics. It begins with an overview of classical probabilistic methods such as first- and second-moment methods and the local lemma, and of some funda-mental notions and results in extremal combinatorics, such as set systems, graph partitions, and Turán-type problems. The courses then moves on to give an in-depth treatment of the following topics at the cutting-edge of research:the Moser-Tardos algorithm, and derandomization of probabilistic algo-rithms more generally; recent improvements to the Sunflower Lemma and their application to com-puter science and the study of random graphs; the method of Hypergraph Containers and its applications; Vapnik-Chervonenkis dimension and its applications to statistical learning and computational geometry.
Current Topics and Algorithms in Combinatorics, 7.5 credits
Spring Term 2022
24 March 2022
5 June 2022
Type of studies
The course requires a minimum of 90 ECTS in Mathematics or Computer Science, of which at least 60 ECTS must be in Mathematics including a course in Discrete Mathematics of at least 7.5 ECTS and a course in Statistics of at least 7.5 ECTS which includes elementary Probability Theory. Proficiency in English equivalent to Swedish upper secondary course English 5/A. When the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.
Application deadline was
15 October 2021.
The application period is closed.
Application and tuition fees
As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.