# Invited speakers

## Invited speakers

TU, Dresden |
## Ramsey Classes: Examples and ConstructionsThis work is concerned with classes of relational structures that are closed under taking substructures and isomorphism, that have the joint embedding property, and that furthermore have the We give a survey of the various fundamental Ramsey classes and their (often tricky) combinatorial proofs, and about various methods to derive new Ramsey classes from known Ramsey classes. Finally, we state open problems related to a potential classification of Ramsey classes. |

University of Oxford |
## Recent developments in graph Ramsey theoryGiven a graph H. The existence of these numbers has been known since 1930 but their quantitative behaviour is still not well understood. Even so, there has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics. In this survey, we will describe some of this progress. |

Royal Holloway, University of London |
## Controllability and matchings in random bipartite graphsMotivated by an application in controllability we consider maximum matchings in random bipartite graphs |

Hebrew University of Jerusalem |
## Some old and new problems in combinatorial geometry I: Around Borsuk's problemBorsuk asked in 1933 if every set of diameter 1 in d+1 sets of smaller diameter. In 1993, a negative solution, based on a theorem by Frankl and Wilson, was given by Kahn and Kalai. In this work I will present questions related to Borsuk's problem. |

Adam Mickiewicz University, Poznan |

University College Dublin |
## Curves over finite fields and linear recurring sequencesWe investigate what happens when we apply the theory of linear recurring sequences to certain sequences that arise from curves over finite fields. The sequences we will study are #C(F is the number of _{qn})F-rational points on a curve _{qn}C defined over F._{q} |

McGill University, Montreal |
## New tools and results in graph minor structure theoryGraph minor theory of Robertson and Seymour is a far reaching generalization of the classical Kuratowski-Wagner theorem, which characterizes planar graphs in terms of forbidden minors. We survey new structural tools and results in the theory, concentrating on the structure of large |

University of St Andrews, Scotland |
## Well quasi-order in combinatorics: embeddings and homomorphismsThe notion of well quasi-order (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful discriminator between 'tame' and 'wild' such classes. In this work we survey such situations within combinatorics, and attempt to identify promising directions for further research. We argue that these are intimately linked with a more systematic and detailed study of homomorphisms in combinatorics. |

Nanyang Technological University |
## Optimal rate algebraic list decoding of folded algebraic geometry codesWe give a construction of folded algebraic geometry codes which are list decodable from a fraction 1-R-ε of adversarial errors, where R is the rate of the code, for any desired positive constant ε. By using explicit towers, we obtain folded algebraic geometry code with the worst-case list size output O(1/ε), matching the existential bound for random codes up to constant factors. Further, the alphabet size of the codes is a constant depending only on ε – it can be made exp(O(1/ε By using class field towers, we obtain folded algebraic geometry code with the worst-case list size output O(poly(N)). The alphabet size of the codes is a constant depending only on ε. Our code construction is deterministic. Once the code is efficiently encoded, decoding algorithms are efficiently as well. |