On groups with Perfect Order Subsets |

| | Kevin Ford (Urbana), Sergei Konyagin (Moscow), Florian Luca (Mexico) |

| 1. | Introduction |

| 2. | Number theory tools |

| 3. | Proof of Theorem 1 |

| 4. | Proof of Theorem 2 |

Disjoint edges in separated hypergraphs |

| | P'eter Frankl (Budapest) |

| 1. | Introduction |

| 2. | The case *r=k* |

| 3. | The general case |

| 4. | The proof of main result |

Counterexamples to Borsuk's conjecture on spheres of small radii |

| | Andrey Kupavskii and Andrey Raigorodskii (Moscow) |

| 1. | Introduction |

| 2. | Formulation of the problem and statements of the results |

| 3. | Proofs of Theorems 1 and 2 |

| | 3.1. | Construction |

| | 3.2. | Transforming *Omega'* into an *Omega C S*_{r}^{d-1} |

| | 3.3. | Lower bound for * f(Omega ) * |

| | 3.4. | Proof of Lemma 1 |

| 4. | Proof of Theorem 3 |

| 5. | Proof of Theorem 4 |

| 6. | Improving Construction from Subsection 3.1 is hard |

| 7. | Improving Construction from Subsection 3.1 is still possible |

Uni-dimensional models of coalition formation: non-existence of stable partitions |

| | Alexei Savvateev (Moscow, Irkutsk) |

| 1. | Introduction |

| 2. | A universal counterexample: motivation and description |

| 3. | Proof of the main result |

| 4. | Notes on relevant research and bibliography |

Choosability in simple hypergraphs |

| | Dmitry Shabanov (Moscow) |

| 1. | Introduction and background of the problem |

| 2. | Proof of Theorem 6 |

| | 2.1. | Randomized algorithm for hypergraph coloring |

| | 2.2. | Formal construction of random coloring |

| | 2.3. | First event |

| | 2.4. | Second event |

| | 2.5. | Third event |

| | 2.6. | Application of Local Lemma |