The DIAMANT symposium of Spring 2024 will take place on Thursday 11 April in the Boothzaal in venue Utrecht University Library De Uithof. Invited speakers are Clara Stegehuis (Twente University) and Yagna Dutta, University of Leiden.

The Dutch Mathematical Congress (NMC2024) is held at De Werelt in Lunteren on 2 and 3 April and features a DIAMANT session on 2 April including invited speakers Johan Commelin (Utrecht University) and Mireille Boutin (Eindhoven University of Technology).

### How to contribute a talk

PhD students and postdocs are warmly welcomed to submit a contributed talk (20-25 mins.) to the Diamant symposium. In the registration form (see below) there is an option to submit title and abstract. Alternatively, after registration, a title+abstract can be sent to symposiumdiamant@gmail.com at a later date.

### Conference fee + accommodation

There is full DIAMANT support for DIAMANT members. DIAMANT members are full and associate professors listed here, as well as their research group members.

### Programme of the DIAMANT symposium

9:30-10:00 | Walk in & coffee |

10:00-11:00 | Yagna Dutta (Leiden University) – Twists of intermediate Jacobian fibration |

11:00-11:30 | Coffee break |

11:30-12:00 | Zhuan Khye (Cedric) Koh (CWI) – A strongly polynomial algorithm for the minimum cost generalized flow problem |

12:00-12:30 | Finn Bartsch (RU) – Kobayashi-Ochiai’s finiteness theorem for Campana pairs of general type |

12:30-13:45 | Lunch at Educatorium in reserved area Balkon Pi |

13:45-14:15 | Sander Borst (CWI) – Online hypergraph matching |

14:15-14:30 | Farewell retiring board members |

14:30-15:00 | Discussion about role of DIAMANT |

15:00-15:30 | Coffee break |

15:30-16:00 | Margherita Pagano (LU) – Brauer-Manin obstruction and primes of good reduction |

16:00-17:00 | Clara Stegehuis (University of Twente) – Maximal cliques: many or few? |

17:00 | Drinks & snacks |

### Speakers

#### INVISIBLE

#### Yagna Dutta (Leiden University)

##### Twists of intermediate Jacobian fibration

Given an elliptic fibration of a K3 surface, one can reglue the fibres of the elliptic fibration differently to obtain different K3 surfaces. These regluings are governed by a group scheme over the base of the elliptic fibration. My plan for the talk is to tell this story. Moving from curves to 3-folds, we find some very interesting group schemes related to the intermediate Jacobian of a cubic 3-fold. I will report on a joint work in progress with Mattei and Shinder where we consider the family of cubic 3-folds obtained as the hyperplane sections of a fixed smooth cubic 4-fold. The total space this time is a hyperKähler manifold. HyperKähler manifolds are nothing but higher dimensional analogues of K3 surfaces, resulting in impressive parallels with elliptic fibrations of K3 surfaces.

#### Clara Stegehuis (University of Twente)

##### Maximal cliques: many or few?

#### Zhuan Khye (Cedric) Koh (CWI)

##### A strongly polynomial algorithm for the minimum cost generalized flow problem

We give a strongly polynomial algorithm for minimum cost generalized flow, and as a consequence, for all linear programs with at most two variables per inequality. Previously, strongly polynomial algorithms were only known for the primal and dual feasibility problems. Our approach is to show that the path-following interior point method of Allamigeon et al. ’22 terminates in a strongly polynomial number of iterations for minimum cost generalized flow. We achieve this by bounding the ‘straight line complexity’ of the central path, which is the minimum number of pieces required by a piecewise affine curve to multiplicatively approximate the central path.

Based on joint work with Daniel Dadush, Bento Natura, Neil Olver and László Végh.

#### Finn Bartsch (RU)

##### Kobayashi-Ochiai’s finiteness theorem for Campana pairs of general type

The finiteness theorem of Kobayashi and Ochiai states that the set of dominant rational maps from a fixed variety to a fixed variety of general type is finite. We present the extension of this theorem to the setting of Campana pairs. This is joint work with Ariyan Javanpeykar.

#### Sander Borst (CWI)

##### Online hypergraph matching

The online matching problem on bipartite graphs is a classical problem in online optimization. In this talk we go beyond the graph case and consider the problem on k-uniform hypergraphs. For k=3, we provide an optimal algorithm for the fractional version of the problem. For k>=3 we give an integral algorithm for hypergraphs with bounded degree.

#### Margherita Pagano (LU)

##### Brauer-Manin obstruction and primes of good reduction

A way to study rational points on a variety is by looking at their image in the p-adic points. Some natural questions that arise are the following: is there any obstruction to weak approximation on the variety? Which primes might be involved in it? I will explain how primes of good reduction can play a role in the Brauer-Manin obstruction to weak approximation, with particular emphasis on the case of K3 surfaces. I will then explain how the reduction type (in particular, ordinary or non-ordinary good reduction) plays a role.

### Sign up for this event

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