On 24+25 april 2019 the DIAMANT Symposium will be held at Hotel Koningshof in Veldhoven. The Dutch Mathematical Congress (NMC2019) is held at the same location, on 23+24 april 2019.

The NMC2019 will feature two minisymposia in which DIAMANT is involved, one jointly organized with GQT, and one with STAR.

The Diamant symposium proper starts on 24 april at 7 PM with a conference dinner, after the NMC2019 has closed. The scientific programme of the Diamant symposium starts on 25 april at 9 AM.

Invited speakers of the DIAMANT symposium of 25 april include Felix Lucka (CWI), Nicole Megow (U Bremen) and Oriol Serra (UPC Barcelona).

### How to contribute a talk

PhD students and postdocs are warmly welcomed to submit a contributed talk (25-30 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 Robin de Jong 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

The symposium starts with a dinner on Wednesday 24 april, 7:00 PM, after the NMC has closed. The scientific programme starts on Thursday at 9:00 AM and ends around 4:00 PM.

The lectures of the Diamant symposium will take place in room 40 in the red zone of Koningshof. The dinner on Wednesday will take place in restaurant Binnenhof. This is also the place where breakfast and lunch are served on Thursday.

For more information on the topics being presented, see the ‘Speakers’ section of this page.

#### INVISIBLE

#### Wednesday

19:00 | Dinner (location: restaurant Binnenhof) |

20:30 | Meeting “What’s next in Diamant?” |

#### Thursday

9:00-9:55 | Nicole Megow (U Bremen) – Combinatorial optimization with explorable uncertainty |

10:00-10:25 | Francisco Pereira (TU/e) – Quantum BCH and Reed-Solomon Entanglement-Assisted Codes |

10:30-11:00 | Coffee break |

11:00-11:25 | Joey van Langen (VU) – Sums of fourth powers in arithmetic progression |

11:30-11:55 | Peter Koymans (UL) – On Gerth’s conjectures |

12:00-13:30 | Lunch (restaurant Binnenhof) |

13:30-14:25 | Oriol Serra (UPC Barcelona) – Counting arithmetic configurations in random sets |

14:30-14:55 | Josse van Dobben de Bruyn (TUD) – A geometric proof of Kadison’s anti-lattice theorem |

15:00-15:30 | Tea break |

15:30-15:55 | Stefan van der Lugt (UL) – The ring of tautological differential forms |

16:00-16:55 | Felix Lucka (CWI) – Challenges of mathematical image reconstruction |

17:00 | End of the symposium |

### Speakers

#### INVISIBLE

#### Nicole Megow (U Bremen)

##### Combinatorial Optimization with Explorable Uncertainty

A major challenge in solving real-world optimization problems lies in the uncertainty of input data. A rather new model for uncertain input is explorable uncertainty, which refers to settings where parts of the input data are initially unknown, but can be obtained at a certain cost using queries. An algorithm can make queries one by one until it has obtained sufficient information to solve a given problem. The challenge lies in balancing the cost for querying and the impact on the solution quality. In this talk, we give a short overview on recent work on explorable uncertainty for combinatorial optimization problems and then focus on a new scheduling problem.

#### Francisco Pereira (TU/e)

##### Quantum BCH and Reed-Solomon Entanglement-Assisted Codes

Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some resources can be used to improve the parameters of these codes, e.g., entanglement. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this talk, a general method to construct QUENTA codes via cyclic codes is shown. Afterwards, the method is applied to BCH and Reed-Solomon codes.

#### Joey van Langen (VU)

##### Sums of fourth powers in arithmetic progression

A classical Diophantine problem is to study when the sum of *k* *n*-th powers in arithmetic progression is itself a perfect power for various choices of *k* and *n*. In this talk we survey some results in this area and present a solution in the case *k = 3* and *n = 4*. This recent result uses, amongst other techniques, the modularity of *Q*-curves, decomposition of the restriction of scalars and twists of newforms. These techniques give us precise arithmetic control on the levels of the corresponding newforms, in particular bringing the involved computations within reach.

#### Peter Koymans (UL)

##### On Gerth’s conjectures

We start by describing the Cohen-Lenstra heuristics, which are a precise set of conjectures regarding the distribution of class groups in families of number fields. We then explain Gerth’s extension of these conjectures. We next introduce governing fields, which has been the traditional tool to deal with such problems. We show the limitations of these methods, illustrated by the work of Koymans and Milovic, and discuss the recent breakthrough of Smith, who managed to introduce more general “governing fields” to prove Gerth’s conjecture. We finally discuss some recent work of Koymans and Pagano that extends Smith’s work to the family of degree *l *cyclic fields instead of imaginary quadratic fields proving another conjecture of Gerth.

#### Oriol Serra (UPC Barcelona)

##### Counting arithmetic configurations in random sets

The well-known Szemerédi theorem asserts that sets of integers with positive density contain arbitrary large arithmetic progressions. Analogous results for random sets of integers were proved independently by Schacht and by Conlon and Gowers. A combinatorial approach by Balogh, Morris and Samotij and by Saxton and Thomason gives quite precise countings of arithmetic progressions in random sets. In the talk we will discuss these and an extension to general arithmetic configurations given by solutions of linear systems in abelian groups. We will also discuss the analysis of deviations on counting arithmetic configurations in random sets by an extension to the arithmetic context of a recent approach by Goldsmith, Griffiths and Scott for subgraph counting in the random graph model *G(n,m)*.

#### Josse van Dobben de Bruyn (TUD)

##### A geometric proof of Kadison’s anti-lattice theorem

In 1951, Sherman proved that a *C**-algebra is commutative if and only if it is lattice ordered. This led Kadison to ask under which circumstances two Hermitian operators *A* and *B* have a supremum (or infimum) under the positive semidefinite order. His so-called anti-lattice theorem shows that this is only the case if *A* and *B* are comparable, in which case the supremum (infimum) is simply the largest (smallest) of the two. Kadison concludes that the space of Hermitian operators cannot be further away from a lattice (an “anti-lattice”). The original proof relies on the tools of operator theory, and does not relate to the geometry of the underlying Hilbert space. In this talk, we show that the space of Hermitian operators still has a quasi-lattice structure, and outline a new geometric proof of the anti-lattice theorem. We restrict our attention to the finite-dimensional case, allowing us to exhibit the most important geometric ideas without dealing with the subtleties of infinite-dimensional Hilbert space theory.

#### Stefan van der Lugt (UL)

##### The ring of tautological differential forms

On the moduli space of curves of a fixed genus, the ring of tautological classes is a graded ring of Chow or cohomology classes. In this talk, we give a translation to a setting of differential forms. We construct a graded ring of tautological differential forms, and show that forms appear that can not be detected by cohomology. We provide a method of associating forms to graphs, and use this construction to show that the graded ring of tautological differential forms is finite-dimensional in every degree. Moreover, we describe how this construction can be used to compute relations among tautological forms.

#### Felix Lucka (CWI)

##### Challenges of mathematical image reconstruction

Mathematical image reconstruction describes the process of computing images of quantities of interest from indirect observations through algorithms derived from rigorous mathematics. As the observation process can often be modeled by partial differential equations, image reconstruction problems are a classical example of inverse problems and draw from various fields of applied mathematics, including Bayesian inference, variational regularization, compressed sensing, computational optimization, machine learning and numerical analysis. Mathematicalimage reconstruction became a key technique in a vast range of scientific, clinical and industrial applications and in this talk, I want to highlight some of its current trends and challenges, illustrated by my own work on biomedical imaging applications such as X-ray computed tomography (CT), photoacoustic tomography (PAT), electro- and magnetoencephalography (EEG/MEG), magnetic resonance imaging (MRI) and ultrasound computed tomography (USCT).

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