## UNCG Summer School in Computational Number Theory 2015

### Zeta Functions -- New Theory and Computations

From May 18 to May 22, 2015, the University of North Carolina at Greensboro is hosting a summer school entitled**Zeta Functions -- New Theory and Computations**.

The speakers will be

- Fredrik Johansson (INRIA Bordeaux-Sud-Ouest)
- Yuri Matiyasevich (St. Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of Sciences)
- Filip Saidak (UNCG)
- Cem Yıldırım (Bogaziçi University, Istanbul)
- Peter Zvengrowski (University of Calgary)

The summer school in computational number theory fills a gap in the education of many graduate students. Most graduate courses in number theory take a mainly theoretic approach with very little emphasis on the computational aspects of the subject. The goal of the UNCG Summer School in Computational Number Theory is to complement this with a constructive-algorithmic approach. Many of the algorithms used for number theoretic computations are non-trivial, which makes it difficult to cover them in a standard course.

The subjects we plan to cover this year include: A historic approach to the Riemann Zeta function; the distribution of the zeros of zeta functions and their and their derivatives; horizontal cuts of the critical strip; efficient evaluation of zeta functions and their derivatives; related functions; gaps between primes; and twin primes.

On a typical day, external and local experts give talks in the morning, and in the afternoon students solve problems related to this material. The talks early in the week introduce the students to the subject. Talks later in the week cover related areas of current research and unsolved problems. The problems given to the students might be of a theoretical nature but could also involve programming problems and computer experiments. All problems are aimed at increasing the students’ understanding of the material by working with it.

#### Application

We expect to be able to provide support for approximately ten graduate students (travel, dorm accomodation, food). Interested students should contact us via email at s_pauli@uncg.edu by March 22, 2015 with a one paragraph statement of interest and a list of graduate courses taken and also have a letter of reference sent to the same address. We will respond with funding decisions by April 6, 2015.

#### Preliminary Schedule

Time | Monday 5/18 | Tuesday 5/19 | Wednesday 5/20 | Thursday 5/21 | Friday 5/22 |
---|---|---|---|---|---|

9:00 | Welcome | Coffee | |||

9:30 | Participants: Introductions | Peter Zvengrowski | Cem Yıldırım | Yuri Matiyasevich | Peter Zvengrowski |

10:45 | Coffee | ||||

11:15 | Filip Saidak: A short history of Zeta |
Cem Yıldırım | Peter Zvengrowski | Cem Yıldırım | Yuri Matiyasevich |

12:30 | Lunch | ||||

14:00 | Fredrik Johansson | Yuri Matiyasevich | Excursion | Fredrik Johansson | Fredrik Johansson |

15:15 | Coffee | Coffee | |||

15:30 | Problem Session | Problem Session | Problem Session | All |

#### Local information

Information for visitors, including directions to UNCG and Petty Building. The PANTS 13 pages contain a list of local restaurants.

#### Organizers

- Brett Tangedal (UNCG)
- Dan Yasaki (UNCG)
- Filip Saidak (UNCG)
- Sebastian Pauli (UNCG)

#### Acknowledgements

The summer school in computational number theory is supported by UNCG and the NSF (DMS-1303565).