## UNCG Summer School in Computational Number Theory 2016

### Function Fields

From May 30 to June 3, 2016, the University of North Carolina at
Greensboro will host the UNCG Summer School in Computational Number Theory: **Function Fields**.

The speakers will be

- Florian Hess (Universität Oldenburg)
- Michael Jacobson (University of Calgary)
- Renate Scheidler (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: Integral bases, ideal arithmetic, splitting of places, efficient ideal arithmetic for hyperellptic curves, Riemann-Roch spaces, construction of algebraic geometric (AG) codes, divisor class groups, invariant computation for hyperelliptic curves, and cryptographic applications.

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 studentsâ€™ understanding of the material by working with it.

#### Applications

We expect to be able to provide support for approximately ten graduate students (travel, dorm accomodation, food). Interested students should contact should fill out the application form by April 4, 2016 AND have a letter of reference sent to d_yasaki@uncg.edu. We will respond with funding decisions by April 14, 2016.

#### 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 NSA (H98230-16-1-0027) and the NSF (DMS-1303565).