## UNCG Summer School in Computational Number Theory 2017

### Modular Forms

From May 22 to May 26, 2017, the University of North Carolina at
Greensboro will host the UNCG Summer School in Computational Number
Theory: **Modular Forms**.

The speakers will be

- Matt Greenberg (Calgary)
- Paul Gunnells (UMass): to be confirmed
- David Roe (University of Pittsburgh)

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.

Modular forms play an increasingly important role in number theory and arithmetic geometry. The main focus of the summer school is the study of computational aspects of modular forms and related objects. Topics may include classical modular forms and modular symbols, group cohomology and Galois representations, and lattice enumeration and isometry testing techniques to compute with spaces of modular forms for compact forms of classical groups.

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 complete the online application
and have a letter of reference sent via email to d_yasaki@uncg.edu by
**March 22, 2017**. We will respond with funding decisions by April 6, 2017.

#### 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-1602025).