# Research: Number Theory

## Summer School 2019: Computational Aspects of Buildings

From June 24 to 28, 2019, the University of North Carolina Greensboro will host the UNCG Summer School in Computational Number Theory and Algebra: **Computational Aspects of Buildings**.

Buildings provide a rich class of simplicial complexes with very nice local structure. They play key roles in several areas of mathematics, including number theory, geometry, algebra, and combinatorics. In this workshop, we will begin by studying the basic combinatorial and geometric structure of buildings. We will then explore applications and open questions related to their large scale geometry, structure of their automorphism groups, existence of buildings with cocompact lattices and prescribed vertex link, and their role in algebraic combinatorics and the study of symmetric functions.

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.

### Speakers

- Yusra Naqvi (University of Sydney, Australia)
- Xiangdong Xie (Bowling Green State University)
- Thibaut Dumont (University of Jyväskylä, Finland)

### Application

We expect to be able to provide support for approximately fifteen graduate students (travel, dorm accommodations, food). Interested students should complete the online application and have a letter of reference sent via email to t_fernos@uncg.edu by **April 21, 2019**. We will respond with funding decisions by May 13, 2019.

### Organizers

### Acknowledgements

The summer school in computational number theory is supported by UNCG and the NSF (DMS-1602025, DMS-1802448).