Department of Mathematics and Statistics

Number Theory

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UNCG Summer School in Computational Number Theory 2014

Modular Forms and Geometry

summer school 2014 poster

From May 19 to May 23, 2014, the University of North Carolina at Greensboro is hosting a summer school entitled Modular Forms and Geometry.

Modular forms play an increasingly important role in number theory and arithmetic geometry. The main focus of the summer school is the study of computional 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 gave talks in the morning, and in the afternoon students solved problems related to this material. The talks early in the week introduced the students to the subject. Talks later in the week covered 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 were aimed at increasing the students’ understanding of the material by working with it.


All talks took place in Room 219 in the Petty Building (campus maps and directions). Directions from the Biltmore Hotel to Petty. (Switch to walking directions.)

TimeMonday 5/19Tuesday 5/20Wednesday 5/21Thursday 5/22Friday 5/23
9:30Participants: Introductions slidesPaul Gunnells: Classical modular symbols II Matt Greenberg: Algebraic modular forms
Paul Gunnells: Classical modular symbols IIIMatt Greenberg: Lattice neighbors and Hecke operators
11:15Paul Gunnells: Classical modular symbols I
Avner Ash: Galois representations, group homology, and reciprocity (exercises) Avner Ash: How to compute Hecke operators for GL(n)/QAvner Ash: The case of reducible Galois representationsRump session
14:00 Matt Greenberg: Spherical Harmonics and Hecke operators (exercises) Problem SessionExcursion to Battleground parkProblem SessionProblem Session
15:00Problem SessionProblem Session Problem SessionProblem Session
19:00ACC Baseball

Lecture notes

  • Ash lectures: Notes by Dan Yasaki from three lectures by Avner Ash.
  • Gunnells lectures: Expanded notes from three lectures given by Paul E. Gunnells.

Local information

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

summer school 2014 participants summer school 2013 participants summer school 2013 participants




NSA logo NSF logo The summer school in computational number theory is supported by UNCG, the NSA (H98230-13-1-0253), and the NSF (DMS-1303565).