# Research: Number Theory

## Summer School 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.

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.

### Schedule

All talks will take place in Room 213 in the Petty Science Building (campus maps and directionsGoogle map).

Monday 5/22
9:15-9:30 Organizers: Welcome
9:30-11:00 Participants: Introductions
11:15-12:15 Paul Gunnells: Modular forms and modular symbols I (notes (PDF))
Lunch
2:00-3:00 David Roe: Congruences between and Interpolation of Modular Forms
3:30-5:00 Problem Session
Tuesday 5/23
9:30-10:30 Paul Gunnells: Modular forms and modular symbols II
11:15-12:15 Matt Greenberg: Lattices — structure and symmetry groups
Lunch
2:00-3:00 David Roe: Computing with Modular Symbols in Sage
3:30-5:00 Problem Session
Wednesday 5/24
9:30-10:30 Paul Gunnells: Modular forms and modular symbols III
11:15-12:15 Matt Greenberg: Automorphic forms and lattices
Lunch
3:30 David Roe: An introduction to Sage
Thursday 5/25
9:30-10:30 Matt Greenberg: Computing automorphic forms in the totally definite case
11:15-12:15 Mark McConnell: The Well-Rounded Retract and the Voronoi Polyhedron
Lunch
2:00-3:00 David Roe: Overconvergent Modular Symbols and $p$-adic L-functions3:30-5:00 Problem Session
Friday 5/26
9:30-10:30 Mark McConnell: An algorithm for Hecke Operators for SL in higher rank
11:15-12:15 Problem Session
End

### Participants

1. Angie Babei (Dartmouth College)
2. Matthew Bates (UMass Amherst)
3. Ben Breen (Dartmouth College)
4. Benjamin Carrillo (Arizona State University)
5. Sara Chari (Dartmouth College)
6. Mariagiulia De Maria (University of Luxembourg and Université de Lille 1)
7. Marcus Elia (University of Vermont)
8. Nathan Fontes (UNCG)
9. Yu Fu (UMass Amherst)
10. Hugh Geller (Clemson University)
11. Matt Greenberg (University of Calgary)
12. Paul Gunnells (UMass Amherst)
13. Seoyoung Kim (Brown University)
14. Andrew Kobin (University of Virginia)
15. Huixi Li (Clemson University)
16. Mark McConnell (Princeton University)
17. Jonathan Milstead (UNCG)
18. Sebastian Pauli (UNCG)
19. Michael Reed (UNCG)
20. David Roe (University of Pittsburgh)
21. Manami Roy (University of Oklahoma)
22. James Rudzinski (UNCG)
23. Sandi Rudzinski (UNCG)
24. Filip Saidak (UNCG)
25. Chris Steinhart (Universitaet des Saarlandes)
26. Makoto Suwama (University of Georgia)
27. Brett Tangedal (UNCG)
28. Debbie White (UNCG)
29. Luciena Xiao (California Institute of Technology)
30. Yuan Yan (UMass Amherst)
31. Dan Yasaki (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).