Research: Number Theory

Summer School 2017: Modular Forms

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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.

Speakers

Matt Greenberg (University of Calgary)
Paul Gunnells (UMass Amherst)
Mark McConnell (Princeton University)
David Roe (University of Pittsburgh)

Schedule

All talks will take place in Room 213 in the Petty Science Building (campus maps and directions, Google 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

Gunnells: Exercises 1 (PDF)
GP script sample to play with Eisenstein series
Roe: Exercises 1 (link)
CoCalc formerly known as SageMathCloud: Create a free account, and contact David to get access to his worksheet.

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

Gunnells: Exercises 2 (PDF)
GP script sample to play with Eisenstein series
Greenberg: Exercises 1 (PDF)
Roe: Exercises 2 (link)
CoCalc formerly known as SageMathCloud: Create a free account, and contact David to get access to his worksheet.

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

Gunnells: Exercises 3 (PDF)
GP script sample to play with modular symbols
Greenberg: Exercises 2 (PDF)
Roe: link

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