Research: Number Theory

Summer School 2013: Computational Algebraic Number Theory

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From May 20 to May 24, 2013, the University of North Carolina at Greensboro is hosting a summer school entitled Computational Algebraic Number Theory. This summer school will cover fundamental algorithms for number fields. It will complement what students learn in a standard course on algebraic number theory. The methods presented, such as methods for arithmetic, integral basis, unit groups, class group, and Galois group computations, are essential for further computations in number theory and algebraic geometry.

On a typical day, external and local experts will give talks in the morning, and in the afternoon students will solve problems related to this material. The talks early in the week will introduce the students to the subject. Talks later in the week will 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 will be aimed at increasing the students’ understanding of the material by working with it.

Schedule

All talks will take place in Room 213 in the Petty Building (29 on the campus map). See directions for additional maps and directions.

Time Monday 5/20 Tuesday 5/21 Wednesday 5/22 Thursday 5/23 Friday 5/24
9:00 Welcome Coffee Coffee Coffee Coffee
9:30 Participants:
Introductions I		 David Ford:
Integral Bases
notes handout slides exercises		 David Ford:
Polynomial Factorization I
notes		 David Ford:
Polynomial Factorization II
notes		 Dave Roberts:
Computing Galois Groups II
slides
10:30 Coffee Coffee Coffee Coffee Coffee
10:45 Participants:
Introductions II
slides		 Michael Pohst:
Lattices
slides exercises		 Michael Pohst:
Unit and Class Groups I
slides exercises		 Michael Pohst:
Unit and Class Groups II
slides exercises		 Michael Pohst:
Diophantine equations
slides exercises
11:45 Coffee Coffee Coffee Coffee Coffee
12:00 Dave Roberts:
Introduction to Number Fields
slides exercises
exercisesmagma		 John Jones:
Computing Number Fields I
slides handout exercises		 Dave Roberts:
Computing Galois Groups I
slides		 John Jones:
Computing Number Fields II		 John Jones:
Computing Number Fields III
13:00 Lunch Lunch Lunch Lunch Lunch
14:30 Sebastian Pauli:
Intro to Computing
slides magma handbook		 Problem Session Excursion Problem Session Problem Session
15:00 Problem Session Problem Session Problem Session Problem Session
19:00 Grasshoppers

Workshop

Time Saturday 5/25
9:00 Coffee
9:30 Brian Sinclair: A Guide to the OM Algorithm
10:30 David Ford: Key Polynomials slides maclane v zx maclane v p
11:30 David Roberts: Hurwitz Number Fields slides
12:30 Michael Bush: Finding p-class towers of length 3 slides
13:00 Lunch

Participants

Locals

Speakers

Organizers

Local information

Information for visitors, including directions to UNCG and Petty Building.

Acknowledgements

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