Department of Mathematics and Statistics

Number Theory

2014   2013   2012  

UNCG Summer School in Computational Number Theory 2013

Computational Algebraic Number Theory

summer school 2013 poster

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.

TimeMonday 5/20Tuesday 5/21Wednesday 5/22Thursday 5/23Friday 5/24
9:00WelcomeCoffeeCoffeeCoffeeCoffee
9:30Participants: Introductions IDavid 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
10:30CoffeeCoffeeCoffeeCoffeeCoffee
10:45Participants: Introductions II slidesMichael 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
11:45CoffeeCoffeeCoffeeCoffeeCoffee
12:00Dave 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 IIJohn Jones: Computing Number Fields III
13:00LunchLunchLunchLunchLunch
14:30Sebastian Pauli: Intro to Computing slides magma handbook Problem SessionExcursionProblem SessionProblem Session
15:00Problem SessionProblem SessionProblem SessionProblem Session
19:00Grasshoppers

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

Participants

summer school 2013 participants
Locals
Speakers
Organizers

Application and Travel Support

We expect to be able to provide support for approximately ten graduate students (travel, dorm accomodation, food). Interested students should contact us via email at d_yasaki@uncg.edu by March 15, 2013 with a one paragraph statement of interest and a list of graduate courses taken. We will respond with funding decisions by April 1, 2013.

Local information

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

The PANTS 13 pages contain a list of local restaurants.

Acknowledgements

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).