Research: Number Theory
Summer School 2016: Function Fields
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From May 30 to June 3, 2016, the University of North Carolina at Greensboro will host the UNCG Summer School in Computational Number Theory: Function Fields.
The speakers will be
- Florian Hess (Universität Oldenburg)
- Michael Jacobson (University of Calgary)
- Renate Scheidler (University of Calgary)
The summer school in computational number theory fills a gap in the education of many graduate students. Most graduate courses in number theory take a mainly theoretic approach with very little emphasis on the computational aspects of the subject. The goal of the UNCG Summer School in Computational Number Theory is to complement this with a constructive-algorithmic approach. Many of the algorithms used for number theoretic computations are non-trivial, which makes it difficult to cover them in a standard course.
Schedule
All talks will take place in Room 213 in the Petty Building (campus maps and directions).
| Time | Sunday 5/29 | Monday 5/30 | Tuesday 5/31 | Wednesday 6/1 | Thursday 6/2 | Friday 6/3 |
|---|---|---|---|---|---|---|
| 9:00 | Arrival | Welcome | Coffee | |||
| 9:30 | Participants: Introductions slides |
Florian Hess: Magma slides slides for print examples 1 examples 2 examples 3 |
Renate Scheidler: Elliptic function fields | Renate Scheidler: Hyperelliptic function fields | Mike Jacobson: Discrete Logarithm Computation slides |
|
| 10:30 | Coffee | |||||
| 11:00 | Renate Scheidler: Valuations and function fields slides exercises |
Florian Hess: Algorithms for function fields slides commented slides |
Florian Hess: Algorithmic number theory for function fields slides |
Mike Jacobson: Improving ideal arithmetic slides exercises |
Florian Hess: Algorithmic geometry and function fields slides |
|
| 12:00 | Lunch | |||||
| 13:30 | Renate Scheidler: Divisor and genus | Florian Hess: Function fields in Magma slides slides for print examples 1 examples 2 examples 3 examples 4 examples 5 examples 6 |
Excursion | Mike Jacobson: Alternative Models: Infrastructure slides |
Mike Jacobson: Cryptographic Applications slides |
|
| 14:30 | Coffee | Coffee | ||||
| 15:00 | Renate Scheidler: Extensions; divisors and ideals | Problem Session | Problem Session | |||
| 17:00 | Problem Session | |||||
| Old Town Draught House | Grasshoppers | |||||
HEC: Hyper Elliptic Curves
References
- Magma Handbook: Function Fields
- Harald Niederreiter: Algebraic Function Fields over Finite Fields, tutorial lecture notes
- Henning Stichtenoth: Algebraic Function Fields and Codes, book
Participants
- Chad Awtrey (Elon)
- Giulia Bianco (Neuchatel)
- Benjamin K. Breen (Dartmouth)
- Marguerite Delcourt (Lausanne)
- Lance Everhart (UNCG)
- Ricky Farr (UNCG)
- David Ford (Concordia, Montreal)
- Jeroen Hanselman (Ulm)
- Austin Lawson (UNCG)
- Sumin Leem (Calgary)
- Junxian Li (Illinois)
- Sebastian Lindner (Calgary)
- Abel Lourenco (Campinas)
- Tianyi Mao (CUNY)
- Jonathan Milstead (UNCG)
- Michael Musty (Dartmouth)
- James Rudzinski (UNCG)
- Sandi Rudzinski (UNCG)
- Samuel Schiavone (Dartmouth)
- Nicolas Smoot (Georgia Southern)
- Jana Sotáková (Regensburg and Leiden)
- Emerald Stacy (Oregon State)
- Keller Vandebogert (Georgia Southern)
Organizers
- Brett Tangedal (UNCG)
- Dan Yasaki (UNCG)
- Filip Saidak (UNCG)
- Sebastian Pauli (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).
