Department of Mathematics and Statistics

Number Theory

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UNCG Summer School in Computational Number Theory 2016

Function Fields

summer school 2015 poster 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

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 5/29Monday 5/30Tuesday 5/31Wednesday 6/1Thursday 6/2Friday 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

Participants

group photo 2016
  • 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

Acknowledgements

NSA logo NSF logo The summer school in computational number theory is supported by UNCG and the NSA (H98230-16-1-0027) and the NSF (DMS-1303565).