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

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


Participants & FacultyParticipants

  • 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

NSF logoNSA LogoThe summer school in computational number theory is supported by UNCG and the NSA (H98230-16-1-0027) and the NSF (DMS-1602025).