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 Florian Hess: Magma Renate Scheidler: Elliptic function fields Renate Scheidler: Hyperelliptic function fields Mike Jacobson: Discrete logarithm computation for HEC
10:30 Coffee
11:00 Renate Scheidler: Valuations and function fields Florian Hess: Algorithms for function fields Florian Hess: Algorithmic number theory for function fields Mike Jacobson: Efficient ideal arithmetic for HEC Florian Hess: Algorithmic geometry and function fields
12:00 Lunch
13:30 Renate Scheidler: Divisor and genus Florian Hess: Function fields in Magma Excursion Mike Jacobson: Infrastructure of a real hyperelliptic function field Mike Jacobson: Cryptographic applications
14:30 Coffee Coffee
16:00 Renate Scheidler: Extensions; divisors and ideals Problem Session Problem Session
17:00 Problem Session
Old Town Draught House Grashoppers

HEC: Hyper Elliptic Curves

References

Local information

Information for visitors, including directions to UNCG and Petty Building. The PANTS 13 pages contain a list of local restaurants.

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)
  • Sumin Leem (Calgary)
  • Junxian Li (Illinois)
  • Michael Leshowitz (UNCG)
  • Abel Lourenco (Campinas)
  • Tianyi Mao (CUNY)
  • Jonathan Milstead (UNCG)
  • Sebastian Lindner (Calgary)
  • Michael Musty (Dartmouth)
  • James Rudzinski (UNCG)
  • Sandi Rudzinski (UNCG)
  • Jana Sotáková (Regensburg and Leiden)
  • Samuel Schiavone (Dartmouth)
  • Nicolas Smoot (Georgia Southern)
  • 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).