Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices

  • Christoph Koutschan (Speaker)

Activity: Talk or presentation › Contributed talk › unknown

Description

We study the lattice Green's functions of the face-centered cubic lattice (fcc) in up to six dimensions. We give computer algebra proofs of results that were conjectured by Guttmann and Broadhurst for the four- and five-dimensional fcc lattices. Additionally we derive a differential equation for the six-dimensional fcc lattice, a result that was not believed to be achievable with current computer hardware. We also present some conjectures concerning the nature of the lattice Green's function in arbitrary dimensions.
Period06 Oct 2011
Event titleConference on Applied Algebraic Geometry (Minisymposium "Symbolic Combinatorics")
Event typeConference
LocationUnited StatesShow on map

Fields of science

  • 101002 Analysis
  • 101013 Mathematical logic
  • 101001 Algebra
  • 101012 Combinatorics
  • 101020 Technical mathematics
  • 102 Computer Sciences
  • 101 Mathematics
  • 101009 Geometry
  • 102011 Formal languages
  • 101006 Differential geometry
  • 101005 Computer algebra
  • 101025 Number theory
  • 101003 Applied geometry
  • 102025 Distributed systems

JKU Focus areas

  • Computation in Informatics and Mathematics