Research in
spectral graph theory and Internet mathematics

• Guessing secrets , a problem that arose in connection with Internet traffic routing.
  
  • Abstract| paper | SODA paper .
  • Coauthoers: Tom Leighton, Ronald Graham
• Massive graphs
  • Abstract| some descriptions | paper | other related papers
  • A simulation project for massive graphs.
  • The STOC talk in ppt (Math type notation required).
  • Coauthors -- Bill Aiello, Lincoln Lu.
• Internet tomography
  • Abstract| some descriptions
  • A talk on this topic.
  • A paper
    Distance realization problems with applications to Internet tomography
    coauthored with Ronald Graham, Mark Garrett and David Shallcross.
• Dynamic location problems with finite look-ahead
  • Abstract| some descriptions
  • A paper
• Chip-firing and load balancing in distributed networks.
  Various methods are based on an interesting question:
  Can you hear the shape of a graph? An implementation can be found in a neat webpage designed by Robert Ellis.
  A simulation of several chip-firing games is under construction.
  Abstract| papers on this topic.
• Selected research topics in spectral graph theory :
  • Isoperimetric inequalities
    Abstract| descriptions | paper | other related papers
  • Green's functions
    Abstract| descriptions | paper | other related papers
  • Heat kernels and spanning trees
    Abstract| descriptions | two papers | other related papers
  • Harnack inequalities
  • Discrete Sobolev inequalities
  • Logarithmic Sobolev inequalities
  • Random walks
• Selected topics in extremal graph theory and random graph theory
  • Tur'an problems
    Abstract| descriptions | paper | other related papers
  • Diameter of random sparse graphs
    Abstract| descriptions | paper | other related papers
  • Papers in
    • universal graphs,
    • unavoidable graphs,
    • graph labelings,
    • graph embeddings.
    • graph decomposition.