Research Interests

  • Discrete Morse theory:
  • Number theoretic discrete Morse theory: I am currently working on a joint project with fellow Dartmouth College alum Dominic Klyve from Central Washington University. Since Dominic is a number theorist and I am only a number theory groupie, We are using discrete Morse theory to study what would otherwise be awkward properties of the integers. We are defining different discrete Morse functions on infinite graphs and studying the number theoretic properties of the induced homological sequence. It's pretty fun, but still in the blastocyst stage, though implantation is just around the corner. More substantive details will hopefully be given in the future.
  • Simplicial and discrete Lusternik-Schnirelmann category
  • Homology and Boolean functions
  • Homotopy of digital images
  • (Classical) Lusternik-Schnirelmann category and cone-length

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    Last modified on August 26, 2016