Faculty Directory: Jeremy Martin

Faculty Directory


Jeremy Martin

Research Interests

Discrete Geometry

Prof. Martin's primary research area is combinatorics, the mathematical study of discrete structures. A central theme of his work is the interplay of combinatorics, particularly graph theory, with geometry and topology. A long-term goal of Prof. Martin's has been to understand fundamental geometric invariants by studying certain algebraic varieties whose points parametrize the embeddings of a graph. A more recent research interest is cellular and simplicial generalizations of the matrix-tree theorem, and their consequences for tree enumeration.

Selected Publications

  • Simplicial matrix-tree theorems (with A.M. Duval and C.J. Klivans), Trans. Amer. Math. Soc. 361, no. 11 (2009), 6073--6114.
  • Rigidity theory for matroids (with M. Develin and V. Reiner), Comment. Math. Helv. 82 (2007), 197--233.
  • The slopes determined by n points in the plane, Duke Math. J. 131, no. 1 (2006), 119--165.
  • On the topology of graph picture spaces, Adv. Math. 191, no. 2 (2005), 312--338.
  • Geometry of graph varieties, Trans. Amer. Math. Soc. 355, no. 10 (2003), 4151--4169.