Gregg Musiker

Welcome to my homepage. I am an NSF Mathematical Sciences Postdoctoral Fellow and Instructor in Applied Mathematics at MIT working with Richard Stanley. This fall, I am a research member at MSRI participating in their program in Tropical Geometry. I am on the job market this year. Please see my application materials below.

I received my Ph.D. in Mathematics at the University of California at San Diego, where I studied Combinatorics and topics in Arithmetic Geometry under the guidance of Adriano Garsia.



Contact Info:

Gregg Musiker
Department of Mathematics, Room 2-336
Massachusetts Institute of Technology
77 Massachusetts Ave.
Cambridge, MA 02139

musiker (at) math.mit.edu
617-253-6584


Job Application Materials

  • My CV
  • My Research Statement: Cluster Algebras, Invariant Theory, Jacobians, and Tropical Curves
  • My Teaching Philosophy

    Teaching and Seminars:

  • Spring 2009: 18.312: Algebraic Combinatorics
  • 2008-2009: Organized the Combinatorics Seminar at MIT with David Speyer and Lauren Williams

    Publications (Annotated list with abstracts available here):

  • Linear Systems on Tropical Curves with Christian Haase and Josephine Yu (submitted)
  • Positivity for cluster algebras from surfaces with Ralf Schiffler and Lauren Williams (submitted)

  • Cluster expansion formulas and perfect matchings with Ralf Schiffler (To appear in the Journal of Algebraic Combinatorics.) Also on the Arxiv.
  • The critical groups of a family of graphs and elliptic curves over finite fields. Journal of Algebraic Combinatorics: Vol. 30, Issue 2 (2009), 255--276
    Preprint also presented at FPSAC '07 at Tianjin, China.
  • Invariants, Kronecker Products and Combinatorics of some Remarkable Diophantine systems (Extended Version) with Adriano Garsia, Nolan Wallach, and Guoce Xin.
    Adv. in Appl. Math. 42 (2009), no. 3, 392--421
  • A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type (To appear in the Annals of Combinatorics.) Also on the Arxiv, and presented at FPSAC 2008.
  • A new characterization for the m-quasiinvariants of S_n and explicit basis for two row hook shapes
    with Jason Bandlow. J. Combin. Theory Ser. A 115 (2008), no 8, 1333-1357 Also presented at FPSAC 2008.
  • Combinatorial Aspects of Elliptic Curves Seminaire Lotharingien de Combinatoire 56 (2007), Article B56f
    Also presented at FPSAC '06 at San Diego.
  • Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type with Jim Propp
    Electronic Journal of Combinatorics. Vol. 14 (R15), 2007.
  • Quasiinvariants of S_3 with Jason Bandlow. J. Combin. Theory Ser. A 109 (2005), no 2, 281-298

    Slides from selected Talks:

  • Elliptic Curves and Chip-Firing Games on Graphs: Stanford University - October 20, 2009
    (Also given at UC Berkeley, University of Kentucky, UCSD, Dartmouth, UC Davis, MIT, University of Kansas, Tulane University, Georgia Tech, and San Francisco State University)
  • Cluster Algebras of Triangulated Surfaces and Snake Graphs: University of Washington - October 7, 2009
    (Also given at MIT, University of Michigan, at the Maurice Auslander Distinguished Lectures and International Conference, and at UQAM.
    Abridged versions given at FPSAC 2009, the AMS Fall 2009 Eastern Sectional at Penn State, and MSRI.)
  • Graph Theoretical Cluster Expansion Formulas: International Conference on Cluster Algebras and Related Topics - Mexico City - December 19, 2008
  • A Graph Theoretic Interpretation for Cluster Algebras of Classical Type: Northeastern University - Representation Theory Seminar - March 14, 2008
    (Also given at UMass Amherst, University of Pennsylvania, and MIT)
  • A Combinatorial Comparison of Elliptic Curves and Critical Groups of Graphs: UCSD - Thesis Defense - May 29, 2007
  • The Zeta Function of a Cyclic Language with Connections to Elliptic Curves and Chip-Firing Games: Recent Progress in Combinatorics on Words - CRM - March 14, 2007
  • Combinatorial Aspects of Elliptic Curves over Finite Fields (abridged): FPSAC 2006 - June 19, 2006
  • Combinatorial Aspects of Elliptic Curves over Finite Fields: UQAM - December 20, 2005 (Also given at UCSD on October 12, 2005)
  • The m-Quasiinvariants of S_n: Joint Meetings of the AMS and MAA at Phoenix - January 9, 2004

    Theses and other Documents:

  • My Ph.D. Thesis- A Combinatorial Comparison of Elliptic Curves and Critical Groups of Graphs
  • My undergraduate thesis - Cluster Algebras, Somos Sequences, and Exchange Graphs.

  • Combinatorial Interpretations for the Markoff Numbers (Unpublished preprint) with Andy Itsara, Jim Propp, and Rui Viana, as part of the REACH program
  • Schoof's Algorithm for Counting Points on E(F_q) (Math 168 Project under direction of William Stein)

    Some Mathematical Links:

  • International Conference on Formal Power Series and Algebraic Combinatorics
  • SAGE: Open Source Mathematics Software
  • Research Experiences in Algebraic Combinatorics at Harvard
  • IAS/Park City Mathematics Institute
  • ARCS Foundation