Gregg Musiker

Welcome to my homepage. I am an NSF Postdoctoral Fellow in Mathematics at MIT working with Richard Stanley. I recently received my Ph.D. in Mathematics at the University of California at San Deigo, 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


TEACHING:
  • Math 18.312: Algebraic Combinatorics

    • PAPERS:
  • Positivity for cluster algebras from surfaces with Ralf Schiffler and Lauren Williams
  • Cluster expansion formulas and perfect matchings with Ralf Schiffler
  • The critical groups of a family of graphs and elliptic curves over finite fields
    (To appear in the Journal of Algebraic Combinatorics) Preprint also presented at FPSAC '07 at Tianjin, China.
  • Invariants, Kronecker Products and Combinatorics of some Remarkable Diophantine systems with Adriano Garsia, Nolan Wallach, and Guoce Xin
    (Abridged version to appear in Advances in Applied Mathematics)
  • A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type
    (To appear in the Annals of Combinatorics) Also on Arxiv
    Also 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.
  • My Ph.D. Thesis- A Combinatorial Comparison of Elliptic Curves and Critical Groups of Graphs
  • 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
  • My undergraduate thesis - Cluster Algebras, Somos Sequences, and Exchange Graphs.


    SLIDES FROM SELECTED TALKS:
  • Georgia Tech - January 23, 2009
    (Also given at UC Berkeley, University of Kentucky, UCSD, Dartmouth, UC Davis, MIT, the University of Kansas, and Tulane University)
  • International Conference on Cluster Algebras and Related Topics - Mexico City - December 19, 2008
  • Northeastern University - Representation Theory Seminar - March 14, 2008
    (Also given at UMass Amherst on November 14, 2007, University of Pennsylvania on November 27, 2007, and MIT on April 14, 2008.)
  • UCSD - Thesis Defense - May 29, 2007
  • Recent Progress in Combinatorics on Words - CRM - March 14, 2007
  • FPSAC 2006 - June 19, 2006
  • UQAM - December 20, 2005 (Also given at UCSD on October 12, 2005)
  • Joint Meetings of the AMS and MAA at Phoenix - January 9, 2004

    OTHER DOCUMENTS:
  • Combinatorial Interpretations for the Markoff Numbers (Unpublished preprint) with Andy Itsara, Jim Propp, and Rui Viana, as part of REACH program
  • Schoof's Algorithm for Counting Points on E(F_q) (Math 168 Project under direction of William Stein)
  • My CV (as of January 2007)
  • My Research Statement: Combinatorics of Elliptic Curve Groups and a Variety of Positivity Conjectures
  • My Teaching Philosophy

    SOME LINKS:
  • Research Experiences in Algebraic Combinatorics at Harvard
  • IAS/Park City Mathematics Institute
  • ARCS Foundation
  • The Internet Movie Database
  • The Food Network