Jo Ellis-Monaghan Professor of Mathematics and Statistics

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Ph.D. University of North Carolina, Chapel Hill
M.S. University of Vermont
B.A. Bennington College

View my personal website

Areas of Expertise:

Algebraic combinatorics, especially graph polynomials, and applied graph theory in statistical mechanics, computer chip design and bioinformatics.

Courses I Teach:

Calculus I, II, III, Applied Graph Theory, Linear Algebra, Real Analysis, Abstract Algebra, Senior Seminar


Selected Publications



J. Ellis-Monaghan, I. Moffatt, Graphs on Surfaces: Twisted Duality, Polynomials, and Knots, SpringerBriefs in Mathematics, 2013.


Book Chapters

J. Ellis-Monaghan, “Reading, ‘Riting, and Reals”, chapter in Innovative Techniques for Teaching Proof-Writing.

J. Ellis-Monaghan, G. Pangborn, L. Beaudin, D. Miller, N. Bruno, A. Hashimoto, “Minimal Tile and Bond-Edge Types for Self-Assembling DNA Graphs”, chapter in Discrete and Topological Models in Molecular Biology, Jonoska & Saito, eds. Natural Computing Series, Springer, 2013.

J. Ellis-Monaghan, C. Merino, “Graph polynomials and their applications I: the Tutte polynomial”, chapter in Structural Analysis of Complex Networks, Mattias Dehmer, ed., Birkhauser, 2010.

J. Ellis-Monaghan, C. Merino, “Graph polynomials and their applications II: interrelations and interpretations”, chapter in Structural Analysis of Complex Networks, Mattias Dehmer, ed., Birkhauser, 2010.

Selected Recent Journal articles

  1. J. Ellis-Monaghan, G. Pangborn, “An example of practical organization for undergraduate research experiences”, PRIMUS.
  2. J. Ellis-Monaghan, I. Moffatt, “A Penrose polynomial for embedded graphs,” European Journal of Combinatorics, 34 (2013) 424-445.
  3. J. Ellis-Monaghan, I. Moffatt, “Twisted duality and polynomials of embedded graphs,” Trans. Amer. Math. Soc. 364 (2012), 1529-1569.
  4. J. Ellis-Monaghan, I. Moffatt, “The Tutte-Potts connection in the presence of an external field,” Advances in Applied Mathematics, 47 (2011) 772-782.
  5. J. Ellis-Monaghan, G. Pangborn, “Using DNA self-assembly design strategies to motivate graph theory concepts,” Math. Model. Nat. Phenom, 6, no. 6 (2011) 96-107.

During the academic year and summers, in collaboration with Greta Pangborn in the CS department, I work with several students on collaborative research projects. I have facilitated interdisciplinary work with students doing research in mathematics and also in computer science, physics, biology, or chemistry.

Self Assembly Design Strategies

Awards & Recognitions

Editorial and Advisory Positions

  • Editor-in-Chief of PRIMUS: Problems, Resources, and Issues in Undergraduate Mathematics, 2011-present. Associate Editor, 2010. Editorial Board, 2006-2009
  • Editor, Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interaction. 2013-present
  • Discrete Math Days in the Northeast Steering Committee, 2012-present
  • Center for Undergraduate Research in Mathematics Advisory Board, 2012-present

Selected Recent External Grants and Awards

(PI unless otherwise noted.)

  • NSF EFRI-ODESSEI – Foldable self replicating DNA nanostructures for organization of functional nanomaterials and 3D meta-material assembly (co-PI, W. Goddard, Caltech, PI). August 2013-July 2017.
  • NASA – Vermont Space Grant Consortium Grant, Summer Student Mentoring. Design Strategies for Self-Assembly, Summer 2012 (co-PI, G. Pangborn PI).
  • NASA – Vermont Space Grant Consortium Grant, Summer Student Mentoring, Design Strategies for Self-Assembly, Summer 2011.
  • NSF Algebra, Number Theory, and Combinatorics, New Graph Theory from and for Nanoconstruct Design Strageties, June 2010-May 2013.
  • NASA – Vermont Space Grant Consortium Grant, Design Strategies for Self-Assembly, September 2010-August 2011.
  • NSF CSTEM award for computer science and mathematics scholarships (co-PI, G. Pangborn PI), June 2008-May 2013.
  • Vermont Genetics Network/INBRE Baccalaureate Funding, Graph Polynomials and DNA Structures, September 2005-May 2010.
  • Center for Undergraduate Research in Mathematics, Applied Graph Theory Undergraduate Research Group, AY 2009-2010.
  • NASA – Vermont Space Grant Consortium Student Mentoring Grant, DNA Nanostructures, Summer 2009.
  • Vermont EPSCoR, The Potts/Tutte Model for nearest neighbor complex systems, June 2009-May 2010.
  • National Security Agency Standard Grant, Fiscal Years 2007 and 2008.

I have been a visiting fellow or participant in the combinatorics and statistical mechanics programs at the Issac Newton Institute, Cambridge University in Cambridge, England, at the Leibnitz Institute at Schloss Dagstul, Germany, and at the Schrodinger Institute in Vienna, Austria.


Life Off Campus:

Outside of Saint Michael’s, I paint and make pots. I grew up on an island in Alaska, and can gut and gill a salmon in under fifteen seconds. I still live on an island and grow lots of fruits and vegetables.

Jo Ellis-Monaghan, professor of mathematics, and Greta Pangborn, associate professor of computer science, on July 21, 2015, hosted the conference “Summer Combo in Vermont” on the Saint Michael’s College campus. The (more or less) annual small and informal conference brings together regional cominatorics scholars “for a day of collaboration, congeniality and an opportunity to learn about one another’s investigations,” including talks, speakers and poster presentations. Other organizers with Jo and Greta were Melanie Brown of Champlain College and Christino Tamon of Clarkson University. Combinatorics is the branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those of graph theory.
(posted September 2015)

Professors Joanna Ellis-Monaghan and Greta Pangborn awarded $2 million NSF grant with CalTech & NYU teammates.

Jo Ellis-Monaghan, professor of mathematics, will make a presentation, “The Shapes of Sea Shells: Mathematical Beauty in the Natural World,” at the Advancement of Science (AAAS) 2013 Annual Meeting in Boston on February 15, 2013. Here’s how Jo describes her presentation for the meeting’s program: “Part of the natural beauty of seashell derives from the visual rhythm of their self-replicating whorls. We give a mathematical model that captures sea shell morphology using space curves, parameterized surfaces, and Frenet frames. We show how the growth parameters of this model may be measured from x-rays or cross sections of actual shells, and then 3-D computer generated simulations of the intact shell produced.  We conclude with a gallery of ‘fantasy’ shells, that is, shells created solely for their artistic appeal, but which also demonstrate the effects of manipulating the parameters of the model. The basic shell model may be taught at the undergraduate level (e.g. calculus III, vector calculus, or differential geometry), and provides a beautiful and engaging introduction to mathematical modeling. It is available as a ‘discovery-learning’ module through ILAP/COMAP.”