jopix2.jpg (12204 bytes) S. M. C.
Department of Mathematics
Saint Michael's College
Winooski Park
Colchester, VT  05439

 
phone: 802 654 2660
fax: 802 654 2610
e-mail: jellis-monaghan@smcvt.edu
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Jo Ellis-Monaghan
Contact me On Campus Courses Advising
Student Research My Research Papers Talks
St. Mike's Links Other Stuff Vita  

On Campus

ON   SABBATICAL FOR 2007-2008.    

Some classes from prior semesters

Student Research:  Here are a few presentations (mostly PowerPoint) by past and current students--talks from Senior Seminars,  Hudson River, Parents' Weekend, and some Independent Study results.  Note:  The mathematics in some of the presentations requires MathType to be viewed properly.  

 

Research

Doctorate in Mathematics:  University of North Carolina, Chapel Hill, NC.   fall 1995.  Advisor: James D. Stasheff.

Areas of Research :  Algebra and Combinatorics.

I am interested in both graph theory and abstract algebra, particularly in using algebraic techniques to achieve graph theoretic results. My recent work has been primarily with graph polynomials, constructing them and embedding them in algebraic structures sufficiently rich to extract new information from them. I have been able to use Hopf-algebras to derive new identities for the Martin polynomials of both oriented and unoriented Eulerian graphs, as well as for the Tutte polynomial along the diagonal y = x.  My interests also include applications of graph theory to problems arising from computer chip design and from DNA sequencing and biomolecular computing.

Talks with available overheads:  

PDF and/or Postscript files are available for the overheads for some of my talks. PDF files require Adobe Acrobat Reader.  Postscript files can be viewed and printed using Ghostview, which is available on line--click here to go to the site.  The mathematics in some of the PowerPoint presentations requires MathType to be viewed properly.  

Multivariable Tutte and Transition Polynomials, Combinatorics and Statistical Mechanics Programme at the Isaac Newton Institute for the Mathematical Sciences, Cambridge University.  multivariable extensions 2.pdf  Video at http://www.newton.cam.ac.uk/webseminars/pg+ws/2008/csm/csmw03/0410/ellis-monaghan/

Graph Models for DNA Structures, Villanova, 10/1/07.  Graph Models DNA.ppt, Graph Models DNA.pdf

Minimum Tile Types. MathFest 2007, San Jose, 8/5/07.  Talks/Minimum tile types.pdf

A Little Statistical Mechanics for the Graph Theorist.  South Eastern, Boca Raton, 3/9/07. A Little Stat Mech.pdf

From Potts to Tutte and back again:  A graph theoretical view of statistical mechanics, (with applications).  UPenn 11/15/06.  The Potts-Tutte model3.pdf

An introduction to the Potts Model.  SMC/UVM joint applied combinatorics seminar, 10/26/06. Intro to Potts.pdf

From Potts to Tutte and back again:  A graph theoretical view of statistical mechanics.  Middlebury College, 10/27/05. From Potts to Tutte and back again.ppt, From Potts to Tutte and back again 4.pdf

Weak Tutte Functions of Matriods, 2nd Workshop on the Tutte Polynomial and its Applications, 10/5/05.  Weak Tutte Functions of Matroids.pdf (scanned notes for 'chalk talk')

A Duality Relation for the Topological Tutte Polynomial, AMS Eastern Section Meeting Special Session on Graph and Matroid Invariants,  Bard College, 10/9/05. A Duality Relation.pdf  (scanned overheads)

Graph models for DNA structures, Vermont Genetics Network Workshop 8/17/05. DNA struct (html), DNA struct.pdf, DNA struct.ppt

Properties of the interlace polynomial, AMS Pittsburgh, 11/7/04.  interlace properties.pdf

Graph models from the Kevin Bacon game to biomolecular computing and beyond!  Skidmore Colloquium, 10/20/04.  Graph Models 3.pdf, Graph Models 3.ppt

Crazy Cubes and other applications of graphs and networks.  UVM highschool contest awards ceremony, 5/6/04 Crazy CubesUVM.pdf or CrazyCubesUVM.ppt

Graph Theoretical Problems in Next Generation Chip Design.  South Eastern, Boca Raton, 3/3/03. [Graphs in chip design--PowerPoint]

A Hopf-algebraic structure for generalized transition polynomials.  Special Session on Combinatorial Hopf Algebras at the AMS meetings in Montreal, QC, 5/5/2002 [abstract and ps file--583 KB]

Independent Studies with Industry Partnership.  MathFest 2002, Burlington VT.  [PowerPoint--461 KB]

Practical Applications and the Universality of the Tutte Polynomial.  UVM Colloqium Talk, 2/15/2002.  [Links]

Relations for Skein-Type Graph Polynomials.  South Eastern, Baton Rouge, 2/26/2001.  [Abstract]  [Click here for postscript file--866 KB].

The Circuit Partition Polynomial and Integer Evaluations of the Tutte Polynomial.  CoNE, Smith College, 2/10/2001.   [Click here for postscript file--1550 KB]  (sorry so large--26 color slides done in Word take up a lot of space....)  Proofs for much of what was covered in this talk can be found in Identities for the Circuit Partition Polynomials... below.

Papers

[Research]  [Pedagogy]

PDF and/or  Postscript files are available for several of these papers.  PDF files require Adobe Acrobat Reader.   They can be viewed and printed using Ghostview, which is available on line--click here to go to the site.  If any paper is not available electronically, or if any fail to download properly, please email me directly for a copy.

RESEARCH PAPERS:

  1.  L. Beaudin*, J. Ellis-Monaghan, G. Pangborn, R. Shrock, “A little statistical mechanics for the graph theorist,” submitted.

  2.   A. Dean, J. Ellis-Monaghan, S. Hamilton*, G. Pangborn, “Unit rectangle visibility graphs,” submitted.

  3.  M. Cox#, J. Ellis-Monaghan, T. Hughes, K. Mondanaro, “Hydrocarbon links in an octet truss,” The Journal of Mathematical Chemistry, 43, no. 2 (2008) 874-891.

  4. J. Ellis-Monaghan, I. Sarmiento, “Distance hereditary graphs and the interlace polynomial,”  Combinatorics, Probability and Computing., 16, no.6 (2007) 947-973  http://arXiv.org/abs/math/0604088

  5. J. Ellis-Monaghan, P. Gutwin, J. Lewis, G. Pangborn, “Principles of force directed floorplanning”, submitted. (PDF--133 KB)

  6. D. Archdeacon, P. Bonnington, J. Ellis-Monaghan, “How to exhibit toroidal maps in space,”  Discrete and Computational Geometry, 38, (2007) 573-594.  (PDF--212 KB)

  7. J. Ellis-Monaghan, I. Sarmiento, “Isotropic systems and the interlace polynomial,”  (Postscript--320 KB,  figures, postscript 30 to 90 KB each: fig 1 pivot, fig 2 circle, fig 3 state, fig 4 medial., fig 5 complementation, fig 6 pendant duplicate, fig 7 configs in medial)

  8. J. Ellis-Monaghan, D. Pike, Y. Zou, “Decycling of Fibonacci cubes,” The Australasian Journal of Combinatorics 35 (2006), 31-40. postscript files/fibocube.ps

  9. Parameterized Tutte polynomials of weighted graphs and matroids (with Lorenzo Traldi) Combinatorics, Probability, and Computing 15 (2006) 835-854. This version includes detailed computations for prop. 7.2 left to the reader in the submitted version.  (PDF--192 KB)  (details.pdf)

  10.  Transition Polynomials, Double Covers, and Biomolecular Computing, Congressus Numerantium, 166 (2004) 181-192.  (PDF--169 KB)

  11. Some remarks on domination (with D. Archdeacon, D. Fisher, D. Froncek, P. C. B. Lam, S. Seager, B. Wei, and R. Yuster), Journal of Graph Theory, 46 no 3 (2004) 207-210.

  12. Exploring the Tutte-Martin connection, Discrete Mathematics, 281, no 1-3 (2004) 173-187. [click here for postscript file--799 KB]  

  13. Identities for the circuit partition polynomials, with applications to the diagonal Tutte polynomial, Advances in Applied Mathematics, 32 no. 1-2, (2004) 188-197. . [Click here for postscript file--305 KB].  

  14. Graph Theoretical Problems in Next Generation Chip Design (with P. Gutwin),Graph theoretical problems in next generation chip design, Congressus Nu me rantium, 163 (2003) 143-159.  [click here for postscript file--810 KB]  

  15. Generalized transition polynomials (with I. Sarmiento), Congressus Numerantium 155 (2002) 57-69.[click here for postscript file--491 KB].

  16. Medial graphs and the Penrose polynomial (with I. Sarmiento), Congressus Numerantium 150 (2001), 211–222.[click here for postscript file--2 files]   

  17. Differentiating the Martin polynomial.   Congressus Numerantium 142 (2000), 173–83.[click here for postscript file--449 KB]

  18. Martin polynomial miscellanea. Congressus Numerantium 137 (1999), 19–31. [click here for postscript file--481 KB]

  19. New results for the Martin polynomial. Journal of Combinatorial Theory, series B 74 (1998), 326–52. [click here for postscript file--4 files]

PEDAGOGY PAPERS:

  1. J. Ellis-Monaghan, "Considering the chalkless classroom," submitted.

  2. Financing your dream home (with George Ashline), submitted.  

  3. G. Ashline, J. Ellis-Monaghan, “How high?  How fast?  How long?  Modeling water rocket flight with calculus,” PRIMUS XVI, no. 2 (2006), 121-137

  4. G. Ashline, J. Ellis-Monaghan, “A house of your own: The mathematics of the American dream, part II,” The New Jersey Mathematics Teacher 63 no. 2 (2005)  20-26.

  5. G. Ashline, J. Ellis-Monaghan, “Credit cards and cars: The mathematics of the American dream, part I,” The New Jersey Mathematics Teacher, 63 no. 1 (2005) 16-23.

  6. Surreal Seashells (with A. Daniels, SMC '04) , The Pi Mu Epsilon Journal, 12 no. 1 (2004) 36.

  7. The lottery: A dream co me true or a tax on people who are bad at math?  (with G. Ashline),  PRIMUS XIV no. 4 (2004) 303-314.

  8. Water rockets in flight: Calculus in action (with George Ashline and Alain Brizard), UMAP/ILAP Modules, 2002-2003: Tools for Teaching.  151-189.

  9. Home sweet home: A financial incentive for the lower level mathematics course (with George Ashline), PRIMUS XI, no. 1 (2001), 16–26.

  10. How many people are in your future? Elementary models of population growth (with George Ashline),  in Making meaning: Integrating science through the case study approach to teaching and learning, ed. S. Kuntz et al,  McGraw-Hill Primis, 1999, pp. 42–80.

  11. How many people are in your future? Elementary models of population growth (with George Ashline) (updated version), Case studies in ecology, ed. S. Kuntz et al., accompanying the 1st editions of Manuel Molles’ text Ecology: Concepts and Applications. WCB McGraw-Hill, New York, 1999.

  12. Interdisciplinary population projects in a first semester calculus course (with George Ashline), PRIMUS IX (March 1999), 39–55.

  13. Microcosm to macrocosm: Population models in biology and demography (with George Ashline), Tools for Teaching, UMAP unit 777 (1999), 39–80

Saint Michael's-related links

For more information, you may want to check out these.

Other Stuff

Maple Home Page   Very, very cool Maple stuff--including lots of demos for understanding calculus concepts for example.  Check out the Maple Applications and the Student pages.

http://www.lactamme.polytechnique.fr/ Gorgeous math/science art pictures with explainations.

MathSciNet   This is the foremost research tool for mathematicians--a searchable index, with reviews, to current mathematical articles.

http://birrell.org/andrew/knotwork/  Very cool applet for generating celtic knots

UVM/SMC Joint  Combinatorics Seminar  Biweekly speakers from academia and industry using and developing combinatorial techniques.

Graph Theory Resources   This site has links to people, problems, journals, etc. involved with graph theory.

Math Archives This is a huge archive of all kinds of math related resources, from teaching resources to CAS (eg Maple) support, from graphing calculators to electronic journals.

POPMathematics   What is POP Mathematics?  From the site creators:

http://www.ams.org/careers/mcbb.html   Check out this web site for lots of people doing cool (math-related) things you might be interested in too.

Actuarial Careers  Here are some links providing information about actuarial careers.

The following website has some great explainations and good Java applets for a wide range of mathematical concepts. http://www.math.montana.edu/~frankw/ccp/Java/Overview.htm

The wallpaper on this page was modified from wallpaper taken from http://www.eccentrics.com/scruffypup/ where there are lots of other very lyrical wallpapers.

Family only, please.

Netlist

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When this site was last updated:  04/16/08