Dr. Margaret Symington

Professor of Mathematics

Margaret SymingtonEducation

  • Ph.D. in  Mathematics, Stanford University
  • M.S. in Mathematics, Stanford University
  • Sc.M. in Applied Mathematics, Brown University
  • Sc.M. in Engineering, Brown University
  • B.A. in Mathematics, Brown University
  • B.A. in Engineering, Brown University

Courses Taught

  • Introduction to Finite Mathematics (MAT 104)
  • Precalculus (MAT 133) and College Algebra: Functions and Graphs (MAT 131)
  • Calculus I, Calculus II, Multivariable Calculus, and Calculus for the Social Sciences (MAT 191, 192, 293 and 141)
  • Introduction to Abstract Mathematics (MAT 260)
  • Differential Equations (MAT 330)
  • College Geometry (MAT 350)
  • Special Topics (MAT 390): Topology, Complex Analysis
  • Directed Independent Study (MAT 401): Symplectic Geometry, Contact Geometry, Topology, Partial Differential Equations, Measure Theory, Differential Geometry
  • Abstract Algebra I, II (MAT 461, 462)
  • Building Community (INT 101) – an intedisciplinary writing-instruction course
  • First-Year Student Experience (UNV 101)

Student Projects Supervised

  • Edward (Alex) White ’15, Honors project: Counterpoint Geometry
  • Adam Lewis ’12, Klein and hemispherical models of non-Euclidean geometry
  • Informal research project involving multiple students in 2011 and 2012, Centers of Triangles
  • Chris Kirkland ’12, Locus of Incenters
  • Zuhair Hasan, Bear Day project, 2011: Plane Curves and Linkages
  • Daniel Brown ’10, Project in support of Dr. Klingelhofer’s reaserach in archeology : Geometric model of Fort Raleigh at First Colony
  • Andrew Gainer ’07,  Honors project: PL-Boundaries of Surfaces that Immerse Isometrically in R2

Scholarly and Professional Interests

For the non-specialist: I am interested in  geometry and topology — in fact, any topic in which visualization helps provide insight.  Mathematics research, for me, usually involves drawing lots of pictures.  In my work in symplectic topology (my specialty) I am frequently use two-dimensional diagrams to represent certain four-dimensional spaces. One fun collaboration was with Joshua Lane, a dermatological surgeon. I helped him with a paper of his in the journal Dermatologic Surgery, and that work led to an interesting geometry problem that I described in an expository article, Euclid Makes the Cut, that appeared in Math Horizons.

For fellow researchers: My expertise is in symplectic topology, in particular the topology of symplectic manifolds of dimension four.  I am interested in questions at the interface of symplectic topology, toric geometry, the topology of smooth four-manifolds, and integrable systems.

Current Projects

  • I am writing the symplectic geometry half of a book, Elementary Contact and Symplectic Geometry; Joan Licata (Australian National University) is writing the contact geometry half. The book aims to introduce undergraduates who have had only multivariable calculus and linear algebra to the subjects of contact and symplectic geometry. That’s right; no differential forms.
  • I have an ongoing collaboration with Sonja Hohloch (University of Antwerp), Silvia Sabatini (University of Cologne) and Daniele Sepe (Federal Fluminense University) focused on semi-toric systems, integrable systems with enough symmetry that for a suitable choice of moment map one can understand a lot about the system from its moment map image in R2.

Publications

Most of the mathematics papers listed below are available on the arXiv here.

  • The Mercer Reader: Essential Texts and Voices. XanEdu Press, Acton, MA, 2108. (co-edited with Andrew Silver and Tanya Sharon)
  • Faithful semitoric systems. SIGMA 14 (2018), 084, 66 pages. arXiv:1706.09935. (with Sonja Hohloch, Sivia Sabatini and Daniele Sepe)
  • Euclid makes the cut. Math Horizons. 19 (2012) no. 3, 6-9.
  • Almost toric symplectic four-manifolds. Journal of Symplectic Geometry. 8 (2010) no. 2, 143-187. math.SG/0312165. (with Naichung Conan Leung)
  • Toric structures on near-symplectic four-manifolds. Journal of the European Mathematical Society, 11 (2009) no. 3, 487-520. math.SG/0609753. (with David Gay)
  • Four dimensions from two in symplectic topology. Topology and geometry of manifolds(Athens, GA, 2001), 153{208, Proc. Sympos. Pure Math., 71, Amer. Math. Soc., Providence, RI, 2003.
  • Generalized symplectic rational blowdowns. Algebraic and Geometric Topology, 1 (2001) 503-518 (electronic).
  • Symplectic rational blowdowns. Journal of Differential Geometry, 50 no. 3 (1998) 505-518. A new symplectic surgery: the 3-fold sum. Topology and its Applications 20 (1997) 1-27.
  • Associativity properties of the symplectic sum. Mathematical Research Letters, 3 no. 5 (1996) 591-608. (with D. McDuff)
  • Mathematical modeling of donor skin-sparing full-thickness skin grafts – something does not add up. Dermatologic Surgery. Letter to the editor. 36 (2010) 573-4. (with Joshua Lane)
  • Repair of Large Surgical Defects with a Donor Skin-Sparing Full-Thickness Skin Graft. Dermatologic Surgery. 35(2009) 1-5. (with J. Lane)
  • A finite element method for determining the angular variation of asymptotic crack tip fields. International Journal of Fracture 45 (1990) 51-64. (with M. Ortiz and C.F. Shih)
  • Eigenvalues for interface cracks in linear elasticity. Journal of Applied Mechanics 54 (1987) 973-974.

Contact Dr. Margaret Symington

(478) 301-2815
symington_mf@mercer.edu