Primary
Singularities in celestial mechanics. Other mathematical interests include: discrete dynamics, voting theory, tilings, and mathematics of music composition.

Secondary
Jewish Women's Studies including Women and Jewish Law and the history of Jewish women in America.

Research Visits

• Universidad Autonoma Metropolitana, Mexico City, Research Visit, October 11-17, 2008
• UC, Santa Cruz, Off-campus Scholarly Assignment, September, 2005-July, 2006
• Hadassah Brandeis Institute, Fellowship, July 1-31, 2003
• Boston University, Research Visit, July 1-31, 2003
• Universidad Autonoma Metropolitana, Mexico City, Research Visit, July 7-21, 2001
• University of Victoria, Research Visit, June 1-30, 1999
• University of Minnesota, Geometry Center, Research visit, January 5-13, 1997

• Published
  

  ``Symbolic Dynamics of the elliptic rectilinear restricted three-body problem'' jointly with Lacomba, Ernesto and Llibre, Jaume Discrete and Continuous Dynamical Systems Series S, 1 no. 4, 2008, 541--555. MR 2448929.

  ``A survey of symbolic dynamics and celestial mechanics'' Qualitative Theory of Dynamical Systems 7 no. 1, 2008, 181--193. MR 2438802.

  ``Making the moon reverse its orbit, or, stuttering in the planar three-body problem'' jointly with Levi, Mark and Montgomery, Richard Discrete Contin. Dyn. Syst. Ser. B 10 no. 2-3, 2008, 569--595. MR 2425057.

  ``The Dotty Number'' Mathematics Magazine, 80 (2007), 73--74. MR1573456

  ``The Collision Manifold of the Collinear One-Bumper Two- Body Problem'' Celestial Mechanics January, 2001, 1--14. MR 2002f:70027.
  
  ``A Bifurcation Problem in Sophomore Differential Equations'' jointly with Duff Campbell, Duff. Mathematics Magazine Journal, 73 June 2000, 194--203.
  
  ``Symbolic Dynamics of the Collinear Three-Body Problem'' Geometry and Topology in Dynamics (Winston-Salem, NC and San Antonio, TX), 87--107, Contemp. Math., 246, Amer. Math. Soc., Providence, RI, 1999. MR 2000k:70014.
  
  ``The Collinear One-Bumper Two-Body Problem with Unequal Masses'' Dynamics and Stability of Systems 13 (1998) 27--54 MR 99c:70016.
  
  ``Dynamics of the Collinear One-Bumper Two-Body Problem'' J. Differential Equations, 140 (1997) 378--414 MR 98m:700.
  
  ``The Collinear One-Bumper Two-Body Problem'' Hamiltonian dynamics and celestial mechanics (Seattle, WA, 1995), 87--107, Contemp. Math., 198, Amer. Math. Soc., Providence, RI, 1996. 70F05 MR 97e:70014.
  
  ``Directions of Hamiltonian dynamics and celestial mechanics'' jointly with Cushman, Richard; Hu, Sen; Llibre, Jaume; McCord, Christopher; Saari, Donald G.; Xia, Zhihong Hamiltonian dynamics and celestial mechanics (Seattle, WA, 1995), 229--240, Contemp. Math., 198, Amer. Math. Soc., Providence, RI, 1996. 58Fxx (70Fxx) MR 97g:58059.
  
  

• Submitted

  ``Properties of Certain Random Trees'', with Patrick Bahls, submitted to Studia Scientiarum Math. Hungarica September, 2008

  ``The Portfolio Problem in Vector Calculus'' submitted to PRIMUS, December, 2006. Accepted. Expected publication date is late 2008.
  
  
  
  

Maxx Cho, Research Experiences for Undergraduates, "The Algebraic Compatability of Riemannian Operators' Voice-leading Properties" , Summer 2008

Greg Marcil, Research Experiences for Undergraduates, "Constructability of Closed Hyperbolic k,n Tilings", Summer 2008

Betsy Katz and Colleen McCarthy, Research Experiences for Undergraduates, "Multiple edge graph growth with geographical attachment," with Patrick Bahls and David Peifer, Summer 2008

Theo Schoen, "Power series expressions for the Dottie Number", Spring 2008

Mallory Schaffert, "Hyperbolic Pillows", Spring 2008

Mallory Schaffert, Theo Schoen and Roger Letterman, "Constructability of Hyperbolic Pollows", Fall 2007.

Emily Ward, Research Experiences for Undergraduates, "Hyperbolic Pillows", Summer 2007

Christina Harlow, Undergraduate Research, "Chemistry and Topology", Spring 2005

Katie Senechal, Undergraduate Research, "Applications of Asymmetric Measures to Trial Difficulty", Fall 2004 - Spring 2005

Andrew Layton, Undergraduate Research, "Voting and Markov Processes", Fall 2004- Spring 2005

Loring Watkins, Undergraduate Research, "Chaos and Complex Newton's Method", Fall 2004 - Spring 2005

Jennifer Marshall, Andrew Layton, Kyle Anderson, Undergraduate Research Team Project, "An Interdisciplinary Approach to a Math Web Site", jointly led with Ed Johnson, Summer 2004

Mark Ciccarello and Andrew Nicholson, Undergraduate Research Team Project, "Is the Weather Chaotic?", Summer 2004

Jonathon Meadows, Undergraduate Research, "The Intermediate Value Theorem Without Continuity", Fall 2003 - Spring 2004

Stuart Bateman, Undergraduate Research, "The Laundry Problem: An Introduction to Circle Maps", Spring 2001 - Spring 2003

John Edwards, Undegraduate Research, "Dynamics of two bodies on a circle", Spring 2001

Tim Means, Undergraduate Research, "The two-body Manov problem with an application to satellite orbits.", Fall 1999 - Spring 2000

Lars Ingrao, Undergraduate Research, "A^&pi: Matrices Raised to Arbitrary Powers", Fall 1999 - Spring 2000

Monica Ares, Independent Study, "Markov Chains and Musical Analysis", Fall 1998

Lauren Key, Independent Study, "Tilings and the art of Escher", Spring 1998

Nathan Chandrasekaran, Independent Study, "Oscillator Models in Neurobiology", Spring 1998

Scott Hoenig, Honors Project, "On the dynamics of a frisbee", Fall 1997-Spring 1998

Andrea Vogl, Independent Study, "The geometry of post-tonal music theory", Spring 1997

Associate Professor, University of North Carolina at Asheville

July, 2004 - present

July, 1999 - June, 2004

August, 1996 - June, 1999

Fall 1993 and Spring 1994

Fall 1992 - Spring 1994

Summer, 1992

Fall 1991 and Spring 1992

Summer 1989 and Summer 1990

Fall 1989

Summer 1988 and Summer 1989

``Empowering Teachers and Students through Problem-Based Mathematics''
Math Science Partnership Conference, Washington D.C., January 6, 2009

``Hyperbolic Pillows''
AMS-MAA Joint Math Meeting, San Diego, January 7, 2008

``Can The Moon Reverse its Orbit?''
Colloquium, Wake Forest Univeristy, April 23, 2007

``Stuttering in the Planar Three-Body Problem''
AMS Sectional Meeting, Davidson College, March 3, 2007

``The Geometry of Post-tonal Music Theory''
Undergraduate Symposium at UC, Santa Cruz, March 1, 2006
Undergraduate Symposium at San Jose State University, February 1, 2006
Southeastern SIAM Meeting, March 25, 2005

``Sisterhoods of Personal Service''
Women's History Month, UNC, Asheville March 14, 2005
Memorial Lecture, Beth HaTephila, Asheville, September 25, 2004

``The Restricted Collinear Three-body Problem''
AMS Southeast Sectional Meeting, UNC, Chapel Hill October 24, 2003
International Conference on Dynamical Systems and Applications, Morehouse College, Atlanta, May 21, 2003
Carolina Dynamics Group, UNC, Charlotte, April 12, 2003
Senior Seminar, UNC, Asheville, January 29, 2003
AMS-MAA Joint Math Meeting, Baltimore, January 14, 2003

``Symbolic Dynamics in the Collinear Three-Body Problem''
Department Seminar, Universidad Autonoma Metropolitana July 19, 2001
World Congress of Nonlinear Analysts, Catania, Italy July 24, 2000
Math Department, University of North Carolina at Greensboro, Greensboro, NC, February 24, 1999
AMS Southeast Sectional Meeting, Winston-Salem, October 9, 1998

``Stability of the Helium Atom''
AMS Northeast Sectional Meeting, Lowell, MA April 1, 2000

``Undergraduate Research at UNCA''
Conference on Models for Integrating Research into the Undergraduate Experience, University of Arizona, Tuscon, AZ, February 26, 2000

``Open Problems in Celestial Mechanics''
Senior Seminar, University of North Carolina at Asheville, Asheville, NC, January 26, 2000
Department Seminar, Bowdoin College, Brunswick, ME, April 20, 1998

``From Order to Chaos: The Revolution''
Math Club Talk, North Carolina School of Science and Mathematics, Durham, NC, March 28, 2000
Department Seminar, Trinity College, Hartford, March 5, 1998

``Women and Mathematics Education''
Women's History Month, University of North Carolina at Asheville, Asheville, NC, March 20, 2000

``From Kepler's Monsters to Thurston's Doughnut''
Santa Clara University, May 10, 2006
University of California, Santa Cruz, May 1, 2006
Math Department, University of North Carolina at Asheville, Asheville, NC, February 22, 1999
Math Department, Dickinson College, Carlisle, PA, February 17, 1999
Math Department, Marymount University, Vienna, VA, February 12, 1998

``Dynamics of the Collinear One-Bumper Two-Body Problem''
Department Seminar, University of Connecticut, Storrs, March 6, 1998
Open Seminar, SUNY-Utica, Utica, NY, February 19, 1998
Joint Mathematics Meeting, Baltimore, January 8, 1998

``A Model of the Collinear Three-Body Problem''
AMS-SMM Joint Meeting, Oaxaca, Mexico, December 4, 1997

``Differential Equations and Art''
Gallery Talk, Bowdoin College Museum of Art, Brunswick, ME, October 30, 1997

``Voting Theory''
Department Seminar, Bowdoin College, Brunswick, ME, October 13, 1997

``The Collinear One-Bumper Two-Body Problem''
AMS Southeast Sectional Meeting, Atlanta, October 18, 1997
Midwest Dynamical Systems Conference, University of Minnesota, Minneapolis, September 19, 1997
Institute for Mathematical Sciences, SUNY-Stony Brook, April 11, 1997
Dynamics Seminar, University of Minnesota, January 9, 1997
Department Seminar, Bowdoin College, June 6, 1996
Dynamics Seminar, Boston University, April 1, 1996

``Tilings and Tessellations''
Math Field Day, Boston University, October 25, 1996

``Bifurcations in the Collinear One-Bumper Two-Body Problem''
Bifurcations and Singularities in Dynamical Systems, Geometry Center, Minneapolis, October 20, 1996

I was born and raised in Valdese, North Carolina. My parents, sisters and their families still live in NC. In 1996, my in-laws also moved to North Carolina.

As a graduate student in Boston, I met my wife, Geri Garfinkel. Soon after we moved to Maine, our daughter, Zoe was born. Our son, Abraham, was born not long before we left Maine. Maine was very good to us.

Left: Zoe Sarah Kaplan
Right: Abraham Julius Kaplan
Photo taken in Port Renfrew, British Columbia, 1999