Pictures

Research Interests

• Complex Dynamics
• Complex Analysis
• Fractals

Publications

• Mobius Semigroup Attractors, in Topics in Finite or Infinite Dimensional Complex Analysis: Proceedings of the 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, (2013), 49 - 61.  
  
  
• Complex Dynamics: Chaos, Fractals, the Mandelbrot Set, and More, to appear, this is an 83-page chapter for the NSF funded textbook Explorations in Complex Analysis, Mathematical Association of America.   See http://www.maa.org/ebooks/crm/EXCA.html and http://www.maa.org/ebooks/EXCA/applets.html.

   

• Complex Dynamics of Mobius semigroups, with David Fried and Sabastian Marotta, Ergodic Theory and Dynamical Systems, 32 (2012), no. 06, 1889-1929 (dvi; ps, pdf)
  
  
• Density of repelling fixed points in the Julia set of a rational or entire semigroup, II, Discrete and Continuous Dynamical Systems Ser. A, 32 (2012), 2583 - 2589. (dvi; ps, pdf)
   
• Dynamical properties and structure of Julia sets of postcritically bounded polynomial semigroups, by Rich Stankewitz and Hiroki Sumi, Transactions of the American Mathematical Society, 363 (2011), no. 10, 5293–5319. (dvi; ps, pdf)
   

• Density of repelling fixed points in the Julia set of a Rational or Entire Semigroup, Journal of Difference Equations and Applications, Vol. 16, Nos. 5–6, 763–771. (dvi; ps, pdf)  
   

• Complex Dynamics of Rational Semigroups, with Hiroki Sumi Mathematisches Forschungsinstitut Oberwolfach Report No. 9/2007, Normal Families and Complex Dynamics, pp. 538 - 540.
   

• Random dynamics of polynomials and postcritically bounded polynomial semigroups, authored with Hiroki Sumi, Complex analysis and its applications, 333-338, OCAMI Stud., 2, Osaka Munic. Univ. Press, Osaka, 2007.
   

• Structure of Julia sets of polynomial semigroups with bounded finite postcritical set, by Rich Stankewitz and Hiroki Sumi, Applied Mathematics and Computation 187 (2007) pp. 479-488. (dvi; ps, pdf)
   
• Uniformly perfect sets and complex dynamics, Proceedings of the 12th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (2005), pp. 331-338, Kyushu University Press. 
  
  
• Conjectures and Counterexamples in dynamics of rational semigroups, authored with Toshiyuki Sugawa, and Hiroki Sumi, Advances in Analysis Proceedings of the 4th International ISAAC Congress (2005), pp. 549-556, World Scientific Publishers, (refereed proceedings). 
   

•  Introduction to Quasiconformal Mappings in the plane with an application to quasiconformal surgery, by Nathan Mercer and Rich Stankewitz.   (dvi; ps, pdf) Updated 8-25-07.  Feel free to download the latex file and zipped figures file (figures created by WinFIG) if you are interested in modifying it for your own purposes.  We also welcome any feedback on this, in particular, any suggestions that might make this a more useful learning tool for others.
   

• Some counterexamples in dynamics of rational semigroups, by Rich Stankewitz, Toshiyuki Sugawa and Hiroki Sumi, Ann. Acad. Sci. Fenn. Math. 29 (2004), no. 2, 357--366. (dvi; ps, pdf)
   
• Uniformly perfect analytic and conformal attractor sets, Bull. London Math. Soc. 33 (2001), no.3, pp.320-330 (dvi; ps, pdf)
   
• Uniformly perfect sets, rational semigroups, Kleinian groups and IFS's, Proc. Amer. Math. Soc. 128 (2000), no. 9, 2569--2575. (dvi; ps, pdf)
   
• Completely Invariant Sets of Normality For Rational Semigroups, Complex Variables Theory Appl. 40 (2000), no. 3 , pp. 199-210. (dvi; ps, pdf)
   
• Uniformly perfect sets, rational semigroups, Kleinian groups and IFS's, Proceedings of the Second ISAAC Congress, vol. 1, pp.383--388, Kluwer Academic Publishers (2000)
   
• Dynamics of Rational semigroups (lecture notes based on mini-course given at Georg-August-Universität Göttingen in June 22 - July 2, 1998 by David Boyd and Rich Stankewitz) (dvi; ps, pdf)
   
• Completely Invariant Julia Sets For Polynomial Semigroups, Proc. Amer. Math. Soc. 127 (1999), no. 10, 2889--2898. (dvi; ps, pdf)

Education and Prior Work Experience

•    B.S. in Mathematics from the University of Michigan in 1991
•    Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign with thesis advisor Professor Aimo Hinkkanen in 1998
•     Visiting Assistant Professor of Mathematics at Texas A&M University from 1998-2000
•     Assistant Professor of Mathematics at Penn State University at Erie from 2000-2002

Other Interests

I enjoy basketball, football, golf, weight lifting, softball, ultimate Frisbee, biking, playing cards, watching movies, and dogs.