Research

Dynamical Systems and Connections with Mathematical Physics.  Formerly: Hyperbolic Geometry.

Education

• Ph.D. - Cornell University http://www.math.cornell.edu, 2005.
• Docteur de Mathematiques - Universite de Provence, Aix-Marseille http://www.up.univ-mrs.fr/document.php?project=cmi, 2004.
• B.A. Math - University of California, San Diego http://www.math.ucsd.edu/, 2000.

Publications & Professional Activity

Research partially supported by:

NSF Career grant DMS-1348589. (Formerly by NSF Grant DMS-1102597 and start-up funds from the IUPUI Department of Mathematical Sciences.)

Preprints:

• Scott Kaschner and Roland Roeder Complex perspective for the projective heat map acting on pentagons.
• Pavel Bleher, Mikhail Lyubich, and Roland Roeder. Lee-Yang-Fisher zeros for DHL and 2D rational dynamics, II. Global Pluripotential Interpretation.

Accepted for publication:

• Pavel Bleher, Mikhail Lyubich, and Roland Roeder. Lee-Yang Zeros for the DHL and 2D Rational Dynamics, I. Foliation of the Physical Cylinder.  To appear in Journal de Mathématiques Pures et Appliquées.
• Roland Roeder. Around the Boundary of Complex Dynamics (lecture notes for undergraduates). To appear in EMS Lecture Series book Dynamics done with your bare hands. Center for Mathematics at Notre Dame. Edited by Françoise Dal'Bo, François Ledrappier and Amie Wilkinson.

Published Papers

• Sarah Koch and Roland K.W. Roeder.  Computing Dynamical Degrees.  Ergodic Theory and Dynamical Systems, 36(8): 2538-2579, 2016.
• Jeffrey Diller, Han Liu, and Roland Roeder. Typical dynamics of plane rational maps with equal degrees.  Journal of Modern Dynamics, 10: 353 - 377, 2016.
• Pavel Bleher, Yushi Homma, and Roland Roeder Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials.  International Math Research Notices (IMRN), 2016(11): 3237-3278.
• Scott Kaschner, Rodrigo Perez, and Roland Roeder. Examples of rational map of CP^2 with equal dynamical degrees and no invariant foliation.  Bulletin de la SMF, 144(2): 279-297, 2016.
• Roland K. W. Roeder. The action on cohomology by compositions of rational maps. Math Research Letters, 22(2): 605-632, 2015.
• Scott R. Kaschner and Roland K.W. Roeder. Superstable manifolds of invariant circles and co-dimension 1 Bottcher functions. Ergodic Theory and Dynamical Systems, 35(1): 152 - 175, 2015.
• Pavel M. Bleher, Youkow Homma, Lyndon L. Ji, and Roland K.W. Roeder. Counting Zeros of Harmonic Rational Functions and Its Application to Gravitational Lensing.  International Math Research Notices,  2014(8): 2265-2293.
• Pavel M. Bleher, Youkow Homma, Lyndon L. Ji, Roland K. W. Roeder, and Jeffrey Shen Nearest Neighbor Distances on a Circle: Multidimensional Case. Journal of Statistical Physics, 146(2): 446-465, 2012.
• Roland K. W. Roeder. A dichotomy for Fatou components of polynomial skew products. Conformal Geometry and Dynamics, 15: 7-19, 2011.
• Suzanne Lynch Hruska and Roland K. W. Roeder. Topology of Fatou components for endomorphisms of CP^k: Linking with the Green's current. Fundamenta Mathematicae, 210(1): 73-98, 2010.
• Enrique R. Pujals and Roland K. W. Roeder. Two Dimensional Blaschke Products: Degree Growth and Ergodic Consequences. Indiana University Mathematics Journal, 59(1): 301-326, 2010.
• Omar Antolin-Camarena, Gregory R. Maloney, and Roland K.W. Roeder. Computing arithmetic invariants for hyperbolic reflection groups, In Complex Dynamics: Families and Friends (D. Schleicher editor) pages 597-631, A.K. Peters, 2008.  (See SNAP-HEDRON PARI/GP computer scripts.)
• Roland K.W. Roeder Constructing hyperbolic polyhedra using Newton's Method Experimental Mathematics, 16(4): 463-492, 2007. (See HYPER-HEDRON computer scripts.)
• Roland K.W. Roeder, John H. Hubbard, William D. Dunbar. Andreev's Theorem on Hyperbolic Polyhedra, les Annales de l'Institut Fourier, 57(3): 825-882, 2007.
• Roland K.W. Roeder Topology for the basins of attraction of Newton's Method in two complex variables: linking with currents J. Geometric Analysis. 17 (1): pp. 107-146, March 2007.
• Roland K.W. Roeder Compact hyperbolic tetrahedra with non-obtuse dihedral angles. Publicacions Matematiques, 50 (1): 211-227, 2006 .
• T.E. Evans, R.K.W. Roeder, J.A. Carter, and B.I. Rapoport Homoclinic Tangles, bifurcations and edge stochasticity in diverted tokamaks Contributions to Plasma Physics, 44 (1-3): 235-240, 2004.
• R.K.W. Roeder, B.I. Rapoport, and T.E. Evans Explicit calculations of homoclinic tangles in tokamaks. Physics of Plasmas, 10 (9): 3796-3799, 2003.
• Roland K.W. Roeder On Poincare's fourth and fifth examples of limit cycles at infinity, Rocky Mountain Journal of Mathematics, 33 (3): 1057-1082, 2003.

Unrefereed publications

• T.E. Evans, R.K.W. Roeder, J.A. Carter, et al. Experimental signatures of homoclinic tangles in poloidally diverted tokamaks Journal of Physics: Conference Series 7 (2005) 174-190.
• J. Mahaffy, S. W. Polk, R.K.W. Roeder An age-structured model for erythropoiesis following a phlebotomy. CRM technical report number CRM-2598, 1999.

Theses

• Roland K.W. Roeder Topology for the basins of attraction of Newton's Method in two complex variables Ph.D. Thesis, Cornell University, Aug 2005.
• Roland K. W. Roeder Le Theorem d'Andreev sur polyedres hyperboliques (Andreev's Theorem on Hyperbolic polyhedra, in English) , Doctoral Thesis, Universite de Provence, Marseille France. Defended May, 2004.

Book contributions

• Chapter 14, titled: Andreev's Theorem. in: Teichmuller Theory and Applications to Geometry, Topology, and Dynamics. Volume II: Four Theorems by William Thurston by John H. Hubbard with contributions by Adrien Douady, William Dunbar, and Roland Roeder, as well as Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska, and Sudeb Mitra. In preparation to be published by Matrix Editions, see http://matrixeditions.com/TeichmullerVol2.html.
• Teichmuller Theory and Applications to Geometry, Topology, and Dynamics. Volume I: Teichmuller Theory by John H. Hubbard with contributions by Adrien Douady, William Dunbar, and Roland Roeder, as well as Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska, and Sudeb Mitra. Published by Matrix Editions (2006), see http://matrixeditions.com/TeichmullerVol1.html.

Affiliations

• Associate Professor, Department of Mathematical Sciences, IUPUI http://www.math.iupui.edu/, 2015-present.
• Assistant Professor, Department of Mathematical Sciences, IUPUI http://www.math.iupui.edu/, 2009-2015.
• Lecturer, The Institute for Mathematical Sciences, Stony Brook University http://www.math.sunysb.edu/html/ims.shtml, 2008-2009.
• Postdoctoral Fellow - University of Toronto http://www.math.utoronto.ca, 2006-2008.
• Jerrold E. Marsden Postdoctoral Fellow - Fields Institute http://fields.utoronto.ca, 2005-2006.

Awards

• 2014 Trustees Teaching Award
• 2012  Bernie Morrel Teaching Award