Adrian Jenkins Department of Mathematics Kansas State University 125 Cardwell Hall Manhattan, KS, 66506-2067 USA Phone: (785)532-0595 Email: [email protected]

Citizenship: United States of America

Current and Previous Positions:

• I-Center Postdoctoral Fellow Kansas State University, Manhattan, 2008-present • Research Assistant Professor of Mathematics Purdue University, West Lafayette, 2005-2008. • KTI Fellow University of Wisconsin, Madison, 2004-2005. • Graduate Teaching Assistant University of Wisconsin, Madison, 1998-2004.

Education:

• Doctor of Philosophy in Mathematics University of Wisconsin, Madison, August 2005 Advisor: Xianghong Gong • Master of Arts in Mathematics University of Wisconsin at Madison, December 2000. • Bachelor of Arts in Mathematics Kennesaw State University, Kennesaw, Georgia, June 1997 (Summa Cum Laude)

Research Interests: My research mostly considers the local dynamics of analytic maps defined near a fixed point, with respect to both archimedean and non-archimedean norm. Specifically, I am interested in the following questions:

• What smoothness criteria may be attached to existing conjugating maps between holomorphic func- tions within Cn? • What are the analytic conjugacies present between mappings who eigenvalues possess resonance, in both the archimedean and non-archimedean categories, in two (or more) dimensions? • In the non-archimedean setting, is it possible to give sharp estimates of the coefficients of an expansion of some analytic conjugating map at the fixed point (which is typically chosen to be the origin)? • What connections and comparisons can be drawn between the archimedean and non-archimedean local theories? (The contrasts are often more easily determined.)

See my research statement for a fuller accounting of these topics, as well as for other interests. Publications and Preprints:

• (With Steven Spallone) Local analytic conjugacy of resonant analytic mappings in two variables, in the nonarchimedean setting, preprint • (With Steven Spallone) Lipeomorphic equivalence of p-adic functions: a comparison between com- plex and p-adic dynamics, submitted • (With Steven Spallone) A p-adic approach to local analytic dynamics: analytic flows and analytic mappings tangent to the identity; Ann. Fac. Sci. Toulouse Math., Vol. XVIII, no. 3 (2009), 611- 634. • (With Greg Buzzard) Holomorphic motions and structural stability for polynomial automorphisms of C2; Indiana University Mathematics Journal, 57 (2008), no. 1, 277-308. • Further reductions of Poincare-Dulac´ normal forms in a neighborhood of the origin in Cn+1; Pro- ceedings of the American Mathematical Society, 136 (2008), 1671-1680. • Holomorphic germs and the problem of smooth conjugacy in a punctured neighborhood of the origin; Transactions of the American Mathematical Society, 360 (2008), 331-346. • Equivalences of Holomorphic Mappings in One and Several Complex Variables, Ph.D. Thesis (August 2005); Advisor: Xianghong Gong, University of Wisconsin-Madison

In Preparation:

• (With Harold Blum and Hank Ditton) A sharper estimation of analytic conjugacies in the non- archimedean setting (In conjunction with Kansas State’s Research Experience for Undergraduates)

Selected Presentations:

• Lipschitz Dynamics: A Comparison Between Archimedean and Non-Archimedean Theories; Analysis Seminar, Kansas State University, September 2010. • Local Dynamics: Comparisons of the Euclidean and Non-Archimedean Theories; Karcher Colloquium, University of Oklahoma, October 2008. • Local Dynamics in the Non-archimedean Setting; Mathematics Colloquium, Clemson University, February 2008. • Complex Dynamics in One and Two Dimensions; Mathematics Colloquium, University of Cincinnati, May 2007. • Structural Stability of Hyperbolic Polynomial Automorphisms of C2; Special Analysis Seminar, University of Georgia, March 2007. • Further Normalizations of Poincare-Dulac´ Normal Forms in Cn+1; AMS Spring Sectional Meetings, University of Notre Dame, March 2006 • Smooth Conjugacy of Holomorphic Germs in a Punctured Neighborhood of the Origin in C; Midwest Conference in Several Complex Variables, Indiana University, 2005 • Teaching Mathematics and Science to Non-Majors, L&S Workshop, University of Wisconsin-Madison, August, 2003 Synergistic Activities

• Director, Research Experience for Undergraduates, Kansas State University, Summer 2010; “Sharper estimation of analytic conjugacy in the non-archimedean setting”

• (With Steve Bell and Philip Mummert) Assistant Director, Research Experience for Undergraduates, Purdue University, Summer 2006; “Numerical computation of zeroes of holomorphic functions”

• Fellow, “K-through-Infinity Systems Initiative”; June, 2004 through May, 2005.

Awards and Honors:

• Excellence in Teaching Award, Purdue University, August 2006

• L&S Teaching Fellow, University of Wisconsin–Madison, May 2003

• Sustained Excellence in Teaching Award, University of Wisconsin-Madison, May 2003

• Excellence in Teaching Award, University of Wisconsin-Madison, May 2000

Committee experience:

• Committee on Teaching Assistant Practices and Principles, Fall 2004–Spring 2005.

• TA Evaluation Committee, Fall 2001-Spring 2003.

References:

• Greg Buzzard, Dept. of Math., Purdue University, [email protected]

• Xianghong Gong, Dept. of Math., University of Wisconsin, [email protected].

• Pietro Poggi-Corradini, Dept. of Math., Kansas State University, [email protected]

• Marianne Korten (teaching), Dept. of Math., Kansas State University, [email protected]