Diego Maldonado - Research


I am a member of the Analysis Research Group in the Math Department at KSU. I received my PhD from the University of Kansas in the Summer of 2005 under Rodolfo Torres. After a postdoctoral position at the University of Maryland, College Park, where I worked with John Benedetto in the Norbert Wiener Center for Harmonic Analysis and applications, I became an Assistant Professor at KSU in August 2006. My research is in the areas of
  • partial differential equations: linear/non-linear Elliptic PDE's, Monge-Ampère equations and its applications to geometric function theory;
  • pure harmonic analysis: bilinear singular integrals and pseudodifferential operators, function spaces;
  • applied harmonic analysis: image processing, LIDAR data compression.


Publications




Title
 Co-authors
 Status
13
 PDF
 On the boundedness of bilinear operators on products of Besov and Lebesgue spaces
 V. Naibo Submitted
12
 PDF
 A note on the biLipschitz Jacobian problem
Submitted
11
 PDF
 A mean-value inequality for non-negative solutions to the linearized Monge-Ampère equation
 L. Forzani
 Submitted
10
PDF
Bilinear paraproducts revisited A. Benyi, A. Nahmod, and R. Torres Math. Nachr. to appear
9
 PDF Weighted norm inequalities for paraproducts and bilinear pseudodifferential operators with mild regularity V. Naibo J. Fourier Anal. Appl. to appear
8
 PDF The structure of increasing weights on the real line D. Cruz-Uribe, SFO, and L. Forzani Houston J. Math. 34 (3), (2008), 951-983.
7
 PDF Doubling measures, monotonicity, and quasiconformality L. Kovalev and J.-M. Wu Math Z. 257 (3), (2007), 525-545.
6
 PDF Convex functions and quasiconformal mappings L. Kovalev Contemporary Math., AMS, Vol. 428 (2007), 93-103.
5
 PDF A note on the engulfing property and the $\Gamma^{1+ \alpha}$-regularity of convex functions in Carnot groups L. Capogna Proc. Amer. Math. Soc. 134 (2006), 3191-3199.
4
 PDF Mappings with convex potentials and the quasiconformal Jacobian problem L. Kovalev Illinois J. Math. 49 (2005), no. 4, 1039-1060.
3
 PDF Recent progress on the Monge-Ampère equation L. Forzani Contemporary Math., AMS, Vol. 370 (2005), 189-197.
2
 PDF Properties of the solutions to the Monge-Ampère equation L. Forzani Nonlinear Anal. 57(5-6) (2004), 815-829.
1
 PDF On geometric characterizations for Monge-Ampère doubling measures L. Forzani J. Math. Anal. Appl. 275(2) (2002), 721-732.

Recent talks
  • February Fourier Talks at the Norbert Wiener Center for Harmonic Analysis and Applications. Department of Mathematics, University of Maryland, College Park, MD, February 22-23, 2008.
  • Analysis Seminar, Department of Mathematics, University of Minnesota, MN, October 31st, 2007.
  • Analysis Seminar, Department of Mathematics, Cornell University, NY, April 24, 2006.
  • Workshop on Nonlinear Elliptic Equations and Applications, Mathematical Sciences Research Institute (MSRI), Berkeley, CA. August 16, 2005.
  • Analysis Seminar, Department of Mathematics, University of Arkansas, Fayetteville, AR. December 2, 2004.

Recent short talks
  • Special Session ''Singular Integrals and related Problems'', AMS Central Section Meeting, DePaul University, Chicago, IL, October 5-6, 2007.
  • AMS National Meeting Atlanta 2005, Hyatt Regency Atlanta, Atlanta, GA. January 5-8, 2005.
  • 2004 Fall Western Sectional Meeting. American Mathematical Society, Albuquerque, NM, October 16-17, 2004.
  • 7th International Conference on Harmonic Analysis and PDE's, El Escorial. Madrid, Spain. June 21-25, 2004.
  • 2nd Symposium on Analysis and PDEs. Purdue University. June 7-10, 2004.
  • ShowMe Analysis Meeting. University of Missouri-Columbia. June 3-5, 2004.

Academic advising
  • Sharad Silwal. PhD in Mathematics. Department of Mathematics, KSU.
  • Nicole Wayant. Undergraduate research. Project: Spatial-temporal Analysis of Malaria in Paraguay: Correlating Malaria and Normalized Difference Vegetation Index. This interdisciplinary research project is a collaboration between Prof. Douglas Goodin from the Geography Department at KSU, Nicole Wayant (Math and Geography major), and myself.
  • Akriti Dixit. Masters in Mathematics. Department of Mathematics, KSU. Akriti graduated in July 2008.

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