Roberto Reyes Carranza

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I learned to study mathematics at the National University of Trujillo, Perú http://en.wikipedia.org/wiki/Chan_Chan and now (2013) I have another great opportunity to continue my studies and research at the University of Puerto Rico, Mathematical- Research Campus at Rio Piedras, American Mathematical Society Member, where I feel very comfortable to continue the pleasure of thinking on a wide range of mathematical theories, design of algorithms and computational implementation of several complex processes in mathematics and its modelling. Right now I am doing the following research: "Fundamental Properties of Almost Perfect Nonlinear Functions, a Way to Measure its Nonlinearity and to construct its Highly Nonlinear Functions" and "APN Functions in Differential Cryptanalysis", attacking it from its roots, its definition, and even and again, strongly, with Dr. Moisés Delgado http://arxiv.org/abs/1207.5528 http://esta.uprrp.edu/facultad/mecu-delgadoM.php and Prof. Dr. Heeralal Janwa http://www.cims.nyu.edu/~hjanwa/

Publications http://mathkhipu.blogspot.com/

Moisés Delgado O. and Roberto Reyes (Submitted 2012) “APN Functions for Electronic Commerce Security” International Journal of Information and Computer Security IJICS.

Reyes, Roberto “Comparison of Elastic Plate Theories for Micro- polar Materials” 2011, ProQuest, ISBN: 9781124400891, Publication Number: AAT148756 http://search.proquest.com/docview/837356963#

[Author's Acknowledgments to Roberto Reyes for the computations related with the Bending Problem, pg 23] Steinberg, Lev “Deformation of Micro- polar Plates of Moderate Thickness” 2010 International Journal of Applied Mathematics and Mechanics IJAMM e- Journal System http://ijamm.bc.cityu.edu.hk/ijamm/outbox/Y2010V6N17P1C57668704.pdf

Libraries Produced * Contain analytical work plus the implementation of one rich set of functions.

“Library for Regularized Analytical Solutions for Steinberg- Reissner and Eringen II Families of Elliptic PDE Systems with Mixed Boundary Conditions corresponding to the Bending Problem”, written in Mathematica 4.0, presented at UPR.

“Theorem of the Weighted Directed Graph as a Class of Polynomials, a Generalization, Properties and Implementation”, programmed in wxMaxima- GNU, December 2011.

“A Interactive Computer-Assisted Proof of Convergence and Homogeneity property of Solutions of Elastic Plate Theories for Micro-polar Materials on a Zero Neighborhood”, written in Mathematica 4.0, presented at IX Annual Research Forum, TU, March 2011.

“An Existence Lemma for Classical Differential Geometry Generated by Polynomials”, implemented in Maxima and Mathematica, this work was produced in the Math PhD Students Office at UPR, Apr 2012.

With Dr. Moisés Delgado Olortegui, “APN Checker”, the APN Checker is a powerful computer tool to demonstrate if any function (defined over any finite field of characteristic 2) is APN, the implementation is given in Python and wxMaxima- GNU, from my KHIPU.PYTHON LIBRARY.

Teaching Experience

Instructor at campuses of public and private US universities such as UPR, an AMS member, SUAGM System and Inter American University, an AMS member, with progressive Faculty responsibilities. I feel honored for the support and recommendations I have received from the Mathematics Departments to give extra tuition. Also, I have had the pleasure of welcoming several visiting students interested in my classes.

Presentations

“On Necessary and Sufficient Conditions for Second-order Elliptic Field Equations of Elastic Plate Theories”. XII Congress of Research and Academic Development of UPR at Ponce, Committee of Research and Academic Development, Dean of Academic Affairs, UPR at Ponce, May 13, 2011 PR, https://sites.google.com/a/upr.edu/congresouprp/topics

“Homogeneity property of Maximum Micro- rotation Vector of Steinberg-Reissner and Eringen Models on a Neighborhood of Zero” IX Annual Research Forum, Doctoral Studies Center, University of Turabo at Gurabo, March 11, 2011 PR, US http://www.suagm.edu/utdoctoral/pdfs/Programa-IX-Encuentro-Investigadores-UT.pdf

“Comparison of Elastic Plate Theories for Micropolar Materials” SIDIMXXV Feb 2010 http://sidim.uprh.edu/Memorias/2010/libroSIDIM2010.pdf

“Method of Berlekamp for Factorization of Polynomials over the Field Zp” V Italian- Latin American Conference on Applied and Industrial Mathematics ITLA, Dec 15-18, 2004 http://www.mail-archive.com/notiamca@venus.ceride.gov.ar/msg00484.html

Advisors (Current 2013) Prof. Dr. Heeralal Janwa http://www.cims.nyu.edu/~hjanwa/ Prof. Dr. Lev Steinberg http://math.uprm.edu/people/peoplefind.php?person=Steinberg,%20Lev Prof. Dr. Obidio Rubio Mercedes http://obidio.matematicos.pe/ Prof. Dr. Moisés Delgado Olortegui, UPR at Rio Piedras http://esta.uprrp.edu/facultad/mecu-delgadoM.php http://arxiv.org/abs/1207.5528

I'm involved with Math Khipu Program, which possesses a powerful research and administrative team. I have the honor to introduce my Math Khipu Group, we have set out to continue this great project: Prof. Dr. Moisés Delgado Olortegui, UPR at Rio Piedras moises.delgado@upr.edu Project Advisor Eng. Araceli Feliciano Noriega (and also our Computer Technician) University of Puerto Rico at Mayagüez, celi_feli@yahoo.com aracelis.feliciano@upr.edu and Roberto C. Reyes Carranza PhD (expected- 2014) UPR at Rio Piedras roberto.reyes@upr.edu